ZIRCON (U-Th)/He DATES FROM RADIATION DAMAGED CRYSTALS: A NEW
DAMAGE-He DIFFUSIVITY MODEL FOR THE ZIRCON (U-Th)/He
THERMOCHRONOMETER
by
William Rexford Guenthner
_____________________
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF GEOSCIENCES
In Partial Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
In the Graduate College
THE UNIVERSITY OF ARIZONA
2013
2
THE UNIVERSITY OF ARIZONA
GRADUATE COLLEGE
As members of the Dissertation Committee, we certify that we have read the dissertation
prepared by William Guenthner, entitled Zircon (U-Th)/He Dates from Radiation
Damaged Crystals: A New Damage-He Diffusivity Model for the Zircon (U-Th)/He
Thermochronometer and recommend that it be accepted as fulfilling the dissertation
requirement for the Degree of Doctor of Philosophy.
_______________________________________________________________________
Date: 5/27/2013
Peter Reiners
_______________________________________________________________________
Date: 5/27/2013
Richard Ketcham
_______________________________________________________________________
Date: 5/27/2013
Jibamitra Ganguly
_______________________________________________________________________
Date: 5/27/2013
Peter DeCelles
Final approval and acceptance of this dissertation is contingent upon the candidate’s
submission of the final copies of the dissertation to the Graduate College.
I hereby certify that I have read this dissertation prepared under my direction and
recommend that it be accepted as fulfilling the dissertation requirement.
________________________________________________ Date:
Dissertation Director: Peter Reiners
3
STATEMENT BY AUTHOR
This dissertation has been submitted in partial fulfillment of requirements for an
advanced degree at the University of Arizona and is deposited in the University Library
to be made available to borrowers under rules of the Library.
Brief quotations from this dissertation are allowable without special permission, provided
that accurate acknowledgment of source is made. Requests for permission for extended
quotation from or reproduction of this manuscript in whole or in part may be granted by
the head of the major department or the Dean of the Graduate College when in his or her
judgment the proposed use of the material is in the interests of scholarship. In all other
instances, however, permission must be obtained from the author.
SIGNED: William R. Guenthner
4
ACKNOWLEDGEMENTS
Many people and sources of funding made this dissertation possible. This research
was supported by a grant from the National Science Foundation, the COSA2
collaboration between the University of Arizona and ExxonMobil, an Achievement
Rewards for College Scientists (ARCS) scholarship, and a ConocoPhillips Scholarship.
Discussions with my advisor, Peter Reiners; committee members, Richard
Ketcham, Jiba Ganguly, and Peter DeCelles; and other faculty members, George Davis,
George Gehrels, and Paul Kapp greatly improved the research presented in this
dissertation. Lab analysis could not have been possible without the able assistance of
Uttam Chowdhury and Stefan Nicolescu. Conversations with past and present graduate
students and post-docs—Lynn Peyton, Abir Biswas, Kendra Murray, Nate Evenson,
Alexis Ault, and Julie Fosdick—have improved this research, my understanding of
thermochronology, and my journey through grad school. Finally, I owe a great debt of
gratitude to Jessica Conroy, who, amongst many other things, kept me level throughout
the dissertation process.
5
DEDICATION
I dedicate this dissertation to my father, Thomas Guenthner, and my late
grandfather, Richard Guenthner, two scientists who inspired my pursuit of knowledge.
6
TABLE OF CONTENTS
LIST OF FIGURES .............................................................................................................9
LIST OF TABLES.............................................................................................................10
ABSTRACT.......................................................................................................................11
1. INTRODUCTION .........................................................................................................13
2. PRESENT STUDY........................................................................................................19
3. REFERENCES ..............................................................................................................23
4. APPENDICES ...............................................................................................................30
APPENDIX A: HELIUM DIFFUSION IN NATURAL ZIRCON: RADIATION
DAMAGE, ANISOTROPY, AND THE INTERPRETATION OF ZIRCON (U-Th)/He
THERMOCHRONOLOGY...............................................................................................31
Abstract ..............................................................................................................................32
1. Introduction....................................................................................................................33
2. Methods..........................................................................................................................38
2.1 (U-Th)/He Dating....................................................................................................38
2.2 4He Diffusion Experiments .....................................................................................39
2.2.1 Sample selection..............................................................................................39
2.2.2 Sample preparation, Raman spectroscopy ......................................................41
2.2.3 Sample preparation, slab orientation ...............................................................42
2.2.4 Step-heating experiments ................................................................................43
3. Results............................................................................................................................44
3.1 Zircon He dates: Positive and negative date-eU correlations .................................44
3.2 Raman spectroscopy ...............................................................................................45
3.3 Diffusion experiments.............................................................................................46
4. Discussion ......................................................................................................................51
4.1 Positive date-eU correlations ..................................................................................51
4.2 Negative date-eU correlations.................................................................................54
4.3 Arrhenius trends ......................................................................................................55
4.4 Functional form for damage-diffusivity relationship..............................................58
4.5 Implementation of damage-diffusivity parameterization........................................68
4.6 Impact of eU zonation on zircon date-eU correlations ...........................................75
5. Conclusions....................................................................................................................82
6. Acknowledgements........................................................................................................83
7. References......................................................................................................................84
7
TABLE OF CONTENTS-Continued
APPENDIX B: INTERPRETING DATE-eU CORRELATIONS IN ZIRCON (U-Th)/He
DATASETS USING A NEW MODEL FOR HELIUM DIFFUSION IN ZIRCON: A
CASE STUDY FROM THE LONGMEN SHAN, CHINA ............................................140
Abstract ............................................................................................................................141
1. Introduction..................................................................................................................142
2. Factors causing date-eU correlations ...........................................................................144
3. Model Inputs ................................................................................................................147
4. Model Results ..............................................................................................................153
4.1 LME-18 .................................................................................................................155
4.2 Wenchuan..............................................................................................................156
4.3 WMF footwall.......................................................................................................156
4.4 Summary ...............................................................................................................157
5. Discussion ....................................................................................................................158
5.1 Burial history and structural significance of date-eU correlations........................158
5.2 Cenozoic exhumation history from date-eU correlations .....................................159
6. Conclusions..................................................................................................................163
7. References....................................................................................................................163
APPENDIX C: SEVIER-BELT EXHUMATION IN CENTRAL UTAH
CONSTRAINED FROM COMPLEX ZIRCON (U-Th)/He DATASETS: RADIATION
DAMAGE AND He INHERITANCE EFFECTS ON PARTIALLY RESET DETRITAL
ZIRCONS ........................................................................................................................176
Abstract ............................................................................................................................177
1. Introduction..................................................................................................................178
2. Geologic Setting...........................................................................................................184
3. Methods........................................................................................................................186
3.1 (U-Th)/He dating...................................................................................................186
4. Results..........................................................................................................................187
4.1 Zircon (U-Th)/He ..................................................................................................187
5. Discussion ....................................................................................................................189
5.1 Interpretation of date-eU correlations ...................................................................189
5.2 Overview of model inputs.....................................................................................191
5.3 Stansbury Mountains.............................................................................................193
8
TABLE OF CONTENTS-Continued
5.3.1 tT inputs.........................................................................................................193
5.3.2 Model results—zero-inheritance curve .........................................................199
5.3.3 Model results—inheritance envelope............................................................201
5.4 Oquirrh Mountains ................................................................................................204
5.4.1 tT inputs.........................................................................................................204
5.4.2 Model results—zero-inheritance curve .........................................................206
5.4.3 Model results—inheritance envelope............................................................208
5.5 Mount Timpanogos ...............................................................................................208
5.5.1 tT inputs.........................................................................................................209
5.5.2 Model results .................................................................................................211
5.6 Summary of tT results ...........................................................................................212
5.7 Geologic significance of tT results........................................................................213
6. Conclusions..................................................................................................................217
7. References....................................................................................................................219
APPENDIX D: PERMISSIONS......................................................................................259
Permission for inclusion of Appendix A .........................................................................260
9
LIST OF FIGURES Figure A-1, Positive date-eU correlations ...................................................................124
Figure A-2, Negative date-eU correlations..................................................................125
Figure A-3, Arrhenius plots .........................................................................................126
Figure A-4, Ln(a/a0) plot..............................................................................................128
Figure A-5, Pre-exponential factor (D0) versus radiation damage ..............................129
Figure A-6, Arrhenius trend comparison .....................................................................130
Figure A-7, He diffusivity versus alpha dose ..............................................................131
Figure A-8, Closure temperature versus alpha dose ....................................................132
Figure A-9, Schematic date-eU correlations................................................................133
Figure A-10, Comparison of functional form to diffusion data...................................134
Figure A-11, Representative date-eU models..............................................................136
Figure A-12, Forward date-eU models ........................................................................137
Figure A-13, Zonation effects......................................................................................138
Figure B-1, Longmen Shan regional map....................................................................171
Figure B-2, ZRDAAM results ....................................................................................172
Figure B-3, Samples without negative date-eU correlations .......................................174
Figure B-4, Schematic cross-section............................................................................175
Figure C-1, Representative inheritance envelopes.......................................................239
Figure C-2, Charleston-Nebo Salient regional map.....................................................241
Figure C-3, Sample locations in Stansbury Mtns. ......................................................242
Figure C-4, Sample locations in Oquirrh Mtns. ..........................................................243
Figure C-5, Sample locations at Mtn. Timpanogos ....................................................244
Figure C-6, Date-elevation plots and date pdfs ..........................................................245
Figure C-7, Date-eU plots............................................................................................247
Figure C-8, Summary of tT paths ................................................................................248
Figure C-9, Zero-inheritance curves, Stansbury Mtns.................................................249
Figure C-10, Zero-inheritance curves, Stansbury Mtns...............................................250
Figure C-11, Inheritance envelopes, Stansbury Mtns..................................................251
Figure C-12, Zero-inheritance curves, Oquirrh Mtns. .................................................253
Figure C-13, Inheritance envelopes, Oquirrh Mtns. ....................................................254
Figure C-14, Inheritance envelopes, Oquirrh Mtns. ....................................................255
Figure C-15, Zero-inheritance curves, Mtn. Timpanogos ...........................................256
Figure C-16, Zero-inheritance curves, Mtn. Timpanogos ...........................................257
Figure C-17, Kinematic history in CNS ......................................................................258
10
LIST OF TABLES Table A-1, Zircon slab data ...........................................................................................97
Table A-2, Zircon (U-Th)/He data.................................................................................98
Table A-3, Step-Heating results...................................................................................101
Table A-4, Kinetic parameters.....................................................................................122
Table A-5, Values used in parameterization................................................................123
Table C-1, Zircon (U-Th)/He data ...............................................................................232
11
ABSTRACT
Zircon (U-Th)/He (zircon He) dating has become a widely used
thermochronologic method in the geosciences. Practitioners have traditionally interpreted
(U-Th)/He dates from zircons across a broad spectrum of chemical compositions with a
single set of 4He diffusion kinetics derived from only a handful of crystals (Reiners et al.,
2004). However, it has become increasingly clear that a “one-size-fits-all” approach to
these kinetics is inadequate, leading to erroneous conclusions and incongruent data. This
dissertation develops a more grain-specific approach by showing the fundamental role
that intracrystalline radiation damage plays in determining the He diffusivity in a given
zircon. I present three appendices that seek to quantify the radiation damage effect on He
diffusion in zircon, explain how this effect manifests in zircon He dates, and show how to
exploit such manifestations to better constrain sample thermal histories. Of particular
importance, this dissertation represents the first comprehensive study to concentrate on
the entire damage spectrum found in natural zircon and also the first to show that two
different mechanisms affect He diffusion in zircon in different ways across this spectrum.
In the first appendix, I and my fellow co-authors describe results from a series of
step-heating experiments that show how the alpha dose of a given zircon, which we
interpret to be correlated with accumulated radiation damage, influences its He
diffusivity. From 1.2 × 1016 α/g to 1.4 × 1018 α/g, He diffusivity at a given temperature
decreases by three orders of magnitude, but as alpha dose increases from ~2 × 1018 α/g to
8.2 × 1018 α/g, He diffusivity then increases by about nine orders of magnitude. We
12
parameterize both the initial decrease and eventual increase in diffusivity with alpha dose
with a function that describes these changes in terms of increasing abundance and size of
intracrystalline radiation damage zones and resulting effects on the tortuosity of He
migration pathways and dual-domain behavior. This is combined with another equation
that describes damage annealing in zircon. The end result is a new model that constrains
the coevolution of damage, He diffusivity, and He date in zircon as a function of its
actinide content and thermal history.
The second and third appendices use this new model to decipher zircon He
datasets comprising many single grain dates that are correlated with effective uranium
(eU, a proxy for the relative degree of radiation damage among grains from the same
sample). The model is critical for proper interpretation of results from igneous settings
that show date-eU correlations and were once considered spurious (appendix B). When
applied to partially reset sedimentary rocks, other sources of date variability, such as
damage and He inheritance, have to be considered as well (appendix C).
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1. INTRODUCTION
In its modern reincarnation as a low-temperature thermochronometer, the (UTh)/He dating technique has served an important role in our understanding of a range of
geologic processes. Of the various questions it can address, the chronometer’s ability to
constrain the exhumation histories of rocks makes it a particularly useful tool for
describing the evolution of active and ancient orogens. Researchers have employed a
number of different accessory minerals for (U-Th)/He dating in orogenic systems, but
one of the more versatile is zircon. This mineral’s ubiquity in a range of different
lithologies, coupled with its resistance to chemical and physical weathering and its
relatively high U and Th concentrations, has led to zircon (U-Th)/He (zircon He) dates
being used in numerous studies of orogens from both a bedrock (e.g., Kirby et al., 2002;
Reiners et al., 2003; Cecil et al., 2006; Biswas et al., 2007; Godard et al., 2009;
Guenthner et al., 2009; Gavillot et al., 2010; Wang et al., 2012; Tian et al., 2013) and
detrital (e.g., Rahl et al., 2003; Reiners et al., 2005; Saylor et al., 2012) perspective. The
relatively high nominal closure temperature of ~170-190 °C (Reiners et al., 2002; 2004),
makes zircon He dating well suited for deciphering the timing and rate of exhumation
from crustal depths of roughly 6-10 km. This can also be useful in ancient mountain belts
(e.g. the Sevier fold-and-thrust belt), where later episodes of tectonic or erosional
exhumation may overprint the thermochronologic record of lower temperature systems
(i.e. the apatite (U-Th)/He or apatite fission-track systems).
14
Despite the promising versatility of zircon He dating, examples of date
irreproducibility and incongruence with other age-based observations have at times
hindered its development as a reliable chronometer. The first zircon He dates were
analyzed by Strutt (1910a,b), and came only five years after Rutherford introduced the
concept of radioactive geochronometry. Strutt (1910c) explained though that He dates in
most mineral systems gave only minimum formation ages and were unreliable because
He tended to “leak out” from a given mineral. In several papers published in the mid-20th
century, Hurley and co-authors (Hurley, 1952; Hurley, 1954; Hurley et al., 1956) argued
that the ease with which He diffused out of a zircon was primarily due to metamictisation
(or breakdown of crystal structure) caused by the gradual accumulation of intracrystalline
radiation damage. These and similar findings relegated (U-Th)/He dating in general and
zircon He dating specifically to relative obscurity until Zeitler et al. (1987) showed that
too young (U-Th)/He dates in apatite were more easily explained by a process of
thermally activated volume diffusion. This discovery opened up new possibilities for the
use of (U-Th)/He dating in constraining thermal histories in other mineral systems, and
the zircon He system was subsequently reinterpreted as a thermochronometer (Reiners et
al., 2002; Reiners et al., 2004). Viewed in this context, zircon He dating has seen a
renewed and expanding interest, as evidenced by the studies listed above.
Despite the recent proliferation of zircon (U-Th)/He dating, issues of date
dispersion related to radiation damage have continued to present serious complications to
geologic interpretations. Such issues arise primarily because the canonical diffusion
kinetics determined from a handful of zircons (Reiners et al., 2002; Reiners et al., 2004;
15
Wolfe and Stockli, 2010) may not be applicable to all zircons found in a range of
geologic settings, especially in samples with zircons with a wide spectrum in degree of
radiation damage. For example, Nasdala et al. (2004) described a suite of Sri Lankan
zircons with the same thermal history that spanned a large range in damage and had
mostly reproducible He dates, except for several anomalously young dates at the highest
damage amounts. These dates were negatively correlated with alpha-fluence (a proxy for
radiation damage) and suggested that a metamictisation process, similar to one described
earlier by Hurley and others, might be responsible for the increase in He diffusivity (and
hence decrease in He date) at high damage. Reiners (2005) attempted to fit this negative
correlation with a model that calculated the decreasing crystallinity in a zircon as a
function of fluence (Holland and Gottfried, 1955). This approach appeared to work for
the Sri Lankan data, but failed to explain other zircon suites that also showed negative
date-fluence correlations. The study concluded that He diffusivity in heavily damaged
zircons did not scale linearly with crystallinity and that a more sophisticated treatment of
the problem was required.
Insight on the path forward comes in part from recent work on radiation damage
effects in the apatite He system. In apatite, increasing damage influences apatite He dates
in a slightly counter-intuitive fashion, by decreasing diffusivity with progressive
accumulation (Shuster et al., 2006). This results in higher closure temperatures and older
He dates for grains with higher actinide concentrations. Perhaps of greatest relevance for
this dissertation, the work of Shuster et al. (2006) showed that the kinetics of He
diffusion in apatite were dependent on a proxy for damage (4He concentration), grain-
16
specific, and followed a functional form derived in part from first principles. Subsequent
work by Shuster and Farley (2009) confirmed that He diffusion kinetics in apatite were
directly dependent on radiation damage, as opposed to simply being dependent on a
proxy. In the apatite He system (e.g. Flowers et al., 2007), the relationship between
damage and diffusivity manifests as positive correlations between single-grain dates from
the same hand sample and effective uranium (eU, another proxy for damage, equal to the
alpha-productivity-weighted sum of U and Th concentrations). Flowers et al. (2009)
further developed this with the related goals of both explaining the processes responsible
for positive date-eU correlations, and using date-eU correlations to in turn constrain
thermal histories. Gautheron et al. (2009) also recognized the potential of the damagediffusivity relationship in apatite for constraining thermal histories and took a similar
approach in their study. Both groups of authors parameterized a predictive model
accounting for the coevolution of radiation damage accumulation, annealing, He
diffusivity, and (U-Th)/He date in a single crystal. Ultimately, they showed that radiation
damage effects on He diffusion were not necessarily problematic, but were instead
advantageous because each individual apatite in a given hand sample could be viewed as
a separate thermochronometer with its own unique kinetics and closure temperature. By
dating a range of apatites with different levels of damage from the same sample, Flowers
et al. (2009) and Gautheron et al. (2009) in effect used a multiple thermochronometric
approach to tightly constrain thermal histories.
In this dissertation, I apply a similar, but in some ways very different, approach to
the zircon He system. The primary goals are: 1) derive and parameterize a functional
17
form of the He diffusivity-damage relationship across the entire spectrum of damage
found in natural zircon, and 2) demonstrate how this new parameterization can be used to
constrain the thermal histories of rocks in several geologic settings. A key contribution of
this work is to examine the damage-diffusivity relationship at low as well as high
amounts of damage. Early evidence of a possible increase in He retentivity and radiation
damage at low radiation dosages comes from Reiners et al. (2005), who observed partial
resetting in very young zircons at temperatures well below that expected from kinetics
observed in specimens with higher alpha doses. Farley (2007) also suggested that at low
dosages radiation damage may decrease He diffusivity by observing very high He
diffusivities in synthetic REE-phosphates with zircon-like structure. The data presented
in this dissertation represents the first systematic treatment of low damage effects on He
diffusivity in natural zircon. This dissertation is also the first systematic treatment of high
damage affects. As mentioned above, several studies documented or inferred an increase
in diffusivity at high amounts of damage, but did not attempt to measure these kinetics in
a quantitative fashion as is done here. To achieve the first goal, the diffusion data
gathered from zircons with both low and high degrees of damage is incorporated into a
zircon radiation damage and annealing model (ZRDAAM) that describes how damage
accumulates and anneals through time, and how that in turn affects He diffusion in
zircon.
The utility of ZRDAAM is demonstrated by its application to deciphering date
dispersion among single grain zircon He dates in real datasets. As will become clear in
the subsequent appendices, the damage-diffusivity relationship manifests in zircon He
18
datasets as positive and negative date-eU correlations (and occasionally both types in the
same sample). ZRDAAM reproduces these correlations and allows a researcher to
constrain thermal histories by comparing the model results to the real correlations in
either a forward or inverse sense. In igneous settings, this approach can be used to model
time-temperature paths of rocks from zircon He dates that show significant variability
and were previously considered to be spurious (see appendix B). Zircon He results from
sedimentary rocks can also be interpreted with ZRDAAM, and, in some cases, date-eU
correlations in these rocks help constrain thermal histories. But date variability in these
datasets is influenced by other factors (e.g. damage and date inheritance from a zircon’s
pre-depositional history) and some of these datasets are difficult to fully explain even
with a full ZRDAAM approach (see appendix C). By exploring the model’s ability to
address challenging and non-ideal datasets, this dissertation highlights both the progress
made in understanding the factors that influence zircon He dating and areas of future
research.
As the science of low-temperature thermochronology by the (U-Th)/He method
continues to mature and proliferate, thermochronologists have recognized the need to
better understand the kinetics of each system. At the same time, this understanding
should be grounded in a manner that practitioners of the technique find accessible and
useful for solving geologic problems. The body of work presented in this dissertation
represents one such step towards advancing our understanding and application of a
complex but powerful thermochronometric system.
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2. PRESENT STUDY
In the following appendices, I present the methods, results, and
conclusions of this dissertation as three papers formatted for publication in professional
journals. Appendix A focuses on the development of ZRDAAM with some basic insights
on its use for constraining thermal histories from date-eU correlations, while appendices
B and C show applications of the model in igneous and sedimentary rocks, respectively.
Below, I summarize some of the key findings in each appendix.
The first study (appendix A) presents a series of He diffusion measurements that
document the importance of alpha dose, which I and my co-authors interpret to be
correlated with accumulated radiation damage, on He diffusivity. Our diffusion
experiments consist of cycled step-heating experiments on pairs of crystallographically
oriented slabs of zircon with alpha doses ranging from ~1016 to 1019 α/g. He diffusion in
zircon has been shown to be anisotropic, with He diffusing preferentially parallel to the caxis (Farley, 2007; Reich, 2007; Cherniak et al., 2009; Saadoune et al., 2009), and we
must control for anisotropy in our experiments. Results from these experiments suggest
that radiation damage affects He diffusion in zircon in two contrasting ways, both of
which have much larger effects on He diffusivity than crystallographic anisotropy. From
1.2 × 1016 α/g to 1.4 × 1018 α/g, the frequency factor, D0, measured in the c-axis parallel
direction decreases by roughly four orders of magnitude, causing He diffusivity to
decrease dramatically (e.g., by three orders of magnitude at temperatures between 140
and 220 °C). At doses greater than ~2 × 1018 α/g, however, activation energy decreases
20
by a factor of roughly two, and diffusivity increases by about nine orders of magnitude by
8.2 × 1018 α/g. We propose that the initial decrease and eventual increase in diffusivity
can be describe by two different, but related, physical mechanisms. As damage begins to
accumulate within a pristine zircon, diffusion pathways become increasingly clogged by
crystallographically amorphous damage zones with high ionic density borders, which
causes an increase in tortuosity and a decrease in He diffusivity. Eventually, enough
damage accumulates such that amorphous damage zones become interconnected,
shrinking the effective diffusion domain size and increasing diffusivity. The research
presented in this appendix goes beyond simply describing experimental results though, as
I and my co-authors parameterize the damage-diffusivity relationship and link this
parameterization to an equation that describes damage annealing as a function of time
and temperature. Together, these elements constitute ZRDAAM and this appendix
concludes with several simple demonstrations of its ability to reproduce positive or
negative date-eU correlations in real samples.
A more detailed example of ZRDAAM’s utility is presented in appendix B. Here,
I and my co-authors re-evaluate several previously published zircon He datasets (Godard
et al., 2009; Wang et al., 2012; Tian et al., 2013) from the Longmen Shan, located at the
eastern margin of the Tibetan Plateau. These datasets contain negative date-eU
correlations, and the previous approach was to consider these results as spurious
dispersion. Incongruent dates were either averaged out or, in some cases, discarded and
ignored (e.g. Wang et al., 2012). In appendix B, we explain the cause of this dispersion
with ZRDAAM and use results from this model to constrain the timing of exhumation
21
events and the maximum burial temperatures experienced during these events for each
sample. This in turn provides a more coherent picture of the spatial and temporal
evolution of exhumation in this orogen from the Oligo-Miocene to the present.
Specifically, we document a shift between 20 and 15 Ma from exhumation concentrated
at the front of the range to exhumation concentrated in the interior of the range.
The final appendix attempts to constrain the post-depositional thermal histories of
zircon He datasets collected from partially reset, sedimentary rocks. These datasets
represent a sort of worst-case scenario in terms of deriving interpretations with the new
model and therefore push the limits of our current understanding about the sources of
zircon He date variability. The datasets come from three sub-vertical transects collected
in the Stansbury Mountains, Oquirrh Mountains, and Mount Timpanogos in the Wasatch
range near Provo, UT. Each range sits in the hanging wall of a major thrust sheet and
collectively these thrust sheets compose part of the Charleston-Nebo Salient (CNS), a
segment of the Cretaceous Sevier fold-and-thrust belt. From a geologic perspective, the
goal of this appendix is to use the zircon He datasets to describe episodes of cooling (or
exhumation) in the CNS during the Mid to Late Cretaceous (i.e. during the Sevier
orogeny). To do this, we use ZRDAAM to examine date-eU correlations in each group of
detrital samples that result only from post-depositional time-temperature paths. Although
this approach seems to work well for our Mount Timpanogos results, the Stansbury and
Oquirrh Mountain samples show date variability that cannot be explained solely by postdepositional radiation damage effects. Another factor that appears to influence these dates
is inherited He and radiation damage from each grain’s pre-depositional history.
22
Appendix C presents a new approach to dealing with such datasets that combines the
output from ZRDAAM with the concept of an “inheritance envelope.” We get mixed
results using this approach for the Stansbury transect, but tT constraints from inheritance
envelopes in the Oquirrh transects suggest a pulse of exhumation in the Oquirrh
Mountains beginning at either 110 or 100 Ma. Despite the complexity of some of the
datasets discussed in appendix C, we are motivated to interpret their thermal histories as
they represent some of the only in situ constraints of Cretaceous exhumation from the
entire US Cordillera.
23
3. REFERENCES
Biswas, S., Coutand, I., Grujic, D., Hager, C., Stockli, D., Grasemann, B., 2007,
Exhumation and uplift of the Shillong plateau and its influence on the eastern Himalayas:
New constraints from apatite and zircon (U-Th-[Sm])/He and apatite fission track
analyses: Tectonics, v. 26, doi:10.1029/2007TC002125.
Cecil, M.R., Ducea, M.N., Reiners, P.W., and Chase, C.G., 2006, Cenozoic exhumation
of the northern Sierra Nevada, California, from (U-Th)/He thermochronology: Geological
Society of America Bulletin, v. 118, p. 1481-1488.
Cherniak, D.J., Watson, E.B., and Thomas, J.B., 2009, Diffusion of helium in zircon and
apatite: Chemical Geology, v. 268, p. 155-166.
Farley, K.A., 2007, He diffusion systematics in minerals: Evidence from synthetic
monazite and zircon structure phosphates: Geochimica et Cosmochimica Acta, v. 71, p.
4015-4024.
Flowers, R.M., Shuster, D.L., Wernicke, B.P., and Farley, K.A., 2007, Radiation damage
control on apatite (U-Th)/He dates from the Grand Canyon region, Colorado Plateau:
Geology, v. 35, p. 447-450.
24
Flowers, R.M., Ketcham, R.A., Shuster, D.L., and Farley, K.A., 2009, Apatite (U-Th)/He
thermochronometry using a radiation damage accumulation and annealing model:
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30
4. APPENDICES
31
APPENDIX A: HELIUM DIFFUSION IN NATURAL ZIRCON: RADIATION
DAMAGE, ANISOTROPY, AND THE INTERPRETATION OF ZIRCON (U-Th)/He
THERMOCHRONOLOGY
Published in the professional journal: American Journal of Science
Copyright 2013 American Journal of Science. Reproduced with permission.
32
HELIUM DIFFUSION IN NATURAL ZIRCON: RADIATION DAMAGE,
ANISOTROPY, AND THE INTERPRETATION OF ZIRCON (U-Th)/He
THERMOCHRONOLOGY
William R. Guenthner, Peter W. Reiners, Richard A. Ketcham, Lutz Nasdala, and Gerald
Giester
Abstract
Accurate thermochronologic interpretation of zircon (U-Th)/He dates requires a realistic
and practically useful understanding of He diffusion kinetics in natural zircon, ideally
across the range of variation that characterize typically dated specimens. Here we present
a series of date and diffusion measurements that document the importance of alpha dose,
which we interpret to be correlated with accumulated radiation damage, on He
diffusivity. This effect is manifest in both date-effective uranium (eU) correlations among
zircon grains from single hand samples and in diffusion experiments on pairs of
crystallographically oriented slabs of zircon with alpha doses ranging from ~1016 to 1019
α/g. We interpret these results as due to two contrasting effects of radiation damage in
zircon, both of which have much larger effects on He diffusivity and thermal sensitivity
of the zircon (U-Th)/He system than crystallographic anisotropy. Between 1.2 × 1016 α/g
and 1.4 × 1018 α/g, the frequency factor, D0, measured in the c-axis parallel direction
decreases by roughly four orders of magnitude, causing He diffusivity to decrease
dramatically (for example by three orders of magnitude at temperatures between 140 and
220 °C). Above ~2 × 1018 α/g, however, activation energy decreases by a factor of
roughly two, and diffusivity increases by about nine orders of magnitude by 8.2 × 1018
α/g. We interpret these two trends with a model that describes the increasing tortuosity of
33
diffusion pathways with progressive damage accumulation, which in turn causes
decreases in He diffusivity at low damage. At high damage, increasing diffusivity results
from damage zone interconnection and consequential shrinking of the effective diffusion
domain size. Our model predicts that the bulk zircon (U-Th)/He closure temperature (Tc)
increases from about 140 to 220 °C between alpha doses of 1016 to 1018 a/g, followed by
a dramatic decrease in Tc above this dose. Linking this parameterization to one describing
damage annealing as a function of time and temperature, we can model the coevolution
of damage, He diffusivity, and (U-Th)/He date of zircon. This model generates positive
or negative date-eU correlations depending on the extent of damage in each grain and the
sample’s time-temperature history.
1. Introduction
Over the last decade, numerous studies have used zircon (U-Th)/He (zircon He)
thermochronology to interpret thermal histories and geologic processes. Accurate and
realistic interpretations using this thermochronometer, as well as constraints on
convenient indices like closure temperature (Tc) and the partial retention zone (PRZ),
require quantitative understanding of the kinetics of He diffusion in zircon, including the
effects of temperature, crystallographic orientation, and radiation damage. Most zircon
He dating studies thus far have assumed that the kinetics measured on a few zircons from
a limited number of locations (Reiners and others, 2002; Reiners and others, 2004; Wolfe
and Stockli, 2010) apply to all zircons found in a wide range of geologic settings. This
assumption may be appropriate, at least to first order, in some cases, as demonstrated by
34
geologically consistent results from settings such as deep drill cores (Wolfe and Stockli,
2010). But several aspects of He diffusion in zircon are likely to be more complicated,
which may lead to more complex results in some applications.
Anisotropic He diffusion in zircon is one such complication. Molecular dynamic
simulations (Reich and others, 2007; Saadoune and others, 2009; Bengston and others,
2012) and laboratory measurements (Farley, 2007; Cherniak and others, 2009) have
demonstrated that He diffusion is faster in the c-axis parallel direction than the c-axis
orthogonal direction, at least in specimens with little or no radiation damage or other type
of defects. These studies might suggest that grain aspect ratios may influence diffusion
kinetics. Watson and others (2010) introduced analytical and numerical methods that
allow consideration of the degree to which anisotropy affects both the calculation of bulk
He loss from a zircon and step-heating results. However, results from our study suggest
that anisotropy is a relatively minor problem for interpreting zircon He dates compared
with the effects of radiation damage, which are less well understood.
Damage results from self-irradiation, primarily by recoils of heavy daughter
nuclei upon emission of an alpha particle, but also by spontaneous fission events and the
alpha particles themselves. Because radiation damage can be annealed at elevated
temperatures (for example Zhang and others, 2000), its extent in a grain can be predicted
only roughly by calculating time-integrated self-irradiation doses. These doses can be
calculated from the concentration of effective uranium (eU) as scaled for relative alpha
production rate (eU = U + 0.235 × Th), and an estimate of the time since the sample was
cooled below the threshold temperature for long-term damage annealing. Nasdala and
35
others (2004a) showed that alpha doses calculated using a zircon’s U-Pb date may
overestimate the radiation damage present, as their Sri Lankan samples experienced
annealing post-dating each zircon’s U-Pb date. Instead, they calculated “effective alpha
doses” by applying a correction factor that accounts for the partial long-term annealing.
This correction factor was in part calibrated with Raman spectroscopy, a more direct
technique than estimating alpha dose for quantifying damage. Unfortunately, this
calibration was specific to Nasdala and other’s (2004a) particular suite of zircons, which
makes it difficult to broadly use in constraining the threshold temperature of long-term
annealing. Furthermore, as we will discuss in greater detail in later sections, there is no
consensus on how to model the kinetics of alpha recoil damage on either laboratory and
geologic timescales. For samples with simple thermal histories, it may be possible to
roughly estimate the duration over which radiation damage has accumulated from the
density of spontaneous fission tracks. To the best of our knowledge, the kinetics of
fission-track annealing are the only ones available that describe damage annealing of any
type in zircon on geologic timescales (for example Rahn and others, 2004; Tagami, 2005;
Yamada and others, 2007), and if the apatite system serves as a comparison (for example
Shuster and Farley, 2009), then it is reasonable to expect that they correlate with the
kinetics of alpha recoil damage annealing. Current estimates of the ZFT partial annealing
zone (that is, threshold temperature for annealing) are 262 to 330 °C at an isothermal
hold-time of 10 my (Yamada and others, 2007), although Garver and others (2005) have
shown that annealing temperatures can be as low as 180 °C in heavily damaged zircons.
Again, we leave a more detailed discussion of the limitations of comparing these two
36
types of damage annealing to a later section, but for now assume that ZFT kinetics
provide an estimate of the degree of structural annealing in zircon. Thus, as long as
zircon He dates are either similar to ZFT dates, or if we can assume from geologic
constraints that He dates record a pulse of rapid cooling from temperatures consistent
with the ZFT partial annealing zone, then He dates can be used to estimate the duration
over which radiation damage has accumulated, and this, combined with effective U
concentration, provides an estimate of the “effective alpha dose.” In this paper, we report
alpha doses following this assumption, unless stated otherwise.
Previous work on He diffusion in zircon focused mostly on differences between
specimens from the same rock sample with alpha doses greater or less than ~2 × 1018 α/g
(Hurley, 1952; Holland, 1954; Hurley and others, 1956; Reiners, 2005). At doses higher
than ~2 × 1018 α/g, zircon He dates in these studies become systematically younger with
increasing damage. Nasdala and others (2004a) proposed this was likely due to the
extensive inter-connection of boundaries between crystalline and amorphous domains at
moderate degrees of radiation damage, at damage levels beyond the first percolation
point as proposed by Salje and others (1999), which opens up a three-dimensional
network of pathways for He migration. Subsequent modeling by Ketcham and others (in
press) indicated that the important percolating phase may be damage from spontaneous
fission, as alpha recoil damage percolation occurs at two orders of magnitude lower alpha
dose. Reiners (2005) attempted to match the progressively younger dates with the trend
line of decreasing fraction of remaining crystallinity as determined by another
percolation-based model that accounts for the double-overlapping of damage cascades
37
(Weber and others, 1994). This approach had only limited success, however, as only one
dataset conformed to this model. This suggests a more sophisticated understanding of the
damage-diffusivity relationship at high amounts of damage is required.
In contrast to the relatively well documented behavior at high extents of damage
in zircon, little attention has been paid to potential damage-diffusivity relationships at
low degrees of radiation damage, where the effects on He diffusion may be quite
different. In apatite, for example, He diffusivity decreases with increasing damage
(Shuster and others, 2006; Flowers and others, 2009; Gautheron and others, 2009;
Shuster and Farley, 2009). This has been interpreted as a result of preferential
partitioning (that is, “trapping”) of He in damage zones, impeding diffusion. This is
manifest as positive correlations between apatite He date and eU, which, among
specimens from a sample that experienced a common time-temperature (t-T) history, is a
proxy for relative extents of radiation damage.
In this study, we found that zircon He dates from some geologic settings also
display positive date-eU correlations, which we interpret to be a result of damage at low
alpha doses. We also observe negative date-eU correlations and, in some instances, both
types of correlations may be present in a single sample. Throughout this paper, we use
the span in eU concentrations for zircons from the same sample as a first-order proxy for
each zircon’s degree of radiation damage. Although more direct measurements of
radiation damage (for example, Raman spectroscopy) would be ideal, for cases where
such data are lacking and where zircons share a common thermal history (that is, all
zircons experienced any annealing at the same time), date-eU correlations manifest the
38
effect that damage has on He diffusivity. A quantitative explanation of these correlations
requires a new, damage-based model for He diffusion in zircon. To develop this model,
we conducted a series of step-heating diffusion experiments on zircons with selfirradiation doses spanning nearly three orders of magnitude (~1016 to 1019 α/g). With the
kinetics from these experiments, we parameterize a relationship between alpha dose and
radiation damage, and He diffusivity, that accounts for decreases in diffusivity at low
damage and increases in diffusivity at high damage. Finally, similar to the apatite
radiation damage accumulation and annealing model (RDAAM, Flowers and others,
2009), we combine this new damage-diffusivity parameterization with a damage
annealing model to use various date-eU correlations to constrain candidate t-T paths. Our
new zircon damage and annealing model both explains zircon He datasets that do not
conform to the canonical kinetics of Reiners and others (2004), and allows geologists to
use zircon He date-eU correlations to place additional constraints on a sample’s t-T
history.
2. Methods
2.1 (U-Th)/He Dating
To demonstrate correlations between zircon He date and eU that we interpret as
resulting from radiation damage effects on He diffusivity, we show results from samples
from both newly reported and previously published zircon He datasets. Zircon He dates
from the Sri Lankan dataset were reported previously by Nasdala and others (2004a)
while new data include samples from the Miocene Marnoso-Arenacea Formation in the
39
Italian Apennines, sedimentary and basement units associated with the US Cordillera in
Utah and Wyoming, and meta-sedimentary rocks from the Cooma Metamorphic
Complex in Australia. Our Utah sample resides in the hanging wall of a major Sevier belt
thrust sheet (Absaroka). Balanced cross-sections from this location suggests that this
sample has undergone kilometer-scale tectonic and sedimentary burial (DeCelles, 1994).
The other western US sample is a well sample from La Barge, Wyoming, that was
collected in the footwall of the Hogsback thrust at a depth of ~4 km.
We report single-grain zircon He dates, which were analyzed by a number of
researchers over the last decade at both Yale University and the University of Arizona.
Analytical methods were similar for all samples. Mineral separation followed standard
crushing, sieving, and magnetic and density separation procedures. Analysts used
methods described by Reiners (2005) that included Nd:YAG and CO2 laser heating,
cryogenic purification, and quadrupole mass spectrometry for 4He analysis, and isotope
high-resolution inductively coupled plasma spectrometry for U and Th analysis. Results
are reported using the method of Hourigan and others (2005) for the alpha ejection
correction.
2.2 4He Diffusion Experiments
2.2.1 Sample selection
For new diffusion experiments we selected samples based on three criteria: 1) the
sample was large enough to allow preparation of crystallographically oriented slabs with
high aspect ratios (~10) , 2) U and Th concentrations were uniform and slabs came from
zircon interiors so as to avoid alpha ejection loss or diffusive rounding of He, and 3) the
40
extent of structural radiation damage was characterized by Raman analyses. In addition to
characterizing the degree of damage, we also calculate the alpha dose of each sample.
Because we desire samples with both a rapid high temperature to low temperature
cooling history, and samples whose radiation damage can be measured by some direct
method (Raman, IR spectroscopy, TEM, et cetera), we have selected several zircon
specimens (RB140, BR231, M127, G3, and N17) from the Sri Lankan dataset of Nasdala
and others (2004a). The geo- and thermochronologic characteristics of these zircons, as
well as their structural damage, have been well characterized with a number of different
techniques. Results suggest that they have all experienced a similar, probably
geologically rapid, cooling event at about 420-440 Ma. As a check for uniform U and Th
distribution in our Sri Lankan zircons, we rely on the backscattered electron and
cathodoluminescence images reported by Nasdala and others (2004a), which
demonstrated that all of the zircons from the Sri Lankan suite possess little or no U and
Th zonation (images for M127 were not detailed by these authors, but this zircon was
subjected to the same analyses and yielded similar results). We also note that the Raman
spectra for the Sri Lankan zircons were uniform, further evidence against zonation. We
calculated alpha doses using the previously reported zircon He dates for each sample
(Nasdala and others, 2004a), except in the case of N17, which—due to the fact that it
loses significant amounts of He at room temperature—was calculated using a date
consistent with the other Sri Lankan samples (430 Ma). Our calculated doses range from
4.7 × 1017 to 8.2 × 1018 α/g (table 1).
41
We also measured diffusion properties on a zircon specimen from the Mud Tank
carbonatite in Australia, to provide an example with relatively low amounts of damage.
We calculate an “effective alpha dose” using an age of 300 Ma, which corresponds to the
timing for regional exhumation associated with the Alice Springs orogeny as determined
from Rb-Sr dates on biotite and apatite fission track dates (Green and others, 2006). Mud
Tank has been used previously in He and Pb diffusion studies (for example Cherniak and
others, 2009; Cherniak and Watson, 2003) and adequately satisfies our other two
selection criteria. Uniform U and Th concentration was checked in part through the use of
Raman spectroscopy, detailed below.
2.2.2 Sample preparation, Raman spectroscopy
As a direct quantification of radiation damage, we use the full width at halfmaximum (FWHM) of the v3(SiO4) Raman band near the 1000 cm–1 Raman shift (for
example Nasdala and others, 2001). This FWHM broadens from initially <2 cm–1 for well
crystallized to >30 cm–1 for severely radiation-damaged zircon (Nasdala and others,
1995). Nasdala and others (2004a) obtained FWHM numbers for the Sri Lankan samples
used in our study, and we include these values in table 1.
FWHM numbers for the Mud Tank zircon have not been previously reported and
we therefore measured new Raman spectra for this zircon. As a check for possible
damage annealing caused by the step-heating experiments, we also measured Raman
spectra on pieces of M127 after step-heating and after the final degassing by laser
heating. We obtained several Raman spectra at room temperature with a dispersive
Horiba Jobin Yvon LabRAM HR 800 spectrometer. This system was equipped with an
42
Olympus BX41 optical microscope, an Olympus 100× objective (n.a. = 0.90), a
diffraction grating with 1,800 grooves/mm, and a Si-based, Peltier-cooled charge-coupled
device (CCD) detector. Spectra were excited with the He–Ne 632.8 nm emission (3 mW
at the sample). We calibrated the spectrometer using the Rayleigh line and neon lamp
emissions. The wavenumber accuracy was better than 0.5 cm–1, and the spectral
resolution was determined at ∼0.8 cm–1. Band fitting was done after appropriate
background correction, assuming Lorentzian-Gaussian band shapes. We corrected our
measured FWHMs for the experimental band broadening (that is, apparatus function),
and real FWHMs were calculated according to the simplified procedure of Dijkman and
van der Maas (1976). Total uncertainties of corrected FWHMs are assessed to vary
between ±0.4 cm–1 (FWHM values smaller than 6 cm–1) and ±1.2 cm–1 (FWHM values of
∼20 cm–1).
2.2.3 Sample preparation, slab orientation
To control for crystallographic direction, we oriented each millimeter-scale
sample with single-crystal X-ray diffraction analysis. Samples were attached individually
to a glass fiber and placed in a Nonius Kappa CCD diffractometer. Ten frames with a
step width of 2° were taken with Mo–K radiation. We registered several hundred Bragg
α
reflections, which was more than sufficient to determine the sample’s crystallographic
orientation. A small glass capillary was oriented parallel to the sample’s crystallographic
[001] direction and then glued onto the specimen. For the grinding and polishing process,
we attached our samples to a glass slide, with the glass capillary oriented either parallel
or perpendicular to the slide. The attachment was done with an acetone-soluble glue that
43
hardens, and can be dissolved, at room temperature (UHU hart). After the top polished
side was finished, we detached our samples from the glass slide, turned them over, and
attached them again, to produce plane-parallel, doubly polished slabs. Temperatures
never rose above ~40 °C throughout the entire preparation process. The slab thicknesses
(in the range of 40–110 µm) were chosen, depending on slab sizes, to get aspect ratios of
10:1 or higher. This process produced two oriented slabs per sample, one in the c-axis
parallel direction (PAR_C), the other c-axis orthogonal (ORT_C).
2.2.4 Step-heating experiments
We conducted our diffusion experiments on a He extraction/measurement line at
the University of Arizona and used the cycled, step-heating procedure and projector-bulb
furnace setup of Farley and others (1999). Slabs were held isothermally for durations
between 10 and 1590 minutes, and the gas released by each step was cryogenically
purified and analyzed for 4He with a quadrupole mass spectrometer. In general, we
maintained a similar time-temperature schedule for all slabs: an initial low temperature
step at 150 °C, followed by a prograde series of steps in 10 degree increments to 500 °C,
followed by a retrograde series of steps to 265 °C, and a final prograde cycle back up to
500 °C. Due to differences in slab size, and in order to release more than just a few
percent of gas, some deviations in the length of certain temperature steps were necessary.
Time-steps on the initial retrograde cycle often varied and some slabs required additional
cycling between 400 and 500 °C. The schedules for samples G3 and N17 involved lower
maximum temperatures (383 °C and 270 °C, respectively) and several short time steps
(10-30 minutes) because of their high diffusivities. After the step-heating extractions, we
44
completely degassed each sample by laser heating to measure the remaining fraction. A
significant fraction of gas was accidentally pumped away and lost during the final
degassing of one sample, M127_PAR_C. As such, we calculate the total amount of gas
for this sample using the measured U and Th concentration, the zircon He date, and our
measured slab dimensions. The same calculation from nearly all of our other samples
agrees with observed releases within a few percent. We include this sample in all
subsequent tables and figures.
3. Results
3.1 Zircon He Dates: Positive and Negative Date-eU Correlations
We report zircon He dates for all previously unpublished samples in table 2.
These data are plotted in figures 1 and 2 and show positive, negative, and sometimes both
types of correlations between date and eU in the same sample between date and eU. Each
correlation (except for Cooma) represents a collection of single grain dates from a single
igneous or sedimentary sample. Importantly, all of the grains in a given correlation have
experienced the same t-T history for igneous samples, and the same post-depositional t-T
history for sedimentary samples.
A comparison between figures 1 and 2 highlights several features of both types of
correlations. In figure 1, the correlations are generally positive and show an increase in
date with eU. In all samples the oldest dates in each one span a range from roughly 30
Ma to as great as 300 Ma, while eU concentrations are as low as ~100 ppm, but no
greater than ~1500 ppm. In contrast, samples with negative date-eU correlations (fig. 2)
45
tend to have older maximum dates and higher eU concentrations. These correlations
include new results from the Archean basement exposed in the Bighorn Mountains, WY
and the Minnesota River valley, MN, and placer zircons from Sri Lanka (Nasdala and
others, 2004a). The oldest dates in each of these samples range from approximately 300
Ma to nearly 1.0 Ga and are almost all significantly older than any dates shown in figure
1. Although concentrations of eU overlap somewhat with samples shown in figure 1, the
highest concentrations in the Minnesota, Sri Lankan and Big Horns samples are all
greater than 2000 ppm, and a few Sri Lankan grains are greater than 4000 ppm. We also
observe differences in the shape of the negative correlation for each sample: some are
broadly continuously negative (for example Minnesota, Bighorns), whereas others appear
to have a date plateau followed by a steep decline at high damage amounts (for example
Sri Lanka). The rollover from reproducible dates to negative trends begins at different eU
concentrations in each sample, which further suggests that each correlation has a unique
form. Similar to the Sri Lankan grains, a composite sample, Cooma, shows a drop off in
dates at a threshold eU; however, instead of a date plateau this appears to have a slight
positive correlation at lower eU concentrations. Thus, we observe positive, negative, and
sometimes both types of date-eU correlations in certain samples. In general, negative
correlations occur in samples with old maximum dates (100-1000 Ma) and high eU
concentrations (>2000 ppm), and positive correlations occur in samples with young
maximum dates (10-100 Ma) and low eU concentrations (10-1500 ppm).
3.2 Raman Spectroscopy
46
The Mud Tank zircon yielded measured Raman FWHMs in the range of 2.0-2.3
cm-1. These FWHMs refer to the main SiO4 stretching band, which was observed at
1008.2-1008.4 cm-1. After mathematical correction for the artificial band broadening due
to the spectrometer's limited spectral resolution, we transformed the measured FWHM
values to real FWHMs of 1.7-2.0 cm-1. Both parameters are indistinguishable from
Raman values of synthetic ZrSiO4 of 1008.3 cm-1 Raman shift and 1.8 cm-1 FWHM
(Nasdala and others, 2002). Consequently, the Mud Tank material represents an
extremely low degree of radiation damage, which is close to, or even below, the detection
sensitivity of the Raman technique. Also of importance, the Raman spectra for Mud Tank
show little variation from spot to spot, which suggests that radiation damage (and
therefore U and Th concentration) is uniform in our samples. Mud Tank’s low damage is
further supported by a low calculated alpha dose of 1.2 × 1016 α/g and a broad-band
yellow cathodoluminescence (Nasdala and others, 2004b), which is only observed at
extremely low defect densities (Nasdala and others, 2011).
After step-heating, the FWHM for M127 was 11.2-13.2 cm-1 observed at 1001.51002.5 cm-1. Compared to the published results for unannealed M127 (13.7-14.7 cm-1 at
999-1000 cm-1), these values represent a minor degree of annealing and suggest that our
standard heating schedule is not substantially annealing the amount of damage in our
samples. Following final laser heating, the FWHMs were lowered to ~2.0 cm-1 at ~1008
cm-1, which is close to the values for synthetic, undamaged zircon.
3.3 Diffusion Experiments
47
Results of step-heating experiments are shown in table 3 and as Arrhenius trends
in figure 3. For the Arrhenius trends, we use the fractional gas loss equation for a plane
sheet geometry to calculate D/a2 values at each temperature step (Fechtig and Kalbitzer,
1966). A striking feature in all of these plots is the non-linear behavior of diffusivities in
the initial prograde temperature steps. Other studies have observed such behavior as well
(Reiners and others, 2002; Reiners and others, 2004) and this non-linearity often
manifests as a convex-up curve. In RB140, BR231, and M127, the curve is positioned
above the linear Arrhenius trend, whereas in Mud Tank, G3, and N17 the curve is
positioned below the linear Arrhenius trend. As temperature increased, however, the
trend became linear after the first tenths to couple of percent of gas was released in nearly
all samples (except for N17). This is apparent in a plot of ln(a/a0) as a function of
cumulative gas released (fig. 4). Furthermore, as was observed in previous studies
(Reiners and others, 2002; Reiners and others, 2004), this behavior seemed to disappear
after the highest temperatures were reached in the initial prograde path and was almost
completely absent in all subsequent steps (fig. 4, see table 3 for corresponding fraction
degassed). Interestingly though, a subtle return to this type of non-linear behavior was
apparent in the lowest retrograde temperature steps of some slabs.
To derive kinetic parameters for each slab we linearly regress all steps following
our initial highest temperature step. Table 4 shows the activation energy (Ea) and
frequency factor/diffusion dimension (D0/a2) parameters we obtain from these post-high
temperature steps assuming an plane sheet geometry. We also calculate frequency factors
(D0) using the half-width measurement for each slab and these are listed in table 4 as
48
well. With the exception of one slab (Mud Tank PAR_C), values of Ea for all crystalline
slabs show a relatively restricted range (155 to 172 kJ/mol), compared with the six order
of magnitude range in frequency factors (5.03 × 10-3 to 146 cm2/s). This large span in D0
values is shown in figure 5. The ORT_C samples (oriented orthogonal to c-axis and
dominated by c-axis parallel diffusion) in this study approximate a (log-log) linear
relationship between D0 and alpha dose. Most previously published D0 values are also
reasonably consistent with this trend except for one sample from Reiners and others
(2002) (98PRGB4) and the two samples analyzed in Wolfe and Stockli (2010)
(ZKTB4050 and ZKTB1516). Interestingly, D0 values for the PAR_C samples in this
study remain constant over much of the same range in alpha dose, as figure 5 highlights.
Figure 6 shows Arrhenius trends for each sample using the kinetics derived
above. The difference in diffusivity between the oriented Mud Tank slabs is ~1 order of
magnitude at the same temperature, but this pair has diffusivities that are roughly 3 orders
of magnitude greater than the BR231, RB140, and M127 slabs. The RB140 pair of slabs
also has only ~1 order of magnitude difference in diffusivities at the same temperature.
Another pair of slabs, M127, shows almost no difference between the two directions
(~0.1 log units). The parallel oriented RB140 slab and the orthogonally oriented RB140
slab have a difference in their diffusivities of ~1 order of magnitude at the same
temperature. In contrast, at higher alpha doses, the diffusivity of G3 (also orthogonally
oriented) is roughly 6 orders of magnitude greater than that of BR231, and N17’s
diffusivity is approximately 10 orders of magnitude greater.
49
The relationship between alpha dose and diffusivity is more clearly demonstrated
in figure 7, which shows diffusivity at a constant temperature (180 °C) as a function of
alpha dose. In figure 8, we plot Tc as a function of alpha dose, an alternative, but equally
effective visualization of the damage-diffusivity relationship as Tc combines both kinetic
parameters into a single value that is more intuitive to practitioners of thermochronology.
For completeness and comparison, we also include previously published results from
unoriented zircons in figures 7 and 8 and calculate alpha doses from each sample’s zircon
He date (FCT, 98PRGB18, and 98PRGB4 from Reiners and others, 2002; 1CS15 and
M146 from Reiners and others, 2004; and ZKTB4050 and ZKTB1516 from Wolfe and
Stockli, 2010). Unfortunately, these previous studies did not control for the degree of
radiation damage in each sample and we can only estimate damage when plotting these
results. For samples with either simple thermal histories (FCT and 1CS15) or
independent constraints on radiation damage (M146), alpha dose values derived from a
zircon He date adequately describe the accumulated self-irradiation damage since damage
was last annealed. However, for one sample, 98PRGB18, we used the U-Pb date to
calculate alpha doses, which is appropriate given its thermal history.
Sample 98PRGB18 comes from a relatively shallow part of the Gold Butte block
in Nevada, a ~15 km section of Mesoproterozoic crystalline rock that was rapidly
exhumed by normal faulting at 15-16 Ma. This sample resided at only ~90 °C prior to
Miocene exhumation (Reiners and others, 2000) and most likely never experienced
temperatures high enough to fully anneal its radiation damage. Furthermore, the U-Pb
derived alpha dose values for 98PRGB18 are generally consistent with some (but
50
certainly not all) of the Raman spectra measured on different zircons from the same
sample. Given internal zonation, radiation damage in this crystal is heterogeneous and we
do not report a single value for FWHM. Instead, these values range from 3.6-16.5 cm-1
with a mean of 7.5 cm-1 (1001.5-1007.0 cm-1 shift). The higher values in this range are
consistent with high amounts of radiation damage and it is possible that the diffusion data
for 98PRGB18 comes from similar heavily damaged zircons.
Despite a less than ideal spread, these Raman data provide at least some estimate
for damage in 98PRGB18, and can be compared to the Raman spectra from another
sample from the same crustal block, 98PRGB4. This sample resided at much higher
temperatures (likely >300 °C) prior to exhumation at 16 Ma (Reiners and others, 2000),
and this date—coupled with U-Th concentrations in Reiners and others (2000)—yields an
alpha dose similar to that of Mud Tank. Its FWHM values range from 2.8-10.9 cm-1
(1003.8-1007.5 cm-1 shift) with a mean of 5.7 cm-1 and are generally lower than
98PRGB18. Again, significant spread due to 98PRGB4’s heterogeneous composition
prevents us from assigning a single value for FWHM. Despite the complexity of these
samples, Raman spectra give a best approximation of damage levels in 98PRGB18 and
98PRGB4 and some of these spectra are generally consistent with a zircon He date
calculated alpha doses in 98PRGB4, and a zircon U-Pb date calculated alpha doses in
98PRGB18.
With these calculated alpha doses, our new diffusion data, as well as almost all
previously published kinetics (with the exception of ZKTB1516), define the following
relationship between He diffusion (at any T) and alpha dose: Between ~1 × 1016 to ~5 ×
51
1017 α/g, diffusivity decreases by nearly three orders of magnitude. Diffusivity then
increases again by as much as roughly 10 orders of magnitude at damage extents of N17
(Fig. 7).
4. Discussion
In the following sections, we develop a model for He diffusion in zircon that
explains both our diffusion experiment results and the date-eU correlations in the context
of the alpha dose-diffusivity relationship. We first describe an hypothesis that accounts
for the physical significance of both types of date-eU correlations and provides the
theoretical framework for our subsequent model derivation and parameterization. For this
hypothesis we interpret positive correlations as a consequence of isolated radiation
damage zones acting as impediments to He diffusion by increasing the tortuosity of
diffusion pathways. In contrast, we interpret negative date-eU correlations as a result of
interconnection of damage zones at moderate to high alpha doses (>2 × 1018 α/g), as is
qualitatively consistent with previous observations of increased He diffusion in highly
damaged zircon (Holland, 1954; Hurley, 1954; Nasdala and others, 2004a).
4.1 Positive Date-eU Correlations
Due to similarities between our positive correlations and those observed with
the apatite (U-Th)/He thermochronometer (for example Flowers and others, 2007;
Flowers and others, 2009; Flowers and Kelley, 2011), the effects of radiation damage on
He diffusion in apatite provide context for interpreting zircon He positive correlations.
Shuster and others (2006) showed that He diffusivity in apatite decreased with increasing
52
damage and subsequent studies (for example Flowers and others, 2007) supported this
conclusion with observations of positive date-eU correlations. We suggest that similar
behavior occurs in zircon and leads to positive date-eU correlations. For example, in the
context of a thermal history like that depicted in figure 9, grains with different amounts of
radiation damage, as well as an initial span of uniform dates, are reset to varying degrees
during a reheating event (fig. 9A). If eU is a proxy for the total accumulated radiation
damage (that is, all the zircons in a sample have experienced the same t-T history), then
those grains with low eU lose a larger fraction of their He, resulting in a younger date,
than grains with high eU, leading to a positive correlation. Samples that have undergone
slow, monotonic cooling may also exhibit positive correlations. If a sample spends a
significant amount of time at temperatures low enough for damage accumulation without
annealing, but high enough to be in the PRZ, then arrays of zircon He dates may form a
positive correlation (fig. 9A). Both scenarios demonstrate that this correlation results
from a sample with grains that span a range in eU, and have resided in the PRZ after
disparate amounts of damage have accumulated in those grains.
A key difference between our interpretation of the damage-diffusivity
relationship in zircon and the interpretation for the apatite system, though, is the
mechanism that we suggest causes diffusivity to decrease with increasing damage. In the
apatite He system, the decrease in He diffusivity is hypothesized to result from
accumulation of crystal defects caused by alpha recoil damage that act as He traps. These
traps sequester He (governed by an equilibrium partition coefficient) and prevent or slow
its diffusive migration out of the crystal (Farley, 2000). In contrast to He diffusion in
53
apatite, various authors (Farley, 2007; Reich and others, 2007; Saadoune and others,
2009) have demonstrated that He diffusion in an ideal or defect-free zircon should occur
almost solely along c-axis parallel channels [0 0 1]. Any disruption of these pathways
would force He through c-axis orthogonal openings ([1 0 0], [0 1 0], and [1 0 1]), which
are much less energetically favorable (Reich and others, 2007). We argue that decreases
in He diffusivity in zircon are largely due to the increasing disruption of diffusion fastpaths (c-axis parallel channels) by radiation damage, an effect similar to road blocks
being placed on a major highway. As these barriers are erected inside the zircon, a He
atom’s path becomes more tortuous and the effective diffusivity of the grain decreases.
Evidence for this increasing disruption of c-axis parallel channels comes from figure 5.
The D0 values for orthogonal oriented slabs (diffusion predominantly in the c-axis
parallel direction) decrease across the damage spectrum whereas the D0 values for the
parallel oriented slabs (diffusion predominantly in the c-axis orthogonal direction) remain
the same, with both sets of D0 values becoming similar at high damage. In other words,
diffusion kinetics in the orthogonal direction begin to more closely resemble diffusion
kinetics in the parallel direction with increasing damage, and this increasing similarity
can be explained by tortuosity. Tortuosity may also contribute to lowering He
diffusivities in apatite, but we envision this phenomenon is more important for He
diffusion in zircon due to its strongly anisotropic behavior in specimens with little or no
accumulated damage. We do not rule out that damage zones in zircon may also trap some
amount of He, but we suggest that this effect is secondary compared to the closing of
preferred diffusion directions, which are probably not present in apatite.
54
4.2 Negative Date-eU Correlations
Like the positive date-eU correlations, previous research provides some context
for interpreting our negative date-eU correlations. Various authors (Holland, 1954;
Hurley, 1954; and Nasdala and others, 2004a) have suggested that He diffusivities
increase abruptly once zircon reaches a certain threshold of radiation damage. As damage
increases, Reiners (2005) proposed that zircon He dates scale with the remaining
crystalline fraction of the zircon as determined by the double-overlapping cascade model
(Gibbons, 1972). This further suggests that above a threshold, interconnected damage
zones form through-going channels in the zircon lattice and create fast diffusion
pathways for He. In order to reach this interconnection or percolation threshold, zircons
must sustain long-term damage accumulation at temperatures low enough to prevent
annealing. Zircons may achieve a heavily damaged state in which either significant He
loss and resetting occurs at surface temperatures, or some brief, low-temperature
reheating event may cause resetting (fig. 9B). In detail, some amount of less diffusive
material must remain in heavily damaged zircons as most negative correlations are
gradual (that is Minnesota River Valley, Bighorn suite) and not so abrupt. However, in
general, both scenarios could result in negative correlations and are plausible
explanations for the datasets plotted in figure 2. Two of these samples, the Minnesota
River Valley and Bighorn suites, come from Archean rocks that have likely been within a
few kilometers of the surface for 108-109 years and have consequently accumulated large
amounts of radiation damage. The Sri Lankan zircons are not as old but some do have
55
high eU, which in some cases resulted in the complete breakdown of crystal structure (for
example N17, Nasdala and others, 2004a).
The Sri Lankan dataset also shows a potential percolation threshold effect
whereby dates are fairly reproducible up to a critical eU concentration, in this case about
2000 ppm eU, above which they decrease with increasing eU. The Cooma date-eU trend
reinforces the notion of a transition in diffusion behavior as it displays both a positive and
negative correlation with an abrupt transition between each. Damage in-growth since
granulite facies metamorphism at ~433 Ma (Williams, 2001) and a large disparity in eU
concentration (~100-1300 ppm) produced a suite of zircons in which two different
processes affected He diffusion in different parts of the eU spectrum. In this particular
dataset, the transition between the two types of He diffusion occurs at an eU of ~1000
ppm. Similarly, nearly all zircons in our positive correlations contain eU concentrations
below 1000 ppm. The Cooma dataset serves as an important demonstration of how
radiation damage may have contrasting effects on He diffusivity in a suite of grains from
a single sample, and shows the approximate concentration of eU over which a transition
from one process to the other may occur. Because both types of diffusion mechanism
may operate on the same sample, these samples underscore the necessity for
understanding the damage-diffusivity relationship across the entire damage spectrum.
4.3 Arrhenius Trends
There are a number of possible explanations for the non-linear portions of the
Arrhenius plots in figure 4. Some of these plots show concave-up trends in the initial
prograde steps, in which less than ~1-2% of the He is released. In contrast, subsequent
56
temperature steps show much less variation and are more nearly linear. These concave-up
trends can either plot above or below the linear Arrhenius trends. This feature, or ones
similar to it, has been observed previously in zircon (Reiners and others, 2002; Reiners
and others, 2004) and several other minerals, including titanite (Reiners and Farley,
1999), goethite (Shuster and others, 2005), magnetite (Blackburn and others, 2007), and
apatite (Farley, 2000). It has been attributed to inhomogeneous He distributions due to
zonation, alpha ejection, or initial diffusion rounding; surface roughness; multiple
diffusion domains; and radiation damage (for example, Reiners, 2005).
Despite the myriad possible causes, samples with concave-up curves that lie
above the linear trends (RB140, BR231, and M127) are still difficult to explain.
Anisotropy could produce non-Arrhenius behavior of this type in step-heating results if
activation energies of the contrasting diffusion directions are different (Reich and others,
2007; Watson and others, 2010; Bengston and others, 2012). However, our data, as well
as all other experimental He diffusion data on zircon or zircon-structure phases (Farley,
2007; Cherniak and others, 2009), indicate that anisotropy is manifest as differences in
frequency factor, not activation energies, which would not lead to significant departure
from linearity on an Arrhenius plot. Furthermore, if anisotropy in zircon was caused by
differences in activation energy, then large changes in slope should always be evident at
low temperatures regardless of how many prograde and retrograde cycles have been
performed. For the most part, we do not observe this. We therefore rule out anisotropy as
the source of non-Arrhenius behavior in our initial prograde temperature steps.
57
Reiners and others (2002) suggested that this type of non-Arrhenius behavior
could be due to the interaction between radiation damage zones and the zircon surface,
with the damage zones acting as grain boundaries or fast diffusion pathways. Recent
evidence of two diffusion pathways for Ar in quartz (Clay and others, 2010), as well as
investigations of fast path diffusion in other minerals (Yund and others, 1981; Yund and
others, 1989; Yurimoto and others, 1989; Worden and others, 1990; Hacker and Christie,
1991) are consistent with this. For example, because lattice diffusion generally has a
higher Ea than grain boundary diffusion (Chakraborty, 2008), lattice diffusion can be
faster at high temperatures, so diffusion from grain-boundary-like domains could
dominate gas release in early, prograde steps, yielding initially high diffusivities in
Arrhenius plots. With higher temperature steps increasing fractions of gas would derive
from lattice diffusion as a result of the difference in values of Ea, but also because
surficial grain-boundary-like sites would be rapidly depleted in the initial few tenths to
one percent of gas released (fig. 4). If grain-boundary-like sites were reoccupied with He
during high temperature steps, this could also explain persistent release of gas via grain
boundary diffusion in later steps. Arrhenius trends for M127, Mud Tank, RB140, and
BR231 appear to exhibit slight curvature at the lowest temperatures of the post-high
temperature heating steps (after initial 500 °C step), consistent with this explanation.
Concave-up curves that lie below the linear Arrhenius trends (Mud Tank, G3, and
N17) probably result from a combination of the behavior described above and initially
rounded He profiles. N17, with a closure temperature below 0 °C, likely possessed a
rounded concentration profile prior to being step-heated, and, despite our selection of
58
interior parts of the Mud Tank and G3 zircons, some portion from the rounded diffusion
profile of these two samples was included as well. Although the initial He released from
these zircons does not appear to conform to ideal expectations of simple Arrhenius
behavior, its effect after the first few percent of gas release (except for N17) is negligible.
4.4 Functional Form for Damage-Diffusivity Relationship
For the remainder of our discussion, we directly relate alpha dose to structural
damage, and derive a mathematical parameterization of the damage-diffusivity
relationship that fits the data in figure 7. This requires a number of assumptions. As
previously stated, we assume that alpha doses calculated from He ages sufficiently reflect
the total accumulation of alpha-decay events since structural damage was last annealed.
Because most of our diffusion samples have thermal histories involving a phase of
relatively rapid cooling, and because we have direct and independent measurements of a
proxy for structural damage (FWHM) for a subset of them, this is a reasonable
assumption.
We must also assume that He diffusion in zircon scales with both alpha dose and
structural damage in the same way. This is an important consideration as alpha dose is a
calculated damage proxy and not a direct measure of damage (we detail below the
reasons for using alpha dose). We again rely on observations from the apatite He system
to support this assumption. Shuster and Farley (2009) showed that the amount of ionizing
kinetic energy released into a sample (kerma) and the fission-track density had similar
effects on He diffusivity. They demonstrated that He diffusivity in apatite changes
systematically with both increasing and decreasing kerma (through annealing) caused by
59
either artificial irradiation or natural, self-irradiation as monitored by fission track
density. Flowers and others (2009) expanded on this and derived a term, effective
spontaneous fission track density, that directly related alpha dose, accumulation and
annealing of fission tracks, and He diffusivity. Unfortunately, experimental observations
analogous to those of Shuster and Farley (2009) are currently lacking for zircon. But both
of these studies suggest that, at least to first order, fission track density (which is itself a
measure of one type of structural radiation damage) scales with “effective alpha dose”,
and can therefore be related to bulk He diffusivity.
Finally, we are assuming that the negative correlation between alpha dose and
diffusivity at low doses is not due to the effects of He (or Pb) concentration on He
diffusivity. Shuster and Farley (2009) clearly showed that radiation damage, not He
concentration, controls diffusivity in apatite. But as stated above, the types of
experiments performed by Shuster and Farley (2009) do not yet exist for zircon, so we
cannot completely rule out a concentration-dependency for He diffusion. However, the
data of Shuster and Farley (2009) provide some confidence that similar processes are
occurring in zircon, and this could be confirmed in the future by applying their
methodology to zircon samples.
Although these assumptions are required, we suggest that linking alpha doses
(preferentially those calculated using FT or He ages) to radiation damage is an
appropriate choice for our purposes as these assumed “effective alpha doses” provide a
straight-forward method for calculating damage accumulation through time. Furthermore,
as we detail below, it provides a crucial link between equations describing He diffusivity
60
and those describing damage annealing. The alpha dose is therefore the best measurement
for integrating He diffusion, damage accumulation, and damage annealing over geologic
timescales into an easily accessible thermochronometric modeling tool, which is our
primary objective in this section. With this in mind, we first derive a parameterization for
the damage-diffusivity relationship and then integrate this parameterization into a He
diffusion and damage annealing numerical model.
A mathematical description of the damage-diffusivity relationship must account
for both the initial decrease and ultimate increase in diffusivity across the spectrum of
damage from at least Mud Tank to N17 (~1016 - 1019 α/g). These two samples represent
the damage range encountered for the vast majority of zircon crystals sampled at or near
the Earth's surface. We desire a functional form consistent with the hypothesis that
decreasing diffusivity at low damage is caused by accumulation of isolated damage zones
that block crystallographically preferred He transport pathways and increase the
tortuosity of He migration. At high alpha doses, increasing diffusivity would be due to
decreasing effective domain size of undamaged zircon volumes, which are increasingly
separated by interconnected fast-diffusing damage zones.
In order to explain decreasing diffusivity at low damage, we introduce an
effective diffusivity (De) that represents He diffusion in a damage-free lattice modified by
increasing tortuosity. Increasing radiation damage blocks or constricts easy He migration
paths (for example, c-axis parallel channels) forcing He to take a more tortuous path out
of the zircon. This is analogous to diffusion in a porous medium where effective
diffusivity is expressed as (Cussler, 1984):
61
(1)
Dz is the diffusion coefficient within the pores, or in our case, diffusion along c-axis pipes
in a pristine zircon, and τ is the tortuosity. We represent Dz with the diffusion kinetics
from a minimally damaged zircon. For this zircon’s D0, we fit the ORT_C slabs in figure
5 with a power-law relationship that yields an equation of y=134.89*x-1.578, where y is D0
and x is dose. Projecting this relationship down to 1 × 1014 α/g gives a D0 of 193188
cm2/s (all constants and their values described in the remaining text are listed in table 5).
For the Ea, we average the activation energies from the samples with minimal amorphous
fractions (all samples excluding G3 and N17) and the previously published results.
Although these parameters are both extrapolations, the following equations could be
easily modified to account for future diffusion data from less damaged or more
appropriate zircon specimens.
Tortuosity τ could be represented in a variety of ways, and the atomic-scale
processes by which radiation damage may affect migration pathway dimensions and
diffusivity are complex. Damage may displace atoms into open channels that, depending
on which species is displaced, could cause variable decreases in porosity. C-axis channels
of initially high ionic porosity could be completely blocked and a larger fraction of the
He migration path would be forced to occur orthogonal to the c-axis. Although the exact
geometry or porosity of damage zones is hard to constrain, we predict that most zones
should act as He barriers and τ should increase as the chance increases for a diffusing He
atoms to encounter these barriers. To model this behavior, we use a metric introduced by
62
Ketcham and others (in press) for characterizing the undamaged portion of the lattice,
mean intercept length, lint, which is the average distance a particle can travel in a single
direction without encountering a damage zone. The expression for τ relates the calculated
lint in a given zircon to the mean intercept length in our extrapolated, minimally damaged
zircon, which also displays high diffusivity (lint0):
(2).
The right-hand side of equation (2) is squared in part to improve the fit to our diffusion
data (see below), but tortuousity is often mathematically expressed as the square of pore
spacing or geometry (for example, Epstein, 1988). Ketcham and others (in press) have
derived an empirical relation for lint by modeling the accumulation and percolation of
chains of connected, capsule-shaped alpha recoil tracks. They express lint as a function of
fraction amorphous (fa):
(3)
where SV corresponds to the surface to volume ratio of the capsules (1.669 nm-1). In turn,
fa is described using the direct impact model (Gibbons, 1972):
(4)
63
where Ba is the mass of amorphous material produced per alpha decay (5.48 × 10-19 g/αevent), and α is the alpha dose.
An explanation for the increase in diffusivity at high damage requires a derivation
that accounts for interconnected amorphous zones. We hypothesize that at sufficiently
high self-irradiation levels, amorphous zones caused by damage become interconnected
and connected to the grain’s surface. This represents an important shift from damage
zones acting as barriers to damage zones acting as fast paths. The processes by which this
might occur are not entirely apparent. Various macroscopic and long-range order
properties change at high damage and track with amorphous fraction (for example, Ewing
and others, 2003) and we expect that diffusivity should as well. However, several
different atomistic processes may cause these changes. Devanathan and others (2006)
showed that damage zones are characterized by an amorphous core surrounded by a high
interstitial density rind. These amorphous cores could become connected at high damage
and may form fast paths while the rinds cause increasing tortuosity at lower damage.
Interconnected fission tracks, which only reach a percolation threshold at high damage
(Ketcham and others, in press), are another candidate for creating these fast paths (see
below). Regardless of the exact mechanism, the net effect of this process is creation of an
increasing number of progressively smaller, undamaged zones that are increasingly
isolated from one another by increasingly interconnected and progressively larger
damage zones with much higher diffusivity. These two effects can be accounted for by 1)
modeling a decrease in the size of the diffusion domain of the undamaged portion of the
grain, and 2) describing the bulk diffusivity as a harmonic average (as appropriate for an
64
average of rates) in the undamaged and damaged portions of the grain. In detail, if the
grain had a heterogeneous spatial distribution of U and Th, increasing damage could
conceivably produce an apparent spectrum of diffusion domain sizes that might manifest
itself in step-heating data as decreasing diffusivity or concave-up Arrhenius trends.
We first parameterize our effective diffusivity using an harmonic average and to
do this, we recast equation (1) as:
(5)
where DN17 corresponds to the diffusivity of amorphous N17, and fc’ represents fraction
crystalline and is equal to 1-fa’. We again use the direct impact model to describe fa’ and
fc’, but to improve the fit to our diffusion data we include an additional term (Φ) within
the exponential:
f aʹ′ = 1 − exp( −Ba αφ )
(6).
A value greater than 1 for€Φ causes fa’ to increase more rapidly at lower alpha doses. As
we demonstrate below, a value of 3 for Φ is necessary for a proper fit to the data,
however, we currently have no physical explanation for why this term should be required.
It is possible that, while the direct impact model may adequately describe the buildup of
amorphous zones in zircon, it does not fully account for the interconnection of certain
parts of the zones (for example high-vacancy damage core vs. damage rim), or for the
65
contribution of an additional interacting effect such as accumulation of fission tracks
(Ketcham and others, in press).
In order to account for the reduction of the domain size of the undamaged portion
of the grain, we modify equation (5) by dividing each D by domain size (a):
(7).
In this set-up, a is equal to the initial grain size in an undamaged zircon, which
effectively decreases as fa’ increases following equation (6).
The Φ term in equation (6) and the scaling of domain size with fa’ in equation (7)
are admittedly somewhat empirical and heuristic, respectively, and their relationship to
actual physical phenomena are tenuous. Recent work by Ketcham and others (in press)
may offer some additional insight into this issue. These authors suggest that fission track
interconnection may play an important, but until recently, underappreciated role in
creating the macroscopic and long-range order qualities typically attributed to fa.
Furthermore, they derive an equation for a term that seems to more accurately reflect the
effects of radiation damage on decreasing effective domain size: mean distance to nearest
fission track dn. This number decreases with increasing fission track percolation and
replacing (a*fc’)2 with dn in equation (7) results in a similar functional shape.
Unfortunately, doing so does not provide a better fit to the real data. The current
calculations do not account for whether the nearest fission track is part of a network
connected to the outside of the grain, and improving the model in this respect may result
66
in a better fit. For our present discussion, though, we proceed with equation (7) as it is
currently derived.
Our combined equation for effective diffusivity is:
(8)
where lint0 is equal to 45920 nm (the value of lint calculated from equation (3) at an alpha
dose of 1 × 1014 α/g). Figure 10A shows equation (8) with our step-heating results. Our
parameterization adequately captures the decrease in diffusivity by ~3 orders of
magnitude at low damage and the subsequent increase in diffusivity by ~11 orders of
magnitude at high damage. We also show a comparison between the Tc data from figure
8 and Tc values calculated using equation (8) and an initial grain radius of 60 microns
(fig. 10B). To obtain effective Ea and D0 values for this curve, we use a method that relies
on pseudo-Arrhenius trends calculated at discrete doses with equation (8). These trends
provide the kinetic parameters necessary to then calculate the Tc at the corresponding
dose.
Although diffusional anisotropy may manifest itself in our model through the
importance of increasing tortuosity at low damage, our model does not directly account
for anisotropic diffusion. As figure 6 suggests, the effect of anisotropy on He diffusivity
is minimal compared to the effect of radiation damage and we have not focused on it in
this section. However, our derivation makes several predictions for a relationship
67
between anisotropy and radiation damage. With increasing damage, c-axis parallel
channels might be expected to become increasingly blocked and, correspondingly,
anisotropy should decrease (Farley, 2007). Specifically, Mud Tank—our least damaged,
oriented zircon—should be more anisotropic than all other samples. Figure 5 shows a
large disparity between the D0 values for the two Mud Tank slabs, and the two trends
(constant for PAR_C slabs, decreasing for ORT_C slabs) seem to converge at sample
M127. This suggests that, at least in terms of D0, anisotropic differences decrease with
increasing damage. However, the results in figure 6 complicate this observation. At high
temperatures (500 °C), the difference in diffusivity between the Mud Tank slabs is ~2
orders of magnitude, but at lower temperatures the degree of anisotropy between these
two slabs is comparable to the anisotropy between slabs in the “moderate to high
damage” group (~1 order of magnitude difference, note that the Mud Tank lines have
different slopes in figure 6). This suggests that anisotropy is relatively invariant across
the damage spectrum from Mud Tank to M127, which seems to contradict our hypothesis
that damage decreases the degree of anisotropy. Perhaps the anisotropy in Mud Tank is
similar to the anisotropy in M127 because Mud Tank has a large number of other defects
that also contribute to decreasing anisotropy. But why then would these defects not also
lower diffusivity? We do not have a satisfactory answer for this yet, but point defects
may have a relatively small effect on diffusivity compared to radiation damage, due to
damage’s more chaotic nature. Actual characterization of this difference requires more
work. For now we focus our remaining discussion on using equation (8) to forward
model date-eU correlations.
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4.5 Implementation of Damage-Diffusivity Parameterization
As a demonstration of the utility of our parameterization, we link equation (8) to
another equation describing damage annealing in zircon and forward model date-eU
correlations in a manner similar to the RDAAM (Flowers and others, 2009). Model
inputs consist of an effective diffusion domain lengthscale (assumed to be radius of a
sphere with an equivalent surface-area to volume ratio as the grain), and U and Th
concentrations for each grain, and a discretized t-T history for the entire dataset. With
these, our model calculates the total He production, damage accumulation, damage
annealing, He diffusivity, and He loss at each time step.
Damage accumulation and annealing are quantified with a series of equations
similar to those described by Flowers and others (2009), and rely upon the kinetics of
fission track annealing in zircon. Although we treat alpha damage as the primary factor in
creating tortuosity and interconnections, using a fission track annealing model means we
must assume that alpha damage anneals in a fashion similar to fission tracks. This is a
potential problem in the apatite system as well, but the RDAAM’s ability to predict dateeU correlations from reasonable t-T histories (for example Flowers and others, 2007;
Flowers and Kelley, 2011) shows that, to first order, modeling damage annealing with
fission track kinetics is valid. What works well in apatite, though, may not be suitable for
zircon. Especially problematic is the well-documented observation that alpha damage
annealing in zircon occurs via two disparate processes—epitaxial recrystallization and
ZrO2 nano-crystal formation—at different temperatures and at different initial damage
concentrations (Meldrum and others, 1998; Capitani and others, 2000; Zhang and others,
69
2000; Nasdala and others, 2002; Zhang and others, 2010). Furthermore, Garver and
others (2005) suggested that zircon fission track annealing processes are most likely
damage-dependent as well. A possible solution would be to use an alpha damage
annealing model that accounts for multiple annealing processes, but despite an extensive
literature on alpha damage accumulation and annealing in zircon, to the best of our
knowledge, no kinetic model has been parameterized to describe alpha damage annealing
at time scales beyond hours or days. If such a model is developed, equation (8) could be
easily coupled to it due to our modular model design. More importantly, our main
objective here is not to contrast and compare various annealing models. Rather, we
simply desire a quantitative approximation of damage annealing kinetics in zircon that
seems reasonable for geologic time scales. Given the currently available annealing
models, a fission track model best satisfies this requirement.
In order to combine the total alpha damage produced during a series of discrete
time steps with a fission track annealing model, we introduce αe or equivalent alpha dose
(α/g):
(9)
where the initial factor serves to convert from nmol to decays, α is the number of alpha
decays (in nmol) per gram produced in each time step, and ρr is reduced (normalized)
fission-track density of fission tracks that formed during that time step. The alpha dose
from each time step (t2, t1) is calculated as:
70
(10)
where [238U], et cetera are in nmol/g. Our derivation of ρr starts with length reduction r,
for which we use a simplified version of the fanning curvilinear fit (for example Ketcham
and others, 2007) to the ZFT annealing data of Yamada and others (2007):
(11)
where β = -0.05721, C0 = 6.24534, C1 = -0.11977, C2 = -314.937, and C3 = -14.2868. To
convert from reduced length to reduced density (ρr), we use the relation based on data
reported by Tagami and others (1990), which begins at one and is truncated at a ρ/ ρ0
value of 0.36, below which there are no data:
(12)
Once calculated, values of αe are linked to a diffusion model via equation (8).
With an estimate of the diffusion coefficient from equation (8), we then solve the
diffusion equation numerically for a spherical geometry with the Crank-Nicholson finite
difference scheme used in the thermal modeling software package HeFTy (Ketcham,
2005). Although this is not the best representation of He diffusion in zircon (it implies
isotropic diffusion), a spherical model captures the first-order features of the damagediffusivity relationship. Future versions could incorporate the cylindrical finite element
71
scheme of Watson and others (2010), which accounts for the effects of anisotropy.
Alternatively, a spherical calculation scheme can be employed using the “active radius”
method introduced by Gautheron and Tassan-Got (2010), who described how to
determine the radius of an isotropic sphere that replicates diffusive loss from a prism with
a given aspect ratio and diffusive anisotropy.
Our model demonstration consists of 6 different thermal histories, each designed
to capture aspects of the date-eU correlations in figures 1 and 2. As inputs, we use eU
ranging from ~50 to ~5000 ppm, grain radii of 60 µm, and t-T paths that begin at 600 Ma
and end at the present. For comparison, we also model the single zircon He date that
results from using the kinetics of Reiners and others (2004) with each of our thermal
histories (black diamonds in figure 11B). These t-T paths encapsulate 6 representative
scenarios: 1) slow, monotonic cooling from 600 Ma to the present, 2) early cooling
followed by a pulse of early-stage reheating, 3) early cooling followed by a pulse of latestage reheating, 4) early cooling followed by prolonged time spent in the PRZ and then
subsequent late cooling, 5) long term early heating and subsequent late-stage cooling, and
6) early cooling and prolonged exposure to low temperatures (fig. 11). Model outputs that
result from scenarios 5 and 6 show mostly flat date-eU correlation, which are typical of
most zircon He datasets. These two scenarios also result in He dates that are almost
identical to dates obtained using the kinetics of Reiners and others (2004). For thermal
histories with a single, rapid pulse of cooling from high temperatures, our new model
does not alter interpretations of zircon He datasets made with previously published
kinetics as this style of cooling will most likely not result in a date-eU correlation.
72
Interestingly though, scenario 6 shows a steep negative correlation at high damage,
despite having never been reheated above 20 °C post-500 Ma. These zircons have entered
the PRZ without changing temperature and we note that a similar process may have
occurred in the Sri Lankan dataset to produce the young dates for zircons K6 and N17.
Scenarios 1, 2, 3, and 4 demonstrate the various thermal histories that may
produce positive, negative, or both types of correlations in the same sample. The thermal
history for scenario 1 is characterized by slow cooling through the PRZ and results in a
broad and relatively confined positive date-eU correlation (dates increase from 161 to
210 Ma). Damage in-growth and He diffusion occur simultaneously over a prolonged
time span, which causes the damage amounts for the zircons in this scenario to be
relatively similar while He is diffusing. Given high enough eU concentrations, the t-T
path for scenario 1 also produces negative correlations in the same sample. Although this
particular negative correlation is subtle, an older initial age for the start of slow cooling
could produce a more pronounced negative correlation, as we further demonstrate with
our Minnesota dataset below. Scenario 4 is somewhat similar to scenario 1 as both
samples spend prolonged time periods in the PRZ. However, for most of their history, the
zircons in scenario 4 are held at a lower temperature (180 °C) than those in scenario 1. At
this temperature, damage in-growth outpaces annealing and the thermal history produces
a negative correlation at relatively low eU concentrations once the sample is finally
cooled.
In contrast, relatively short-lived pulses of reheating and cooling result in more
marked positive or negative correlations. The thermal histories for both scenarios 2 and 3
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contain reheating events that take place after the zircons have been held at low
temperatures (20 °C) for at least 100 my. During this time span, the zircons in each
scenario have acquired large differences in damage. In scenario 2, this results in a
positive correlation that spans a date range from 428 to 538 Ma, but also a negative
correlation that drops to zero at the highest eU. Like scenario 6, the PRZ for zircons with
eU in excess of ~3500 ppm is at very low temperatures and they no longer retain He. In
scenario 3, we have chosen both a later start time (100 Ma) and a lower maximum
temperature for the reheating event than scenario 2 (130 °C as opposed to 180 °C). The
resulting plateau of dates at ~550 Ma followed by a steep negative correlation is
somewhat similar to scenario 6, except the steep drop off in dates occurs over much
lower eU concentrations (from ~1500 to 2000 ppm). The late-stage reheating event also
produces a small plateau of ~50 Ma dates at eU concentrations greater than ~2000 ppm.
These dates correspond to the initiation of cooling and illustrate that, given a large span
in radiation damage, multiple pulses of reheating and subsequent cooling could be
recorded in zircons from the same hand sample.
As a final demonstration, we forward model the thermal history of two real
datasets shown in figures 1 and 2. We use one of the Apennines datasets (AP54B) as a
representative positive date-eU correlation, and the Minnesota dataset as a representative
negative date-eU correlation. For each dataset, we present a realistic thermal history that
could have produced the observed data and show the resulting model output in figure 12.
In the Apennines example, we rely on the thermochronometric data from previous
publications to guide our t-T path construction. Bernet and others (2001) obtained ZFT
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dates on the same grains shown in figures 1 and 12A, which yield a peak date of 20.7±3.6
Ma (these author’s P1 population). This translates to a lag time of 6.8 my as the
depositional age of this particular unit in the Marnoso-arenacea Formation is 13.9 Ma.
Zattin and others (2002) conducted a detailed regional study of this Formation and found
that fully and partially reset AFT dates from their hinterland samples (most internal to the
thrust belt) suggest maximum burial temperatures of 120-125 °C and post-depositional
exhumation between 4 and 6 Ma. If we consider these multiple t-T constraints as model
inputs, then we can produce the black line in figure 12A, a positive date-eU correlation
that is in good agreement with the real dataset. In figure 12A, we also show the results
from a simpler thermal history (dotted lines in t-T history and date-eU correlation) in
order to demonstrate that our preferred thermal history (black line) produces a distinctive
date-eU trend that best fits the data. Our new model therefore tightly constrains the
thermal history of a given sample and discriminates between potential t-T paths.
Our Minnesota dataset has fewer t-T constraints and our modeled t-T path is
slightly more speculative. A negative date-eU correlation and an oldest date of ~925 Ma
though suggests that these zircons have experienced very slow cooling rates since the
Proterozoic. With this in mind, we explored several possible slow cooling paths since the
Penokean orogeny at 1870-1820 Ma, which is the most recent episode of regional
metamorphism to affect this area (Holm and others, 1998). Our best fit to the data
consists of an initial cooling event beginning at 1850 Ma and 250 °C that proceeds at a
rate of .06 °C/my. In order to reproduce both the pseudo-plateau of dates at low eU
concentrations and the steep negative correlation at high eU concentrations, we accelerate
75
our cooling rate from .06 °C/my to ~.17 °C/my at 1100 Ma, which matches the age of
opening for the failed Keweenawan Rift system. Again, we include the results from a
couple of simpler histories (dotted and dashed lines in figure 12B) to show that our
choice for the Minnesota thermal history is not arbitrary. Slow cooling rates with a single
value yield date-eU correlations that match either the high eU or low eU trends in the real
data, but not both. We find a good fit to the data only by changing the cooling rate at a
specific time (in this case, 1100 Ma). Despite being somewhat speculative, our model t-T
constraints for the Minnesota dataset agree with the regional geologic history, produce a
reasonable fit to the data, and demonstrate that the Minnesota sample has experienced
very slow cooling at low temperatures for the past 1.8 by.
4.6 Impact of eU Zonation on Zircon Date-eU Correlations
In the above models, we assumed that both our real and model zircons are
homogenous in their U and Th (hence eU) concentrations. Typical zircons, though,
usually possess some degree of U and Th zonation. Although previous studies have
discussed the effects of parent zonation on apatite (U-Th)/He dates in depth (e.g., Farley
et al., 1996; Meesters and Dunai, 2002; Hourigan et al., 2005; Farley et al., 2011; Ault
and Flowers, 2012; Gautheron et al,. 2012), the effects of strong parent zonation in zircon
may be significantly different because of the reversal in damage-diffusivity relationship
with progressive damage accumulation. This means that, for some thermal histories,
different parts of the same zircon grain may have extremely different behavior, both of
which may be very different from that expected from a grain with equivalent bulk eU
homogeneously distributed.
76
Farley and others (2011) detailed three ways in which heterogeneous eU in zoned
apatite (lacking the damage-diffusivity reversal potential) can affect measured ages and
interpreted t-T histories. If an homogenous alpha ejection correction factor (FTH) is used
for a zoned grain, then the resulting He date will be either too young or too old depending
on where the majority of eU is concentrated (rim or core, respectively) (Farley et al.,
1996; Hourigan et al., 2005). This issue can be dealt with by using a zoned alpha ejection
correction (FTZ) that accounts for alpha particle redistribution, which is an option in
HeFTy. Zonation also affects He diffusivity by altering the He concentration profile, and,
because He diffusion is damage dependent, by creating distinct domains with different
diffusion kinetics inside the crystal. In the apatite He system, these three factors can
contribute to He date scatter (Flowers and Kelley, 2011). Ault and Flowers (2012)
suggested, however, that for typical apatites eU concentrations between zones do not vary
by more than a factor of ~2, and for typical thermal histories the resulting relative date
difference between zoned and homogenous apatites with the same bulk eU is no more
than ~10%.
We expect these zonation issues to result in greater fractional date differences
for the zircon He system. Order of magnitude differences in eU zonation are not
uncommon in zircons (for example, figure 13 in Reiners and others, 2004), and these can
cause large discrepancies in both damage and He concentration. Furthermore, unlike
apatite, He diffusivity in zircon will either decrease or increase depending on the eU
concentration of a given zone and the specific t-T path of the zircon. The interplay
amongst the alpha ejection correction factors, He concentration profiles, and damage
77
profiles in zoned zircons with different thermal histories is therefore complicated and a
detailed examination of real He datasets with zoned grains is beyond the scope of our
current study. However, we discuss below the results from several HeFTy models to
show how zonation affects differential damage accumulation within a zircon and sample
date-eU correlations.
These model simulations consist of five representative thermal histories and the
resulting date-eU correlations for a suite of unzoned zircons and zircons with simple
concentric zonation of high eU cores or high eU rims (fig. 13). Both the zoned and
unzoned zircons in each plot have bulk eU concentrations ranging from 250 to 1250 ppm
with radii of 60 microns. The zonation profiles for the zircons in our models have two
main inputs, the core eU concentration and the core’s radial position (rim concentration is
set by the bulk eU). In order to provide some uniformity to our choice of variables, we
use a zonation impact index (mass of eU for the whole grain divided by the mass
difference between the core and rim), which provides a rough estimate of magnitude of
the effect that eU zonation has on a zircon’s He concentration and damage profile. For a
given bulk and core eU concentration, this value reaches a maximum at a certain core
radial position and rim eU concentration. In turn, this particular radial position and rim
eU maximizes the difference in diffusion kinetics between rim and core that result from
He concentration and radiation damage disparities. Because we want to show a worstcase scenario for each date-eU correlation, we have chosen the rim eU concentration and
core radial position that correspond to the maximum zonation impact number. For core
eU concentration, we pick values that differ from the bulk eU concentration by a factor of
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seven (a bulk eU of 500 ppm leads to a core eU of either 71.4 or 3500 ppm), which
results in a core radial position that is 20 microns from the center (total radius of 60
microns) for the enriched core zircons, and a core radial position that is 40 microns from
the center for the enriched rim zircons. In zircons with enriched rims, the ratio between
eU concentrations in the rim and core is 9.52:1, while the same ratio is 1:9.1 for zircons
with enriched cores. A final consideration is the choice of a FTH or a FTZ alpha ejection
correction. For unzoned zircons, we model both the uncorrected date at a given eU and
the FTH corrected date (FTH = FTZ for the unzoned case). For each zoned zircon, we model
the uncorrected date, the FTZ corrected date using the “redistribution” option in HeFTy,
and the FTH corrected date. The FTH for each zoned zircon is calculated by taking the ratio
between the unzoned FTH corrected date at equivalent eU and the unzoned uncorrected
date at equivalent eU. For zoned grains, the FTH date is equivalent to measuring a raw
grain date on a zoned zircon and applying a naive alpha ejection correction assuming no
parent zonation.
The model results for all corrected and uncorrected zircons are shown in figure
13. Thermal histories 1 through 4 are the same as in figure 11. We have omitted t-T paths
5 and 6 from figure 11 as both of these yield nearly flat date-eU correlations for zoned
and unzoned zircons. Instead, we have added a new t-T path 5 to figure 13 that could be
appropriate for zircons from Laramide uplifts of the US Rocky Mountains (for example,
our Bighorn sample). In all t-T scenarios, the FTH corrected zoned dates (large bold
symbols connected by curves in figure 13) for zircons with high eU rims are younger
than their unzoned counterparts. Only some of this discrepancy is due to an improper
79
alpha ejection correction, as the FTZ corrected zoned dates (small bold symbols) are also
younger than unzoned zircons with the same bulk eU. The other causes for younger
dates—which in scenarios 3, 4 and 5, are the predominant ones—are the combined
effects of a heterogeneous He concentration profile and radiation damage. Rims that are
enriched in eU relative to the core cause an increase in effective bulk diffusivity (and
younger dates) because more He is located near the grain boundary, and, at high eU
concentrations, the rims become heavily damaged. This damage effect is particularly
apparent in scenario 3, where the grains with the highest bulk eU concentrations have
accumulated enough damage such that the rim acts as a diffusion fast path. If we model
the high-eU-rim zircon with a bulk eU of 1250 ppm using the kinetics of Reiners and
others (2004), then this scenario yields a date of 544 Ma (as opposed to 256 Ma using the
kinetics presented here), which further suggests that radiation damage is the primary
cause of these younger dates.
Despite being systematically younger, most of the high-eU-rim dates have a
similar style of date-eU correlation as the unzoned dates. One exception is scenario 5,
where a date-eU correlation that is monotonically negative in the unzoned case is positive
at low bulk eU concentrations. Although the rims of the high-eU-rim zircons have
accumulated high degrees of damage prior to cooling, the cores range from low (~5.5 ×
1016 α/g at 50 Ma) to moderate (~1.1 × 1017 α/g at 50 Ma) amounts of damage. This
difference in damage is enough to cause a more retentive core and lower bulk diffusivity
in the 500 ppm bulk eU grain than the 250 ppm bulk eU grain, which in turn results in a
positive date-eU correlation over this eU range.
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To explain the date-eU correlations for the high-eU-core zircons, we must
similarly consider the degree of damage in both the core and the rim and how those two
damage domains combine to affect bulk diffusivity. In scenario 1, dates are either older
or younger than the unzoned dates at the same eU, and the style of date-eU correlation
changes from a positive correlation in the unzoned grains to a positive-negative-plateau
correlation in the high-eU-core grains. The onset of a negative correlation has shifted as
the zircon core accumulates a high degree of damage (and therefore has a high
diffusivity) at relatively low bulk eU concentrations. Interestingly though, a plateau at the
highest bulk eU concentrations suggests that the high diffusivity of the core is somewhat
mitigated by the degree of damage in the zircon’s rim. A similar phenomenon occurs in
scenario 2, and is especially apparent in scenario 3 if we compare the high-eU-rim grains
with the high-eU-core grains. In scenarios 1 and 2, the rims of the high-eU-core zircons
at high bulk eU concentrations have accumulated a moderate amount of damage (roughly
4 × 1017 α/g prior to any thermal event) such that the rim decreases diffusivity and acts to
retard He diffusing out of the crystal, similar to the effects of RDAAM on zoned apatites
with eU enriched rims (Farley and others, 2011; Ault and Flowers, 2012). For the rims of
the high-eU-core grains in scenario 3, the damage accumulation is more substantial, but
the final reheating event occurs at a relatively low temperature. This temperature is low
enough to cause these zircon rims to be more retentive than the corresponding rims in the
high-eU-rim zircons (and thus yield older dates).
In contrast to scenarios 1, 2, and 3, the thermal histories in 4 and 5 result in
damage higher than ~5 × 1017 α/g, and relatively high diffusivity in both the cores and
81
rims for most bulk eU concentrations. In terms of damage, this places almost all of the
domains in these high-eU-core zircons to the high-damage side of the point of lowest
diffusivity in figure 10A. The rims of the high-eU-core zircons with 250 ppm bulk eU
concentrations are the only domains with damage lower than 5 × 1017 α/g (both are ~3 ×
1017 α/g prior to final cooling at 50 Ma) in these two scenarios. The net result in both
scenarios is a date-eU correlation for the high-eU-core grains that is similar in style to the
unzoned zircons, but with systematically younger dates. An exception to this is the
positive correlation for bulk eU concentrations of 250 ppm and 500 ppm in scenario 5.
Among the high-eU-core grains, the rim for the 250 ppm bulk eU grain has a damage
amount of ~2.9 × 1017 α/g at 50 Ma (the age prior to final cooling), while the rim for the
500 ppm bulk eU grain has a damage amount of ~5.8 × 1017 α/g at 50 Ma. This
difference in damage causes the 500 ppm bulk eU grain to have a more retentive rim and
thus lower bulk diffusivity relative to the 250 ppm bulk eU grain, which in turn produces
a slight positive correlation.
These five t-T scenarios illustrate that date-eU correlations for zoned zircons
may be complex because of reasons already discussed in previous studies, but also
because of the reversal in He diffusion behavior with progressive damage accumulation.
In the absence of a priori knowledge of parent zonation patterns, the effects of parent
zonation on He diffusivity may complicate thermochronologic interpretations of date-eU
correlations. We again note that we have purposely chosen worst-case zoning scenarios
in order to convey the full scope of this issue. Real zircons may possess a less extreme
degree or pattern of zonation, which will mitigate some of the date dispersion observed in
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figure 13. Consistent styles but variable degrees of zonation (e.g., enriched rim but with
varying rim thickness or enrichment factor relative to the core) may be expected among
zircons from some rock types. This would produce dispersion in a band of date-eU
correlations between the unzoned case (black curves) and an extreme zoned case (blue or
red curves, depending on zonation style) in figure 13. However, suites of zircons from
some samples may not possess systematic zonation patterns like those in figure 13.
Especially in detrital settings, one may expect to date zircons with a range of zonation
patterns: some may have high eU cores, some may have high eU rims, and others might
be unzoned. In this context, the curves in figure 13 should be interpreted as bounding
constraints for the total range of zonation variability. For a given t-T path, and no
consistent zonation style, real date-eU correlations could potentially plot anywhere within
the black, blue, or red curves.
Despite the apparent severity of the zonation problem, however, parent
zonation may be characterized from laser ablation depth profiles or other techniques,
prior to bulk grain dating. These observations also point to the potential for exploiting
parent zonation to provide date-eU trends within individual grains, for example with insitu laser ablation dating (Vermeesch and others, 2012). Under certain conditions, zircon
grains with zoned parent concentrations may behave similarly to crystals with multiple
He diffusion domains. In-situ measurements and/or step-heating analyses could
potentially be used to interrogate the distribution of He and dates among these domains,
providing powerful constraints on thermal histories from single grains.
5. Conclusions
83
Several suites of single-grain zircon (U-Th)/He dates from single rock samples
show positive and negative correlations with eU. These correlations are a consequence of
the two different ways that radiation damage affects He diffusion in zircon. Evidence for
two contrasting effects of radiation damage (as related to alpha dose) on diffusion comes
from zircon step-heating experiments, which show that between about 1 × 1016 and 5 ×
1017 α/g, diffusivity decreases by about three orders of magnitude. Diffusivity then begins
to increase rapidly with increasing damage, by up to 10 orders of magnitude at damage
levels of sample N17 (~8 × 1018 α/g). We hypothesize that decreases in diffusivity at low
damage are caused by damage zones blocking preferred c-axis parallel pathways. As
damage levels approach N17, these zones become increasingly interconnected and form
through-going fast diffusion pathways that shrink the effective diffusion domain size. We
parameterize the damage-diffusivity relationship with an equation that combines both of
these effects. We also couple our parameterization to an equation for damage annealing
in order to forward model date-eU correlations from specific t-T histories. Our model
offers insight into some of the issues associated with He diffusion in natural zircons and
provides other researchers with a tool for understanding and exploiting the significance of
date dispersion in zircon He datasets.
6. Acknowledgements
This work was supported by NSF grant EAR-0910577 to PWR as well as funding from
the COSA2 Collaboration between UA Geosciences and ExxonMobil. L.N.
acknowledges financial support by the Austrian Science Fund (FWF) through grants
P20028-N10 and P24448-N19. Jiba Ganguly and Sumit Chakraborty provided helpful
84
comments on some of the equations. Sri Lankan reference zircon samples were kindly
made available by Allen K. Kennedy (RB140, BR231, G3) and Wolfgang Hofmeister
(M127, N17). We are grateful to Andreas Wagner for the preparation of the doubly
polished slabs, and to Uttam Chowdhury for analytical assistance. We thank Madalyn
Blondes and Louise Miltich for allowing us to present some of their previously
unpublished zircon He dates from the Apennines and Minnesota, respectively, and we
thank Ian Campbell and Charlotte Allen for the Cooma samples. We appreciate helpful
reviews by David Shuster, Rebecca Flowers, and Andrew Carter.
7. References
Ault, A.K., and Flowers, R.M., 2012, Is apatite U-Th zonation information necessary for
accurate interpretation of apatite (U-Th)/He thermochronometry data?: Geochimica et
Cosmochimica Acta, v. 79, p. 60-78.
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Slab
Thickness
Orientation
(µm)
(relative to c)
Orthogonal
100
Parallel
100
Orthogonal
40
Parallel
90
Orthogonal
50
Orthogonal
90
Parallel
150
Orthogonal
67
n.a.
150
11
11
288
288
772
923
923
2572
5568
U
(ppm)
5
5
122
122
109
439
439
585
344
Th
(ppm)
(U-Th)/He
Fluence (x 1016
Date
FWHM (cm-1)
α/g)
(Ma)
~300
1.22
2.1±0.2
~300
1.22
2.1±0.2
437 ± 20
46.7
6.3±0.5
437 ± 20
46.7
6.3±0.5
438 ± 20
121
11.0±0.8
427 ± 20
148
13.6±1.0
427 ± 20
148
13.6±1.0
441 ± 21
404
30.4±2.5
99.2 ± 4.6
821
n.a.
3. Sri Lankan zircon. (U-Th)/He date, FWHM, and shift have been previously reported in Nasdala and others (2004)
2. (U-Th)/He estimated from biotite Rb-Sr and apatite fission track dates (Green and others, 2006)
1. U and Th concentrations from Cherniak and others (2009)
Notes: Fluence calculated using reported (U-Th)/He date, except for N17, which was assigned a representative date consistent with other Sri Lankan samples (430 Ma).
Mud Tank1,2
Mud Tank1,2
RB1403
RB1403
BR2313
M1273
M1273
G33
N173
Sample
Name
TABLE A1. ZIRCON SLAB DATA
1008.3±0.1
1008.3±0.1
1004.7±0.5
1004.7±0.5
1000.6±0.5
1000.2±0.5
1000.2±0.5
996.2±0.5
n.a.
Shift (cm-1)
97
Sample Location
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Minnesota River Valley
Italian Apennines
Italian Apennines
Italian Apennines
Italian Apennines
Italian Apennines
Italian Apennines
Italian Apennines
Italian Apennines
Sample
Name
04EQ1zA
04EQ1zB
04EQ1zC
04EQ1zD
04EQ1zE
04EQ1zF
04GF1zA
04GF1zB
04MT1zA
04MT1zB
04R1zA
04R1zB
04RF1zA
04RF1zB
04SC1zA
04SC1zB
04SG1zB
04SH1zA
04SH1zB
AP9B39
AP9B69
AP9B112
AP9B124
AP9B136
AP9B147
AP9B186
AP9B187
Detrital
Detrital
Detrital
Detrital
Detrital
Detrital
Detrital
Detrital
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Rock Type
3.37
7.89
1.99
5.96
4.57
6.97
2.41
2.63
4.49
5.96
4.58
2.55
3.87
9.55
10.7
21.9
26.0
31.6
5.96
10.2
16.1
28.8
4.82
25.0
9.72
10.5
17.2
Mass
(µg)
37
53
36
49
36
51
39
33
41
42
36
31
35
43
56
63
67
68
42
51
64
72
47
71
55
50
56
Halfwidth
(µm)
231
397
783
232
450
259
321
426
781
748
894
866
1107
647
247
254
362
346
656
580
84.0
155
422
415
1738
1011
883
U
(ppm)
TABLE A2. ZIRCON (U-Th)/He DATA
59.0
188
197
77.3
237
111
150
38.4
203
218
246
166
351
284
88.4
104
88.8
78.0
167
174
67.3
177
110
111
1171
228
184
Th
(ppm)
17.0
10.4
27.0
61.8
12.8
33.6
27.0
38.5
1156
987
294
144
270
946
948
1023
1183
1012
1382.98
1750
443
619
1663
1667
790
65.6
1144
He
(nmol/g)
4
0.79
0.84
0.78
0.83
0.80
0.84
0.79
0.78
0.75
0.77
0.74
0.70
0.73
0.78
0.82
0.84
0.85
0.86
0.77
0.81
0.83
0.86
0.77
0.86
0.81
0.81
0.83
Ft
12.2
19.2
17.8
9.22
12.4
13.1
17.7
18.4
336
292
76.5
42.0
57.4
307
758
760
638
574
464
619
925
650
843
769
89.2
14.2
271
0.57
0.88
0.84
0.44
0.57
0.60
0.84
0.90
14
16
2.9
2.4
2.9
12
45
30
102
92
18
25
148
104
135
123
3.9
0.57
11
Corr. Age Analyt. ±
(2σ)
(Ma)
98
Italian Apennines
Italian Apennines
Italian Apennines
Italian Apennines
Italian Apennines
Italian Apennines
Italian Apennines
Italian Apennines
Cooma, Australia
Cooma, Australia
Cooma, Australia
Cooma, Australia
Cooma, Australia
Cooma, Australia
Cooma, Australia
Cooma, Australia
Cooma, Australia
Cooma, Australia
Bighorns, Wyoming
Bighorns, Wyoming
Bighorns, Wyoming
Bighorns, Wyoming
Bighorns, Wyoming
Bighorns, Wyoming
Bighorns, Wyoming
Bighorns, Wyoming
Bighorns, Wyoming
Bighorns, Wyoming
Bighorns, Wyoming
Bighorns, Wyoming
AP54B44
AP54B55
AP54B64
AP54B65
AP54B95
AP54B122
AP54B127
AP54B129
ANU03-055-04
ANU03-055-07
ANU03-055-14
ANU03-055-22
ANU03-055-26
ANU03-056-05
ANU03-056-09
ANU03-056-13
ANU03-056-16
ANU03-056-22
BH12zA
BH12zB
BH12zC
BH12zD
BH12zE
BH12zM
BH12zN
BH17zA
BH17zB
BH17zC
BH17zD
BH17zE
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Igneous
Metasedimentary
Metasedimentary
Metasedimentary
Metasedimentary
Metasedimentary
Metasedimentary
Metasedimentary
Metasedimentary
Metasedimentary
Metasedimentary
8.22
46.4
32.6
8.41
4.91
4.93
5.41
10.2
15.0
4.34
1.73
3.32
6.79
13.4
14.8
6.80
10.54
1.53
3.31
3.49
4.17
6.97
56
88
74
50
43
42
42
52
60
39
30
37
67
75
85
67
72
31
43
32
41
46
TABLE A2 (CONTINUED)
Detrital
4.11
51
Detrital
2.84
33
Detrital
3.01
38
Detrital
3.64
50
Detrital
4.49
59
Detrital
4.58
51
Detrital
14.8
61
Detrital
2.93
41
1552
1736
876
1275
1169
1589
1166
300
414
426
439
367
313
92.3
455
131
654
844
1229
576
996
1097
185
934
585
746
259
296
501
124
416
328
214
278
372
329
324
108
255
219
334
219
101
64.8
132
52.8
436
83.8
321
188
167
391
80.6
304
203
49.4
72.1
95.4
204
68.1
227
57.1
779
165
90.1
95.5
107
805
714
1023
655
966
498
153
747
190
1213
1059
1276
822
1111
1227
10.2
76.2
58.2
58.2
18.7
23.6
44.6
8.96
0.80
0.88
0.87
0.80
0.76
0.76
0.77
0.82
0.83
0.75
0.67
0.73
0.82
0.85
0.86
0.82
0.84
0.68
0.76
0.72
0.76
0.78
0.83
0.77
0.78
0.82
0.83
0.82
0.87
0.80
31.7
6.60
178
28.5
17.4
14.0
20.8
542
329
513
343
569
326
303
323
294
345
329
235
336
259
240
11.2
18.3
21.8
17.4
15.1
16.7
17.4
14.8
0.49
0.27
7.2
1.1
0.68
0.56
0.81
8.9
14
22
14
24
15
13
14
13
14
14
10
14
11
10
0.45
0.75
0.84
0.73
0.59
0.64
0.67
0.57
99
La Barge, Wyoming
La Barge, Wyoming
La Barge, Wyoming
La Barge, Wyoming
La Barge, Wyoming
La Barge, Wyoming
La Barge, Wyoming
La Barge, Wyoming
La Barge, Wyoming
Kelvin Formation, Utah
Kelvin Formation, Utah
Kelvin Formation, Utah
Kelvin Formation, Utah
Kelvin Formation, Utah
Kelvin Formation, Utah
EM12907zA
EM12907zB
EM12907zC
EM13270zA
EM13270zB
EM13270zC
EM13105zA
EM13105zB
EM13105zC
Z-AV-K2-8
Z-AV-K2-18
Z-AV-K2-20
Z-AV-K2-40
Z-AV-K2-52
Z-AV-K2-95
Detrital
Detrital
Detrital
Detrital
Detrital
Detrital
3.14
1.31
4.47
1.23
0.443
2.37
38
25
39
31
21
38
TABLE A2 (CONTINUED)
Detrital
6.58
51
Detrital
6.69
59
Detrital
5.33
51
Detrital
4.68
48
Detrital
3.60
45
Detrital
4.72
51
Detrital
2.60
41
Detrital
3.30
42
Detrital
4.54
45
198
217
265
339
1421
483
285
101
70.9
232
134
662
199
292
258
70.3
86
57.7
117
134
113
134
62.2
78.1
145
81.5
244
137
176
110
80.9
87.3
127
437
1585
695
286
29.2
10.6
179
44.9
635
90.2
210
255
0.79
0.71
0.80
0.73
0.64
0.79
0.80
0.81
0.79
0.78
0.76
0.79
0.74
0.75
0.77
87.8
95.4
105
244
309
268
207
57.3
27.9
158
70.7
204
96.9
153
213
3.9
4.4
5.0
14
20
15
8.6
2.6
1.2
7.5
3.3
9.8
4.4
7.2
10
100
101
TABLE A3. STEP-HEATING RESULTS
Step
T °C
seconds
Mud Tank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
Orthogonal
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
3600
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
5400
5400
5400
3600
3600
3600
3600
3600
3600
3600
3600
1800
1800
1800
1800
1800
1800
1800
He (pmol)
fcumulative
ln(D/a2)1
0.0013
0.0014
0.0240
0.0155
0.0059
0.0024
0.0024
0.0007
0.0025
0.0022
0.0025
0.0028
0.0045
0.0073
0.0114
0.0174
0.0184
0.0314
0.0484
0.0454
0.0636
0.0892
0.1175
0.1806
0.2168
0.3518
0.4659
0.2617
0.3459
0.4907
0.5884
0.6934
0.8256
1.062
0.000067
0.000134
0.001323
0.002090
0.002380
0.002500
0.002618
0.002654
0.002777
0.002888
0.003012
0.003151
0.003376
0.003736
0.004300
0.005164
0.006078
0.007637
0.010040
0.012291
0.015446
0.019871
0.025701
0.034663
0.045420
0.062878
0.085997
0.098980
0.116143
0.140492
0.169688
0.204092
0.245054
0.297746
-27.66
-27.23
-22.39
-21.98
-22.68
-23.48
-23.44
-24.59
-23.34
-23.41
-23.25
-23.09
-22.56
-22.00
-21.43
-20.84
-20.32
-19.59
-18.90
-18.33
-17.77
-17.19
-16.66
-15.95
-15.49
-14.70
-14.10
-13.77
-13.34
-12.81
-12.44
-12.09
-11.73
-11.29
4
1. Values calculated from equations described in Fechtig and Kalbitzer (1966) assuming a plane sheet geometry
102
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
490
500
500
495
485
475
465
455
445
435
425
415
405
395
385
375
365
355
345
335
325
315
305
295
285
275
265
273
283
293
303
313
323
343
353
363
373
383
393
TABLE A3 (CONTINUED)
1800
1.246
1800
1.405
1800
1.204
1800
0.8731
1800
0.5510
1800
0.3589
1800
0.2437
1800
0.1600
1800
0.1120
1800
0.0731
1800
0.0471
1800
0.0298
1800
0.0198
3600
0.0254
3600
0.0153
3600
0.0101
5400
0.0075
7200
0.0065
7200
0.0032
14400
0.0042
21600
0.0046
43200
0.0043
43200
0.0024
43200
0.0015
86400
0.0018
86400
0.0010
86400
0.0008
86400
0.0010
86400
0.0017
86400
0.0029
43200
0.0014
43200
0.0029
21600
0.0026
14400
0.0060
7200
0.0048
7200
0.0102
7200
0.0149
7200
0.0235
7200
0.0420
0.359556
0.429261
0.488995
0.532317
0.559656
0.577466
0.589560
0.597497
0.603054
0.606683
0.609019
0.610498
0.611479
0.612738
0.613496
0.613998
0.614370
0.614694
0.614854
0.615060
0.615290
0.615506
0.615626
0.615702
0.615790
0.615841
0.615881
0.615928
0.616015
0.616157
0.616227
0.616370
0.616500
0.616796
0.617033
0.617537
0.618274
0.619440
0.621525
-10.94
-10.64
-10.64
-10.86
-11.25
-11.64
-12.00
-12.40
-12.75
-13.17
-13.60
-14.06
-14.46
-14.91
-15.41
-15.82
-16.53
-16.95
-17.66
-18.10
-18.39
-19.15
-19.73
-20.19
-20.74
-21.29
-21.53
-21.35
-20.75
-20.26
-20.27
-19.55
-18.96
-17.73
-17.26
-16.51
-16.12
-15.66
-15.08
103
TABLE A3 (CONTINUED)
7200
0.0723
7200
0.1189
7200
0.1520
7200
0.2227
3600
0.1597
3600
0.2363
3600
0.3581
3600
0.4370
3600
0.5890
3600
0.7832
3600
0.8300
3.668
20.15
74
75
76
77
78
79
80
81
82
83
84
Final
Total
403
413
423
433
443
453
463
473
483
493
500
Mud Tank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Parallel
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
3600
7200
7200
7200
7200
7200
7200
8100
7200
7200
7200
7200
7200
7200
7200
7200
5400
5400
5400
3600
3600
3600
3600
3600
0.0016
0.0012
0.0010
0.0016
0.0011
0.0012
0.0013
0.0018
0.0018
0.0021
0.0025
0.0030
0.0036
0.0043
0.0054
0.0063
0.0059
0.0072
0.0091
0.0078
0.0106
0.0139
0.0191
0.0253
0.625110
0.631009
0.638550
0.649601
0.657526
0.669252
0.687019
0.708702
0.737928
0.776789
0.817972
1
-14.53
-14.03
-13.77
-13.38
-13.00
-12.59
-12.16
-11.93
-11.59
-11.26
-11.15
0.000063
0.000111
0.000150
0.000211
0.000252
0.000299
0.000350
0.000421
0.000491
0.000572
0.000668
0.000786
0.000927
0.001096
0.001305
0.001552
0.001781
0.002061
0.002416
0.002721
0.003136
0.003682
0.004427
0.005418
-27.77
-27.73
-27.54
-26.76
-26.90
-26.59
-26.34
-25.96
-25.69
-25.40
-25.06
-24.70
-24.36
-24.01
-23.63
-23.29
-22.92
-22.58
-22.19
-21.80
-21.36
-20.93
-20.45
-19.97
104
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
390
400
410
420
430
440
450
460
470
480
490
500
500
495
485
475
465
455
445
435
425
415
405
395
385
375
365
355
345
335
325
315
305
295
285
275
265
273
283
TABLE A3 (CONTINUED)
3600
0.0357
3600
0.0512
3600
0.0706
1800
0.0496
1800
0.0721
1800
0.0993
1800
0.1324
1800
0.1664
1800
0.2080
1800
0.2440
1800
0.2775
1800
0.3234
1800
0.2527
1800
0.1819
1800
0.1195
1800
0.0790
1800
0.0563
1800
0.0461
1800
0.0317
1800
0.0218
1800
0.0147
1800
0.0101
1800
0.0069
3600
0.0093
3600
0.0064
3600
0.0041
5400
0.0042
7200
0.0036
7200
0.0024
14400
0.0030
21600
0.0033
43200
0.0038
43200
0.0024
43200
0.0015
92700
0.0023
86400
0.0013
86400
0.0012
86400
0.0016
86400
0.0019
0.006815
0.008817
0.011579
0.013518
0.016337
0.020222
0.025401
0.031909
0.040043
0.049585
0.060436
0.073084
0.082966
0.090079
0.094754
0.097842
0.100044
0.101846
0.103087
0.103939
0.104514
0.104909
0.105179
0.105544
0.105795
0.105954
0.106119
0.106259
0.106351
0.106468
0.106597
0.106745
0.106840
0.106899
0.106987
0.107039
0.107085
0.107146
0.107219
-19.41
-18.80
-18.21
-17.67
-17.12
-16.60
-16.09
-15.63
-15.18
-14.80
-14.47
-14.12
-14.21
-14.44
-14.79
-15.16
-15.48
-15.66
-16.01
-16.38
-16.77
-17.14
-17.51
-17.90
-18.28
-18.73
-19.10
-19.55
-19.96
-20.42
-20.72
-21.28
-21.72
-22.20
-22.56
-23.02
-23.12
-22.86
-22.67
105
TABLE A3 (CONTINUED)
86400
0.0028
43200
0.0015
43200
0.0024
21600
0.0021
14400
0.0008
7200
0.0033
7200
0.0020
7200
0.0040
7200
0.0063
7200
0.0092
7200
0.0146
7200
0.0217
7200
0.0308
7200
0.0441
7200
0.0626
3600
0.0425
3600
0.0596
3600
0.0796
3600
0.1064
3600
0.1378
3600
0.1277
3600
0.2035
21.86
25.57
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
Final
Total
293
303
313
323
333
343
353
363
373
383
393
403
413
423
433
443
453
463
473
483
493
500
RB140
1
2
3
4
5
6
7
8
9
10
11
12
13
Orthogonal
150
170
180
190
200
210
220
230
240
250
260
270
280
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
0.0165
0.0104
0.0041
0.0036
0.0034
0.0034
0.0033
0.0038
0.0037
0.0042
0.0058
0.0062
0.0071
0.107329
0.107390
0.107485
0.107566
0.107596
0.107726
0.107805
0.107961
0.108206
0.108564
0.109136
0.109984
0.111189
0.112915
0.115363
0.117026
0.119356
0.122469
0.126631
0.132021
0.137013
0.144971
1
-22.26
-22.17
-21.71
-21.18
-21.77
-19.61
-20.10
-19.42
-18.97
-18.59
-18.12
-17.71
-17.35
-16.98
-16.61
-16.29
-15.93
-15.62
-15.30
-15.01
-15.04
-14.53
0.000228
0.000371
0.000428
0.000477
0.000524
0.000570
0.000616
0.000668
0.000719
0.000778
0.000858
0.000944
0.001041
-25.90
-25.39
-26.03
-26.05
-26.00
-25.92
-25.86
-25.64
-25.58
-25.37
-24.97
-24.81
-24.58
106
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
495
485
475
465
455
445
435
425
415
405
395
385
375
365
355
345
335
TABLE A3 (CONTINUED)
0.0092
7200
7200
0.0126
7200
0.0166
7200
0.0198
7200
0.0284
7200
0.0362
7200
0.0468
7200
0.0596
7200
0.0770
7200
0.1005
7200
0.1262
7200
0.1624
3600
0.1086
3600
0.1447
3600
0.1931
3600
0.2472
3600
0.3114
3600
0.3828
3720
0.4810
3600
0.5621
3600
0.7241
3600
0.7958
3600
0.5659
3600
0.3558
3600
0.2340
3600
0.1554
3600
0.0972
3600
0.0638
3600
0.0414
3600
0.0261
7200
0.0328
7200
0.0226
7200
0.0127
7200
0.0091
7200
0.0054
7200
0.0030
14400
0.0037
14400
0.0020
14400
0.0013
0.001168
0.001341
0.001569
0.001841
0.002232
0.002730
0.003375
0.004197
0.005257
0.006641
0.008379
0.010616
0.012112
0.014105
0.016764
0.020170
0.024459
0.029732
0.036358
0.044102
0.054076
0.065039
0.072835
0.077736
0.080959
0.083100
0.084440
0.085318
0.085889
0.086248
0.086701
0.087012
0.087187
0.087312
0.087387
0.087429
0.087480
0.087506
0.087524
-24.21
-23.77
-23.35
-23.01
-22.47
-22.03
-21.57
-21.11
-20.63
-20.14
-19.68
-19.19
-18.72
-18.29
-17.84
-17.41
-16.99
-16.59
-16.20
-15.81
-15.36
-15.07
-15.27
-15.64
-16.01
-16.38
-16.83
-17.24
-17.66
-18.12
-18.58
-18.95
-19.52
-19.85
-20.37
-20.96
-21.45
-22.08
-22.49
107
TABLE A3 (CONTINUED)
0.0012
21600
21600
0.0007
43260
0.0009
43200
0.0006
50400
0.0006
86400
0.0006
86400
0.0004
82800
0.0003
86400
0.0006
50400
0.0005
54000
0.0006
43200
0.0010
28800
0.0011
28800
0.0018
21600
0.0021
14400
0.0037
14400
0.0049
14400
0.0095
7200
0.0073
7200
0.0117
7200
0.0196
7200
0.0324
7200
0.0474
7200
0.0787
7200
0.1188
7200
0.1752
7200
0.2569
7200
0.3596
3600
0.2571
3600
0.3521
3600
0.4319
64.06
72.59
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
Final
Total
325
315
305
295
285
275
265
273
283
293
303
313
323
333
343
353
363
373
383
393
403
413
423
433
443
453
463
473
483
493
500
RB140
1
2
3
4
Parallel
150
160
170
180
7200
7200
7200
7200
0.0338
0.0082
0.0066
0.0058
0.087541
0.087551
0.087563
0.087571
0.087578
0.087587
0.087592
0.087596
0.087604
0.087611
0.087619
0.087634
0.087649
0.087673
0.087703
0.087754
0.087821
0.087953
0.088054
0.088215
0.088485
0.088931
0.089585
0.090669
0.092306
0.094719
0.098258
0.103212
0.106754
0.111604
0.117555
1
-22.97
-23.45
-24.00
-24.44
-24.59
-25.06
-25.42
-25.78
-25.10
-24.62
-24.63
-23.81
-23.33
-22.87
-22.40
-21.43
-21.17
-20.49
-20.06
-19.59
-19.07
-18.57
-18.18
-17.66
-17.24
-16.83
-16.41
-16.03
-15.63
-15.28
-15.03
0.000084
0.000105
0.000121
0.000136
-27.89
-28.49
-28.54
-28.54
108
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
500
495
485
475
465
455
445
TABLE A3 (CONTINUED)
7200
0.0048
7200
0.0047
7200
0.0049
7200
0.0051
7200
0.0062
7200
0.0058
7200
0.0076
7200
0.0086
7200
0.0106
7200
0.0135
7200
0.0174
7200
0.0227
5400
0.0228
5400
0.0306
5400
0.0391
3600
0.0346
3600
0.0461
3600
0.0590
3600
0.0731
3600
0.0906
3600
0.1128
3600
0.1382
3600
0.1600
3600
0.1966
3600
0.2383
3600
0.2806
3600
0.3395
3600
0.4008
3600
0.4694
3600
0.5581
1800
0.3411
1800
0.4238
1800
0.3788
1800
0.2849
3600
0.3603
2760
0.1820
3600
0.1521
3600
0.0969
3600
0.0617
0.000148
0.000159
0.000172
0.000184
0.000200
0.000214
0.000233
0.000254
0.000281
0.000315
0.000358
0.000415
0.000472
0.000548
0.000646
0.000732
0.000847
0.000994
0.001176
0.001402
0.001684
0.002028
0.002427
0.002918
0.003512
0.004212
0.005059
0.006058
0.007229
0.008621
0.009472
0.010529
0.011474
0.012184
0.013083
0.013537
0.013916
0.014158
0.014312
-28.63
-28.56
-28.45
-28.34
-28.07
-28.05
-27.71
-27.50
-27.20
-26.84
-26.47
-26.07
-25.64
-25.20
-24.80
-24.38
-23.95
-23.55
-23.17
-22.79
-22.39
-22.00
-21.67
-21.28
-20.91
-20.56
-20.19
-19.84
-19.50
-19.15
-18.82
-18.50
-18.52
-18.73
-19.12
-19.49
-19.90
-20.33
-20.77
109
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
435
425
415
405
395
385
375
365
355
345
335
325
315
305
295
285
275
265
273
283
293
303
313
323
324
343
353
363
373
383
393
403
413
423
433
443
453
463
473
TABLE A3 (CONTINUED)
3600
0.0400
3600
0.0257
3600
0.0162
3600
0.0101
3600
0.0061
3600
0.0038
3600
0.0023
7200
0.0028
7200
0.0016
7200
0.0010
14400
0.0016
21600
0.0010
43200
0.0012
43200
0.0008
52200
0.0006
93600
0.0008
86400
0.0006
95400
0.0005
86400
0.0031
86400
0.0015
86400
0.0015
54000
0.0009
54000
0.0013
21600
0.0008
25200
0.0014
21600
0.0008
7200
0.0013
7200
0.0023
7200
0.0039
7200
0.0066
7200
0.0112
7200
0.0182
7200
0.0289
7200
0.0459
7200
0.0697
7200
0.1068
7200
0.1589
7200
0.2312
10800
0.4853
0.014411
0.014475
0.014516
0.014541
0.014556
0.014565
0.014571
0.014578
0.014582
0.014585
0.014589
0.014591
0.014594
0.014596
0.014597
0.014599
0.014601
0.014602
0.014610
0.014613
0.014617
0.014619
0.014623
0.014625
0.014628
0.014630
0.014634
0.014639
0.014649
0.014665
0.014694
0.014739
0.014811
0.014926
0.015099
0.015366
0.015762
0.016339
0.017549
-21.19
-21.63
-22.09
-22.56
-23.06
-23.54
-24.03
-24.54
-25.08
-25.59
-25.78
-26.69
-27.18
-27.62
-28.01
-28.36
-28.60
-28.87
-26.92
-27.65
-27.66
-27.70
-27.28
-26.84
-26.45
-25.85
-25.26
-24.71
-24.20
-23.67
-23.13
-22.65
-22.18
-21.71
-21.29
-20.84
-20.43
-20.02
-19.63
110
TABLE A3 (CONTINUED)
7200
0.4399
9000
0.7322
7200
0.6851
7200
0.5364
7200
0.3489
7200
0.2248
7200
0.1486
7200
0.0980
7200
0.1319
7200
0.1955
7200
0.2814
7200
0.3972
7200
0.4744
389.2
401.0
83
84
85
86
87
88
89
90
91
92
93
94
95
Final
Total
483
493
500
496
486
476
466
456
464
474
484
494
500
BR231
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Orthogonal
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
5400
5400
5400
3600
3600
3600
0.1279
0.0344
0.0157
0.0109
0.0105
0.0113
0.0118
0.0134
0.0158
0.0178
0.0200
0.0233
0.0274
0.0328
0.0409
0.0525
0.0491
0.0578
0.0777
0.0709
0.0970
0.1234
0.018647
0.020473
0.022181
0.023519
0.024389
0.024950
0.025320
0.025565
0.025894
0.026381
0.027083
0.028074
0.029257
1
-19.26
-18.89
-18.65
-18.83
-19.21
-19.62
-20.01
-20.42
-20.11
-19.70
-19.31
-18.94
-18.72
0.000503
0.000638
0.000700
0.000742
0.000784
0.000828
0.000874
0.000927
0.000989
0.001059
0.001138
0.001229
0.001337
0.001466
0.001627
0.001833
0.002026
0.002253
0.002559
0.002838
0.003219
0.003704
-24.31
-24.81
-25.44
-25.73
-25.71
-25.57
-25.48
-25.29
-25.07
-24.88
-24.70
-24.47
-24.23
-23.96
-23.64
-23.28
-22.95
-22.68
-22.27
-21.84
-21.41
-21.03
111
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
370
380
390
400
410
420
430
440
450
460
470
480
490
500
500
495
485
475
465
455
445
435
425
415
405
395
385
375
365
355
345
335
325
315
305
295
285
275
265
TABLE A3 (CONTINUED)
3600
0.1547
3600
0.1881
3600
0.2706
3600
0.3494
3600
0.3823
3600
0.5844
3600
0.5252
3600
0.7263
3600
0.7794
3600
0.9852
3600
1.192
3600
1.346
1800
0.8142
1800
1.040
1800
0.8920
1800
0.7145
3600
0.9032
2760
0.4327
3600
0.3922
3600
0.2576
3600
0.1638
3600
0.0986
3600
0.0624
3600
0.0424
3600
0.0260
3600
0.0146
3600
0.0114
3600
0.0074
7200
0.0083
7200
0.0051
7200
0.0028
14400
0.0033
21600
0.0029
43200
0.0030
43200
0.0020
52200
0.0012
95400
0.0014
86400
0.0009
93600
0.0006
0.004312
0.005052
0.006116
0.007490
0.008993
0.011290
0.013355
0.016210
0.019274
0.023147
0.027835
0.033128
0.036328
0.040416
0.043923
0.046732
0.050283
0.051984
0.053526
0.054539
0.055183
0.055570
0.055816
0.055983
0.056085
0.056142
0.056187
0.056216
0.056249
0.056269
0.056280
0.056293
0.056304
0.056316
0.056324
0.056328
0.056334
0.056337
0.056340
-20.66
-20.31
-19.77
-19.32
-19.04
-18.40
-18.32
-17.81
-17.56
-17.14
-16.77
-16.47
-16.15
-15.80
-15.86
-16.01
-16.40
-16.82
-17.15
-17.55
-17.99
-18.49
-18.94
-19.32
-19.81
-20.38
-20.63
-21.07
-21.63
-22.13
-22.74
-23.27
-23.79
-24.45
-24.85
-25.56
-25.99
-26.35
-26.82
112
TABLE A3 (CONTINUED)
86400
0.0017
86400
0.0016
86400
0.0021
54000
0.0016
54000
0.0037
21600
0.0020
25200
0.0037
21600
0.0022
7200
0.0038
7200
0.0065
7200
0.0111
7200
0.0203
7200
0.0314
7200
0.0486
7200
0.2473
7200
0.1493
7200
0.1959
7200
0.2856
7200
0.4981
7200
0.6177
10800
1.324
7200
1.253
9000
2.201
7200
1.982
7200
1.629
7200
1.022
7200
0.6770
7200
0.4594
7200
0.2950
7200
0.4177
7200
0.5898
7200
0.8262
7200
1.149
7200
1.393
222.7
254.4
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
Final
Total
273
283
293
303
313
323
324
343
353
363
373
383
393
403
413
423
433
443
453
463
473
483
493
500
496
486
476
466
456
464
474
484
494
500
M127
1
Parallel
150
3600
0.2379
0.056346
0.056352
0.056360
0.056367
0.056381
0.056389
0.056403
0.056412
0.056427
0.056453
0.056496
0.056576
0.056700
0.056891
0.057863
0.058450
0.059220
0.060343
0.062301
0.064730
0.069934
0.074861
0.083516
0.091308
0.097713
0.101732
0.104393
0.106199
0.107359
0.109001
0.111320
0.114568
0.119086
0.124564
1
-25.74
-25.79
-25.51
-25.32
-24.47
-24.15
-23.71
-23.09
-22.41
-21.87
-21.34
-20.74
-20.30
-19.86
-18.22
-18.72
-18.43
-18.04
-17.46
-17.21
-16.79
-16.37
-15.94
-15.72
-15.84
-16.25
-16.63
-17.00
-17.43
-17.07
-16.70
-16.34
-15.98
-15.74
0.000057
-27.99
113
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
500
490
485
475
TABLE A3 (CONTINUED)
7200
0.1026
7200
0.0691
7200
0.0638
7200
0.0658
7200
0.0721
7200
0.0787
7200
0.0883
7200
0.0992
7200
0.1105
7200
0.1250
7200
0.1444
7200
0.1673
7200
0.1986
7200
0.2557
7200
0.3126
5400
0.2890
5400
0.3859
5400
0.4842
3600
0.4325
3600
0.5442
3600
0.7023
3600
0.8021
3600
1.058
3600
1.308
3600
1.524
3600
1.769
1800
1.115
1800
1.723
1800
1.777
1800
2.074
1800
2.589
1800
3.113
1800
3.283
1800
3.673
1800
4.943
1800
3.867
1800
2.499
1800
1.925
1800
1.268
0.000081
0.000097
0.000113
0.000128
0.000145
0.000164
0.000185
0.000209
0.000235
0.000265
0.000299
0.000339
0.000386
0.000447
0.000521
0.000590
0.000682
0.000797
0.000900
0.001030
0.001197
0.001388
0.001639
0.001951
0.002313
0.002734
0.002999
0.003409
0.003832
0.004326
0.004942
0.005683
0.006464
0.007338
0.008514
0.009434
0.010029
0.010487
0.010788
-28.63
-28.77
-28.69
-28.52
-28.30
-28.09
-27.85
-27.62
-27.39
-27.15
-26.88
-26.61
-26.31
-25.92
-25.57
-25.22
-24.80
-24.42
-23.99
-23.63
-23.23
-22.95
-22.52
-22.13
-21.81
-21.49
-21.13
-20.59
-20.43
-20.16
-19.81
-19.49
-19.30
-19.06
-18.63
-18.75
-19.10
-19.31
-19.69
114
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
465
455
445
435
425
415
405
395
385
375
365
355
345
335
325
315
305
295
285
275
265
273
283
293
303
313
323
333
343
353
363
373
383
393
403
413
423
433
443
TABLE A3 (CONTINUED)
1800
0.8148
1800
0.5378
1800
0.3505
1800
0.2320
1800
0.1410
1800
0.0935
1800
0.0592
3600
0.0672
3600
0.0472
5400
0.0427
5400
0.0271
5400
0.0333
5400
0.0106
7200
0.0093
21600
0.0137
54000
0.0186
61200
0.0121
65040
0.0122
64800
0.0045
72180
0.0033
137400
0.0040
86400
0.0034
73800
0.0048
88200
0.0085
88200
0.0145
77400
0.0217
43200
0.0210
36060
0.0311
7200
0.0108
7200
0.0182
7200
0.0281
7200
0.0478
7200
0.0811
7200
0.1278
7200
0.2098
7200
0.3249
7200
0.5139
7200
0.7594
3600
0.5520
0.010982
0.011110
0.011194
0.011249
0.011282
0.011305
0.011319
0.011335
0.011346
0.011356
0.011363
0.011371
0.011373
0.011375
0.011379
0.011383
0.011386
0.011389
0.011390
0.011391
0.011392
0.011392
0.011393
0.011395
0.011399
0.011404
0.011409
0.011416
0.011419
0.011423
0.011430
0.011441
0.011461
0.011491
0.011541
0.011618
0.011741
0.011921
0.012053
-20.11
-20.51
-20.93
-21.34
-21.83
-22.24
-22.70
-23.26
-23.61
-24.12
-24.57
-24.36
-25.51
-25.93
-26.64
-27.25
-27.81
-27.85
-28.86
-29.27
-29.73
-29.43
-28.92
-28.53
-27.99
-27.45
-26.90
-26.33
-25.78
-25.25
-24.82
-24.29
-23.76
-23.30
-22.80
-22.36
-21.89
-21.49
-21.10
115
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
453
463
473
483
493
500
500
491
481
471
461
451
441
431
421
411
401
412
422
432
442
452
462
472
482
492
500
500
494
484
474
464
454
444
434
424
414
404
416
TABLE A3 (CONTINUED)
10800
2.405
3600
1.100
3600
1.568
3600
2.041
3600
2.854
3660
3.466
17400
13.69
10800
5.644
11400
3.545
10800
2.159
10800
1.526
14400
1.282
14400
0.8642
14400
0.5545
14400
0.3480
14400
0.2149
14400
0.1340
14400
0.2299
14400
0.3530
14400
0.5193
14400
0.7913
14400
1.206
10800
1.285
10800
1.852
10800
2.679
10800
4.761
10800
4.493
10800
8.004
10800
4.219
10800
2.906
10800
1.816
10800
1.145
10800
0.7717
10800
0.5258
10800
0.3329
10800
0.2021
10800
0.1247
10800
0.0899
10800
0.1600
0.012625
0.012887
0.013260
0.013745
0.014424
0.015249
0.018506
0.019849
0.020692
0.021206
0.021569
0.021874
0.022079
0.022211
0.022294
0.022345
0.022377
0.022432
0.022516
0.022639
0.022828
0.023115
0.023420
0.023861
0.024499
0.025632
0.026701
0.028605
0.029609
0.030301
0.030733
0.031005
0.031189
0.031314
0.031393
0.031441
0.031471
0.031492
0.031530
-20.70
-20.35
-19.97
-19.67
-19.29
-19.06
-19.12
-19.40
-19.87
-20.28
-20.60
-21.05
-21.43
-21.87
-22.33
-22.81
-23.28
-22.74
-22.30
-21.91
-21.48
-21.05
-20.69
-20.31
-19.92
-19.30
-19.32
-18.69
-19.28
-19.62
-20.07
-20.52
-20.91
-21.29
-21.74
-22.24
-22.72
-23.05
-22.47
116
Remaining
Total
M127
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
TABLE A3 (CONTINUED)
4070
4203
Orthogonal
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
3600
3600
3600
3600
3600
3600
3600
3600
3600
0.4160
0.1351
0.1194
0.1402
0.1175
0.1184
0.1271
0.1532
0.1527
0.1716
0.1999
0.1965
0.2475
0.2669
0.3669
0.3787
0.4387
0.5181
0.6108
0.7037
0.8234
1.164
1.252
1.435
1.736
1.967
1.142
1.441
1.766
2.107
2.494
2.891
3.276
3.704
4.123
1
0.000213
0.000282
0.000343
0.000415
0.000475
0.000535
0.000600
0.000679
0.000757
0.000844
0.000947
0.001047
0.001174
0.001310
0.001498
0.001692
0.001916
0.002181
0.002493
0.002853
0.003274
0.003869
0.004510
0.005244
0.006132
0.007137
0.007721
0.008458
0.009361
0.010438
0.011714
0.013192
0.014867
0.016762
0.018870
-26.03
-26.32
-26.20
-25.85
-25.87
-25.73
-25.55
-25.24
-25.13
-24.90
-24.64
-24.55
-24.21
-24.02
-23.58
-23.42
-23.15
-22.86
-22.56
-22.28
-21.99
-21.49
-21.26
-20.97
-20.63
-20.35
-20.09
-19.77
-19.47
-19.19
-18.90
-18.64
-18.40
-18.15
-17.93
117
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
500
500
495
485
475
465
455
445
435
425
415
405
395
385
375
365
355
345
335
325
315
305
295
285
275
265
273
283
293
303
313
323
324
343
353
363
373
383
393
TABLE A3 (CONTINUED)
3600
4.598
3600
4.277
3600
3.088
3600
1.969
3600
1.250
3600
0.8194
3600
0.5460
3600
0.3778
3600
0.2417
3600
0.1627
3600
0.1050
3600
0.1337
7200
0.0923
7200
0.0554
7200
0.0335
7200
0.0204
14400
0.0268
14400
0.0153
22020
0.0143
51000
0.0188
43200
0.0097
43200
0.0071
90000
0.0077
90000
0.0047
90900
0.0040
86400
0.0029
86400
0.0026
86700
0.0039
91800
0.0057
43200
0.0043
43200
0.0076
43200
0.0120
43200
0.0104
21600
0.0177
14400
0.0204
14400
0.0340
7200
0.0305
7200
0.0461
14340
0.1552
0.021222
0.023409
0.024988
0.025995
0.026635
0.027054
0.027333
0.027526
0.027650
0.027733
0.027787
0.027855
0.027902
0.027931
0.027948
0.027958
0.027972
0.027980
0.027987
0.027997
0.028002
0.028005
0.028009
0.028012
0.028014
0.028015
0.028017
0.028019
0.028021
0.028024
0.028028
0.028034
0.028039
0.028048
0.028059
0.028076
0.028091
0.028115
0.028194
-17.70
-17.66
-17.91
-18.31
-18.73
-19.13
-19.53
-19.89
-20.33
-20.72
-21.15
-20.91
-21.97
-22.48
-22.98
-23.48
-23.90
-24.46
-24.95
-25.52
-26.01
-26.33
-26.98
-27.48
-27.64
-27.90
-28.03
-27.63
-27.30
-26.82
-26.26
-25.80
-25.94
-24.25
-24.17
-23.66
-23.07
-22.66
-22.13
118
TABLE A3 (CONTINUED)
7200
0.1140
7200
0.1782
7200
0.2695
7200
0.4023
7200
0.6040
7200
0.8788
7200
1.543
7200
2.129
7200
2.757
7200
3.470
7200
4.104
7200
2.774
7380
1.840
7200
1.211
7200
0.8091
7200
0.8431
7200
0.5338
7200
0.9186
7200
1.305
7500
1.950
7200
2.492
7200
3.294
7200
3.412
1862
1955
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
Final
Total
403
413
423
433
443
453
463
473
483
493
500
492
482
472
462
452
442
456
466
476
486
496
500
G3
1
2
3
4
5
6
7
8
9
10
11
12
Orthogonal
150
160
170
180
190
200
210
220
230
240
250
260
7200
7200
7200
7200
7200
7200
7200
7200
7200
7200
3600
3600
1.080
0.5269
0.5089
0.5485
0.6479
0.8986
1.345
2.096
3.166
4.779
3.531
5.190
0.028253
0.028344
0.028482
0.028687
0.028996
0.029446
0.030235
0.031323
0.032733
0.034508
0.036606
0.038025
0.038966
0.039585
0.039999
0.040430
0.040703
0.041173
0.041840
0.042837
0.044112
0.045796
0.047541
1
-21.75
-21.30
-20.88
-20.47
-20.06
-19.67
-19.09
-18.73
-18.44
-18.16
-17.93
-18.28
-18.68
-19.05
-19.44
-19.39
-19.84
-19.29
-18.92
-18.54
-18.23
-17.92
-17.85
0.000373
0.000555
0.000730
0.000920
0.001143
0.001453
0.001917
0.002641
0.003733
0.005382
0.006601
0.008392
-24.91
-24.72
-24.43
-24.10
-23.71
-23.16
-22.49
-21.75
-21.00
-20.23
-19.56
-18.96
119
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
270
280
290
300
310
320
330
340
350
345
335
325
315
305
295
285
275
265
255
245
235
225
215
205
195
185
175
165
155
163
173
183
193
203
213
223
233
243
253
TABLE A3 (CONTINUED)
3600
7.409
3600
10.15
3600
12.97
3600
16.64
1800
10.77
1800
14.16
1800
17.66
1800
21.92
1800
27.15
1800
21.11
1800
13.72
1800
9.587
1800
6.471
1800
8.414
3600
5.693
3600
4.013
3600
2.443
3600
1.554
3600
0.9890
3600
0.6107
3600
0.3819
7200
0.4727
7200
0.2788
7200
0.1583
7200
0.0902
8100
0.0555
14700
0.0410
10800
0.0204
12600
0.0123
10800
0.0174
7200
0.0230
7200
0.0424
7200
0.0901
7200
0.1790
7200
0.2518
7200
0.4249
7200
0.6855
7200
1.124
7200
1.780
0.010949
0.014450
0.018925
0.024667
0.028383
0.033268
0.039363
0.046928
0.056298
0.063583
0.068316
0.071625
0.073858
0.076761
0.078726
0.080110
0.080953
0.081490
0.081831
0.082042
0.082173
0.082337
0.082433
0.082487
0.082518
0.082538
0.082552
0.082559
0.082563
0.082569
0.082577
0.082592
0.082623
0.082685
0.082771
0.082918
0.083155
0.083543
0.084157
-18.34
-17.76
-17.24
-16.72
-16.27
-15.84
-15.46
-15.07
-14.68
-14.78
-15.12
-15.41
-15.77
-15.47
-16.52
-16.85
-17.33
-17.78
-18.23
-18.70
-19.17
-19.65
-20.18
-20.74
-21.30
-21.91
-22.80
-23.19
-23.85
-23.35
-22.67
-22.06
-21.30
-20.62
-20.27
-19.75
-19.27
-18.77
-18.30
120
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
Final
Total
N17
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
263
273
283
293
303
313
323
333
343
353
363
373
383
380
370
360
350
150
160
170
180
190
200
210
220
230
240
250
260
270
270
265
255
245
235
TABLE A3 (CONTINUED)
7200
3.073
7200
4.241
7200
6.410
7200
9.072
7200
12.89
7200
17.54
3600
12.18
3600
16.09
3600
21.25
3600
27.62
1800
18.60
1800
24.17
1800
30.73
1800
27.26
3600
38.07
3600
26.75
3600
19.45
2339
2898
3600
1200
1200
900
900
900
900
900
600
600
600
600
600
600
600
600
600
600
35.25
9.444
11.88
11.71
14.41
17.88
22.58
27.55
25.65
32.01
40.35
55.14
71.02
66.91
56.95
44.86
33.57
22.79
0.085217
0.086681
0.088893
0.092023
0.096470
0.102524
0.106728
0.112281
0.119615
0.129145
0.135563
0.143903
0.154508
0.163916
0.177053
0.186283
0.192993
1
-17.75
-17.41
-16.98
-16.60
-16.21
-15.84
-15.47
-15.14
-14.81
-14.47
-14.11
-13.80
-13.49
-13.55
-13.84
-14.13
-14.40
0.014650
0.018575
0.023510
0.028378
0.034368
0.041797
0.051180
0.062631
0.073292
0.086596
0.103363
0.126280
0.155796
0.183603
0.207272
0.225915
0.239866
0.249336
-16.88
-16.28
-15.81
-15.33
-14.93
-14.52
-14.09
-13.69
-13.18
-12.79
-12.39
-11.89
-11.43
-11.30
-11.32
-11.46
-11.67
-12.01
121
19
20
21
22
23
24
25
26
27
28
29
30
31
Final
Total
TH62Z2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Final
Total
225
215
205
195
185
193
203
213
223
233
243
253
263
310
350
375
400
425
450
475
500
480
460
440
420
395
495
510
520
530
540
410
TABLE A3 (CONTINUED)
600
16.11
900
16.21
900
11.29
900
7.782
900
4.832
900
6.394
900
9.606
900
13.46
600
13.33
600
18.37
600
24.65
600
31.49
600
39.72
1594
2408
5400
5580
4560
5040
3420
4080
3780
5640
9480
18600
17880
45120
86340
4080
4080
3780
3720
3840
228120
0.0079
0.0112
0.0116
0.0182
0.0163
0.0372
0.0363
0.0686
0.0357
0.0376
0.0132
0.0168
0.0138
0.0139
0.0238
0.0273
0.0383
0.0441
0.0395
1.732
2.243
0.256032
0.262768
0.267459
0.270693
0.272701
0.275358
0.279350
0.284943
0.290482
0.298118
0.308363
0.321450
0.337956
1
-12.33
-12.70
-13.04
-13.40
-13.86
-13.58
-13.16
-12.80
-12.39
-12.04
-11.72
-11.44
-11.16
0.003507
0.008507
0.013676
0.021799
0.029073
0.045666
0.061831
0.092412
0.108338
0.125094
0.130980
0.138467
0.144602
0.150809
0.161405
0.173579
0.190650
0.210311
0.227930
1
-22.34
-20.79
-19.94
-19.12
-18.48
-17.45
-16.99
-16.37
-17.26
-17.72
-18.62
-19.25
-20.04
-16.93
-16.33
-16.03
-15.58
-15.36
-19.45
2. Values for ln(D/a2) calculated with a spherical geometry from equations in Fechtig and Kalbitzer (1966)
Slab
Orientation
(relative to c)
Orthogonal
Parallel
Orthogonal
Parallel
Orthogonal
Orthogonal
Parallel
Orthogonal
n.a.
n.a.
6.6455
3.0385
4.7014
3.0552
4.5667
3.1172
2.6729
2.6320
2.0538
2.6738
(D0/a2)
log
± 0.1071
± 0.1568
± 0.1853
± 0.1504
± 0.1438
± 0.1266
± 0.1045
± 0.0596
± 0.0835
± 0.2583
1σ
110.5
0.0273
0.2011
0.0230
0.2304
0.0265
0.0265
4.193 x 10-3
6.367 x 10-3
0.0170
(cm2/s)
D0
1. Closure temperatures calculated with a spherical geometry for comparison to published results
1σ
+30.9 −24.2
+0.0119 −.0083
+0.1070 −.0699
+0.0095 −.0067
+0.0905 −.0650
+0.0090 −.0067
+0.0072 −.0057
+0.0007 −.0006
+0.0013 −.0011
+0.0138 −.0076
Note: 1σ uncertainties are calculated only from linear regression data after the end of the first prograde series of steps.
Mud Tank
Mud Tank
RB140
RB140
BR231
M127
M127
G3
N17
TH62Z
Sample
Name
167.93
138.22
166.49
166.19
169.75
161.58
162.83
106.53
70.74
145.96
Ea (kJ/mol)
TABLE A4. KINETIC PARAMETERS FROM STEP-HEATING EXPERIMENTS
± 0.68
± 0.99
± 1.15
± 0.97
± 0.92
± 0.81
± 0.68
± 0.31
± 0.40
± 0.44
1σ
132
126
185
207
193
192
195
49
-59
152
(°C)1
Tc a = 60 µm
122
Value (Units)
Ea=165 (kJ/mol), D0=193188 (cm2/s)
45920 (nm)
1.669 (nm-1)
5.48 x 10-19 (g/α-event)
Ea=71 (kJ/mol), D0=6.367 x 10-3 (cm2/s)
3 (n.a.)
-0.05721 (n.a.)
6.24534 (n.a.)
-0.11977 (n.a.)
-314.937 (n.a.)
-14.2868 (n.a.)
Description
Diffusivity of zircon with dose of 1 x 1014 α/g (see text for details)
Mean intercept length of zircon with dose of 1 x 1014 α/g
Surface area to volume ratio for damage capsules
Mass of amorphous material produced per alpha decay event
Diffusivity of amorphous material (N17 kinetics)
Parameterization constant for amorphous fraction interconnectivity
Damage annealing model parameter
Damage annealing model parameter
Damage annealing model parameter
Damage annealing model parameter
Damage annealing model parameter
Symbol
Dz
lint0
SV
Ba
DN17
Φ
β
C0
C1
C2
C3
1,5,7,8
2,8
3
4,6
5,7,8
6
11
11
11
11
11
Equation
TABLE 5. CONSTANTS AND VALUES USED IN PARAMETERIZATION
123
124
Figure A1: Positive date-eU correlations. Individual points in each dataset represent
single grain dates (2 sigma error).
125
Figure A2: Negative date-eU correlations. Individual points in each dataset represent
single grain ages (2 sigma error).
126
500
127
Figure A3: Arrhenius plots for various zircon slabs. In both plots, non-linear trends are
observed in the initial temperature steps (white markers). Linear regression for obtaining
kinetic parameters performed on steps following the high-temperature reached in the
initial prograde path (blue markers).
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Figure A4. Ln(a/a0) plotted as a function of cumulative fraction of He released in stepheating experiments. This term describes the deviation of D/a2 at any given time step
from the D/a2 determined from linear regression. See Reiners and others (2004) for the
derivation. The inset is a magnified version of the main plot. The rectangular box in the
main plot indicates the span of this inset. Despite the initial high deviation in ln(a/a0) at
low cumulative fraction released, almost all samples approach a value of 0 (no deviation)
after roughly the first percent of gas is released.
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Figure A5. Pre-exponential factor (D0) versus radiation damage for samples analyzed in
this study, and those previously published. Dashed lines have been added to highlight
trends. Our ORT_C samples (all samples from this study with diffusion parallel to caxis), as well as most of the published results, fall along a trend of decreasing D0 with
increasing radiation damage. The PAR_C samples (all samples from this study with
diffusion orthogonal to c-axis), however, are constant with increasing damage. Also note
that these two sets of values become similar at damage levels equivalent to those of
M127. The previously published data mostly falls along one of these trends. We represent
the data that agrees with our ORT_C samples in yellow triangles (FCT and 98PRGB18
from Reiners and others, 2002; and 1CS15 and M146 from Reiners and others, 2004),
and the data that agrees with our PAR_C samples in black triangles (98PRGB4 from
Reiners and others, 2002; and ZKTB4050 from Wolfe and Stockli, 2010). The grey
triangle represents a single point that does not fall along either trendline (ZKTB1516
from Wolfe and Stockli, 2010). Error bars are for 1 sigma error, if reported (errors for
some samples are not available).
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Figure A6. Comparison of Arrhenius trends for samples shown in figure A4. Kinetic
parameters used in this comparison are from post-high temperatures steps (blue markers
in figure A4). We have converted from values of D/a2 to D using the half-width of each
slab.
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Figure A7. Plot of He diffusivity versus alpha dose for samples described in figures A4
and A6, as well as samples whose kinetic parameters are already published. Temperature
is held constant at 180 degrees Celsius. Grey triangle represent single sample from Wolfe
and Stockli (2010) (ZKTB1516) that does not fall along our observed trend.
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Figure A8. Plot of closure temperature versus alpha dose for samples described in figures
A4 and A6, as well as samples whose kinetic parameters are already published. Closure
temperatures were calculated using a spherical geometry, diffusion domain size of 60
microns, and cooling rate of 10 °C/my. Grey triangle represents single sample from
Wolfe and Stockli (2010) (ZKTB1516) that does not fall along our observed trend.
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Figure A9. Schematic of possible time-temperature paths that produce date-eU
relationships. The arrows on each plot’s axes indicate the direction in which the given
value increases. Varying eU contents lead to differential accumulations of radiation
damage, which in turn lead to differential He diffusivities. (A) If accumulation is
relatively low, and a sample experiences a thermal pulse, or cools slowly through the
PRZ so that damage in-growth and diffusion happen simultaneously, then a positive
correlation results. (B) Conversely, if damage accumulation is relatively high (due to
older zircons), then a thermal pulse results in a negative correlation, or significant He loss
may occur at low temperatures.
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0
135
Figure A10. (A) Diffusivity as a function of alpha dose calculated at temperatures that
roughly bracket the nominal zircon PRZ. Data points are the diffusivities of the various
samples included in figure A7 (calculated with a domain size of 100 microns) and curves
represent effective diffusivity as defined by equation (8). The various parameters used for
this plot and their values are listed in table A5. (B) Closure temperature as a function of
alpha dose calculated in a manner similar to figure A8. Grey points in both plots
represent single sample that does not fall along our observed trend.
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Figure A11. Representative thermal histories (A) with corresponding forward modeled
date-eU correlations (B). Each numbered t-T path in (A) corresponds to the similarly
numbered correlation in (B). Thermal history number 6 is partially obscured by 2 and 3
because it follows the same path but lacks a post-500 Ma reheating event. For reference,
we also plot the zircon He dates that result from each thermal history in (A) if the kinetics
of Reiners and others (2004) are used. These are represented by the numbered black
diamonds on the y-axis of (B).
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Figure A12. Forward modeled date-eU correlations matched to datasets shown in figures
1 and 2. (A) Positive date-eU correlation (detrital Apennines sample AP54B) with
forward modeled correlation resulting from thermal history shown in the left-hand panel.
This thermal history is characterized by a period of rapid exhumation in the source terrain
(as constrained by ZFT dates from Bernet and others, 2001), deposition and burial in the
Apennine foreland basin, and final exhumation to the surface in the latest Miocene. We
used a grain radius of 48 microns for each model zircon, which is the average for this
dataset. Dotted light grey lines in both panels represent an alternative thermal history and
the corresponding date-eU correlation. (B) Negative date-eU correlation (igneous
Minnesota River Valley sample) with forward model correlation resulting from the
thermal history shown in the left-hand panel. This thermal history begins at the
approximate end of tectonism associated with the Penokean Orogeny in this area and
proceeds at a cooling rate of .06 °C/my until 1100 Ma. This time corresponds with the
initiation of the Keweenaw Rift System (the Minnesota River Valley was situated near
the rift shoulder) and we model this as an increase in the long-term cooling rate to ~.17
°C/my. Again, we used the average grain radius from this dataset (52 microns) as an
input for each model zircon. Dashed and dotted lines in both panels represent two
alternative thermal histories and the corresponding date-eU correlations.
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Figure A13. Time-temperature histories and corresponding date-eU correlations for
unzoned zircons, zircons with high eU rims, and zircons with high eU cores. The
numbering for each t-T path is similar to figure 11, except we have omitted number 6 and
replaced number 5 with a different thermal history. Core eU concentrations are either
enriched or depleted by a factor of 7 relative to the bulk concentration of the whole grain.
For example, if the bulk concentration is 500 ppm, then the core concentration in the high
eU core zircon is 3500 ppm and it is ~71 ppm in the high eU rim zircon. Both the
concentration in the rim and the radial position of the rim are determined by maximizing
the zircon zonation factor (see text for details). All zircons have a radius of 60 microns
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and the core is composed of either the inner 20 or 40 microns of the grain. Large bold
symbols connected by horizontal curves represent FTH corrected dates, small bold
symbols represent FTZ corrected dates, and small transparent symbols represent
uncorrected dates. Lightly colored vertical bars have been added to aid in connecting
corresponding FTH and FTZ corrected dates. See text for details on uncorrected, FTH , and
FTZ corrected zircons. Note that the scale for each y-axis is different.
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APPENDIX B: INTERPRETING DATE-EU CORRELATIONS IN ZIRCON (U-Th)/He
DATASETS USING A NEW MODEL FOR HELIUM DIFFUSION IN ZIRCON: A
CASE STUDY FROM THE LONGMEN SHAN, CHINA
To be submitted to the professional journal: Earth and Planetary Science Letters
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INTERPRETING DATE-EU CORRELATIONS IN ZIRCON (U-Th)/He DATASETS
USING A NEW MODEL FOR HELIUM DIFFUSION IN ZIRCON: A CASE STUDY
FROM THE LONGMEN SHAN, CHINA
William R. Guenthner, Peter W. Reiners, and Yuntao Tian
Abstract
The Longmen Shan, located at the eastern margin of the Tibetan Plateau, has been the
site of numerous low-temperature thermochronologic studies focused on describing the
exhumation history of the orogen. These studies have used a combination of zircon (UTh)/He (zircon He), apatite (U-Th)/He (apatite He) and apatite fission track (AFT)
techniques to document exhumation since both the mid to late Miocene, and also earlier,
pre-Miocene episodes of exhumation (e.g. Wang et al., 2012). Zircon He dating, with its
relatively high closure temperatures, is particularly well suited for capturing these earlier
episodes. In the Longmen Shan, these datasets can be difficult to interpret due to
significant dispersion of single grain dates within a given sample or group of samples,
which is often expressed as a negative correlation between He date and effective uranium
(eU, a proxy for radiation damage). In this study, we explain the cause of this dispersion
in several previously published zircon He datasets with a new, radiation damage-based
model for He diffusion in zircon. Our model results constrain the timing of Cenozoic
rapid exhumation events, the maximum burial temperatures experienced during the
Cenozoic, and the maximum burial temperatures experienced during the Triassic-Jurassic
Longmen Shan orogenic event, at each specific location. Taken together, our
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reinterpreted results allow us to place individual samples or groups of samples within a
cohesive exhumation history for the entire orogen.
1. Introduction
Because it constrains the timing and magnitude of cooling events, bedrock lowtemperature thermochronology by the zircon (U-Th)/He (zircon He) method can be used
to understand the exhumation histories of orogenic belts. Although He dates from
multiple single-grain zircon crystals from individual samples are often reproducible and
consistent with other exhumation constraints, However in some geologic settings, zircon
He dates of single crystals show significant intra-sample dispersion, the origin of which is
not well understood.In some cases this has caused practitioners of the method to
disregard “bad” data or derive average dates over large variations, raising concerns about
the accuracy of the thermal history reconstructions (tT paths).
Several good examples of apparently problematic zircon He datasets come from
the central and southern Longmen Shan on the eastern margin of the Tibetan plateau (fig.
1). This mountain belt is characterized by high relief (~4 km of elevation change over 30
km) and active seismicity (e.g. the M 7.9 Wenchuan Earthquake of 12 May, 2008 and a
M 7.0 earthquake in the southern Longmen Shan on 20 April, 2013). The geodynamics of
the Longmen Shan and surrounding regions also play a critical role in interpretations of
the timing and nature of deformation in the middle and lower crust beneath the Tibetan
plateau (Royden et al., 1997; Tapponier et al., 2001; Replumaz and Tapponier, 2003;
Clark et al., 2005a; Royden et al., 2008, Duvall et al., 2012). For these reasons the
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Longmen Shan has been the focus of several thermochronologic studies attempting to
understand modern and past geodynamic processes using apatite fission track (AFT),
zircon fission track (ZFT), apatite (U-Th)/He (apatite He), and zircon (U-Th)/He (zircon
He) dating techniques.
Several studies from the central Longmen Shan document a rapid exhumation
event between 11 and 5 Ma (Arne et al., 1997; Kirby et al., 2002; Godard et al., 2009).
But evidence for an earlier period of rapid exhumation in the Longmen Shan and adjacent
Sichuan Basin, has also been presented (Richardson et al., 2008; Tian et al., 2012; Wang
et al., 2012). Wang et al. (2012) published apatite and zircon fission-track and He dates
from the central Longmen Shan and used thermal modeling to show that their data were
consistent with a phase of rapid exhumation beginning between 30 and 25 Ma. This event
is not observed in other thermochronologic datasets from the Longmen Shan and seems
to contradict some of the other published results. These contradictory results make it
difficult to place the growing body of thermochronologic data from eastern Tibet into a
single, cohesive tectonic framework.
This confusion could in part result from the difficulty of interpreting the large
dispersion of single-grain zircon He dates found in these datasets, particularly in the
Wang et al. (2012) data. Most of the studies in this region manifest this dispersion as
negative correlations between single-grain zircon He dates and effective uranium (eU, eU
= U + .235*Th). Among grains from the same sample and therefore the same thermal
history, eU provides a proxy for relative alpha dose and radiation damage. Guenthner et
al. (2013) interpreted date-eU correlations of this type as the effect of radiation damage
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on He diffusion, showing how different types of date-eU correlations arise from different
thermal histories, and how they can be combined with a damage-diffusivity model to
constrain single sample thermal histories. In this study, we use this approach to reexamine zircon He datasets of Godard et al. (2009), Wang et al. (2012), and Tian et al.
(2013). Our approach does not exclude any replicates from a given sample, explains most
of the scatter in these zircon He datasets, and, in certain cases, allows us to constrain
thermal histories for single samples with more detail and for much longer time intervals
than previous models. With these single sample thermal histories, we can better assess
the exhumation histories for individual locations within the Longmen Shan, and reconcile
datasets that suggest either an early or late Miocene phase of rapid exhumation.
2. Factors causing date-eU correlations
Our reanalysis consists of generating model-derived thermal histories for three
suites of zircon He dates from the central and southern Longmen Shan: 1) sample LME18 from Wang et al. (2012), 2) the Wenchuan transect from Godard et al. (2009), and 3) a
transect from the footwall of the Wenchuan-Maowen Fault (WMF) from Tian et al.
(2013) (fig. 1). All three of the suites show negative date-eU correlations (fig. 2). We also
note that each publication listed above has additional sets of zircon He dates, but, because
they lack date-eU correlations, they are not modeled. In order to better understand the
geologic importance of our HeFTy results, we first discuss why these correlations are
present in only certain samples.
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Suites of zircon He dates from Longmen Shan samples showing date-eU
correlations all contain numerous single grain or single aliquot dates (at least 12), and
they all possess a large spread in eU. For example, LME-18 (Wang et al., 2012) has 16
single grain dates with at least one order of magnitude difference in eU concentration
(280 to 3748 ppm). In contrast, LME-20 from the same study lacks a clear correlation,
probably because it contains only 5 single grain replicates and a total eU range of only 73
ppm (65 to 138 ppm). Individual grains in a zircon He date suite must also share a
common thermal history in order for date-eU correlations to be interpretable in a tT
context. Except in rare circumstances, this is certainly the case for zircons from the same
igneous hand sample, such as those from LME-18. This single sample is also emblematic
of the date-eU correlation for the entire Wang et al. (2012) dataset (fig. 2a inset), which
suggests that a suite of samples may share a thermal history similar enough that we can
consider eU to be a first-order influence on date dispersion. Although the zircons from
the other two datasets do not all come from the same hand samples (or represent single
grain analyses in the case of the Wenchuan transect), the presence of date-eU correlations
in these two transects suggests that they each share a common tT path and at least permits
us to test this hypothesis with the new zircon radiation damage and annealing model (or
ZRDAAM).
For samples that have a common thermal history and a large spread in eU, the
specific thermal history determines the form of the correlation on a date-eU plot. As
Guenthner et al. (2013) demonstrated, inverse date-eU correlations such as these are only
seen in samples that have spent appreciable periods of time at relatively low
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temperatures. Under these conditions, the zircon grains accumulate varying degrees of
radiation damage, in proportion to their eU concentration. Over time, the different
diffusion kinetics of each zircon yield a significant spread in dates, which is either
positively or negatively correlated with eU depending upon the total accumulated damage
in each grain. The spread in dates could result from a reheating episode, but slow cooling
and even sustained periods at low temperatures whereby the crystal becomes so damaged
that He diffuses at room temperatures, can lead to date-eU correlations. This requires that
annealing of radiation damage is slower than He diffusion that leads to the distinct
thermochronometric behavior in each grain. Guenthner et al. (2013) suggested that the
temperature range for radiation damage annealing corresponds roughly with the ZFT
partial annealing zone (PAZ). These authors used a fanning curvilinear fit to the ZFT
annealing data of Yamada et al. (2007), which, for an isothermal hold-time of 10 Ma,
gives a ZFT PAZ of 310 to 223 °C (mean length reduction ratio of .4 and .8,
respectively). Samples that have experienced temperatures greater than this just before
finally cooling to temperatures below the zircon He partial retention zone (PRZ) will not
display date-eU correlations . In the Longmen Shan, this type of thermal history may
explain the lack of date-eU correlations for zircons from the Xuelongbao transect
(Godard et al., 2009) and the WMF hanging wall (Tian et al., 2013), which otherwise
fulfill the basic requirements for showing a correlation (fig. 3). Given that both datasets
show reproducible dates of ~10 Ma with little or no significant date dispersion, it is likely
that these samples resided at temperatures well above the ZFT PAZ prior to rapid cooling
through the zircon He PRZ in the late Miocene. The relative flatness of these date-eU
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correlations requires rapid cooling, because slow cooling through the PRZ would allow
appreciable differences in damage and date to develop. The qualitative differences in
thermal histories between these two samples and those that have date-eU correlations
therefore reflects the differences in the timing and magnitude of burial and exhumation
between specific sites in the Longmen Shan. As we show below, the ZRDAAM setup and
results give us more quantitative constraints for the record of burial and exhumation at
each sample location.
3. Model inputs
The HeFTy thermal modeling software package (Ketcham, 2005) is our primary
tool for determining these quantitative constraints. This program incorporates the
damage-diffusivity relationship of Guenthner et al. (2013) and uses this relationship,
coupled with a damage annealing equation, to generate date-eU correlations from
modeled thermal histories. The results from the ZRDAAM can then be compared in
either a forward or inverse sense to real date-eU correlations. In this study, we focus on
the inverse aspects of ZRDAAM, which takes multiple single grain He dates and U and
Th concentrations as inputs and attempts to find (using a Monte Carlo approach) thermal
histories that match the data with either “acceptable” (.05 goodness-of-fit) or “good” (.5
goodness-of-fit) results (see Ketcham, 2005 for more details on these statistics). Inverse
modeling in HeFTy can be used in a variety of ways and we describe our approach in
greater detail below.
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HeFTy inverse modeling is best used as a tool to assess the validity of a given
thermal history hypothesis. That is, the user tests whether a prescribed set of tT
constraints is compatible with their data. The constraints are defined by a set of boxes in
tT space that each randomly generated path is forced to pass through. In this study, we
have constructed our constraint boxes to test several aspects of each sample’s thermal
history. Most relevant for recent debates about exhumation in the Longmen Shan, our
HeFTy constraints examine whether certain phases of rapid cooling in the Oligo-Miocene
are compatible with each sample’s date-eU correlation. More specifically, if the data can
be explained with a rapid cooling model, then we want to know when this cooling event
occurred, how much cooling took place, and what the maximum temperature was prior to
the event. Guenthner et al. (2013) demonstrated that date-eU correlations form not only
in response to a sample’s most recent cooling event, but are also shaped by earlier events
in that sample’s thermal history. In the Longmen Shan, the model of Guenthner et al.
(2013) can be used to test the maximum burial temperatures experienced by each sample
following initial cooling, as well as constrain the magnitude of exhumation events that
may have occurred before the Oligo-Miocene. As such, we also included constraint boxes
in our models that both encompass the entire history of each sample from formation to
the present and are consistent with the basic geology of the region.
For these boxes, we considered several key geologic observations. The first is the
crystallization age of the rocks, which provides a maximum allowable duration of
accumulation of both He and radiation damage. All three datasets were collected in
massifs that compose the basement terrane along the southwestern margin of the Yangtze
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block (Zhou et al., 2002). Both the Wenchuan transect and sample LME-18 come from
the Pengguan Massif (fig. 1). Yan et al. (2008) obtained a concordant weighted mean
zircon U-Pb date of 809±3 Ma for granites within the massif. Tian et al.’s (2013) WMF
hanging wall transect was collected in rocks of the Baoxing Massif (fig. 1), which has a
concordant weighted mean zircon U-Pb date of 797±9 Ma (Fu et al., 2012).
Sedimentary units and high-temperature thermochronometers provide constraints
on the early thermal history of the basement rocks. Although neither massif is currently
covered by any younger sediments, the oldest sedimentary units that crop out in the
region are latest Proterozoic to early Cambrian in age (Burchfiel et al., 1995) and it is
reasonable to assume that similar rocks once covered both basement blocks. Since the
earliest Paleozoic and well into the Mid-Triassic, the Longmen Shan region was buried
by an approximately 4-5 km thick sequence of Paleozoic marine, platformal units
(Burchfiel et al., 1995; Chen et al., 1995; Roger et al., 2004). During this orogenic event,
two different episodes of deformation occurred and we consider both in our model
thermal histories. Yan et al. (2011) used muscovite 40Ar/39Ar dates and fault relationships
in the central and northern Longmen Shan to bracket a period of thrust-related
deformation between 237 and 208 Ma, followed by a period of extension between 193
and 159 Ma. These 40Ar/39Ar dates are located in the Bikou terrane, ~150 km northeast of
the central Longmen Shan, while the fault relationships crop out west of the Pengguan
Massif in the hanging wall of the WMF. Although Yan et al. (2008) obtained a single
muscovite 40Ar/39Ar date in the Pengguan Massif of 160 Ma, this sample is in the
immediate footwall of the WMF and the amount of Late Triassic overthrusting and
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subsequent exhumation for most of the Pengguan Massif (or the Baoxing Massif) is
unknown. Evidence for overlying Cretaceous and Paleogene rocks deposited after the
Triassic-Jurassic orogenic event is sparse, but isopachs from the western-most Sichuan
Basin suggest that some deposition may have continued in this region until at least the
Paleogene (Richardson et al., 2008). High-temperature thermochronometers from
Jurassic granites to the west of the massifs, emplaced into the deeper sections of the
Songpan-Ganze basin and currently at the surface, display temperatures greater than 200
°C as late as 78 Ma, and possibly as late as 50 Ma (Roger et al., 2004). This also suggests
that the region remained buried until at least the early Cenozoic.
We use these geologic observations to construct five tT constraint boxes for each
inverse model. The first box spans a temperature range of 600 to 300 °C and 800 to 750
Ma and represents the initial formation of each basement massif. The lower temperature
bound on this box is arbitrary but exists to induce zircon formation at temperatures above
the ZFT PAZ (~310 °C). The second box spans a temperature range of 80 to 20 °C and
750 to 550 Ma and represents the cooling to low temperatures of the massifs, as
suggested by regional deposition of Neoproterozoic to Cambrian sedimentary rocks.
Boxes three and four capture reheating and cooling episodes associated with the
Mesozoic Longmen Shan orogenic event. Thrusting between 237 and 208 Ma likely
resulted in burial of the massifs, while the extension between 193 and 159 Ma may have
led to exhumation. As such, we test the amount of burial by placing box three at 240 to
200 Ma and a fourth box at 200 to 160 Ma to test the amount of exhumation. Although
we expect significant heating and cooling to have occurred during this time, the exact
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amounts are relatively unimportant for constraining the later Oligo-Miocene exhumation
events, which are the main focus of this study. As such, we allow for a wide range of
temperatures to be tested in boxes three and four, with the stipulation that box four sits at
lower temperatures in order to induce HeFTy to cool each sample. We place a fifth box in
the Cenozoic to represent the final episode of reheating (or burial) for each sample. Our
tT choice for this box was in part constrained by the regional geology and the abundance
of Oligo-Miocene dates in each dataset, but this final box is also needed to force HeFTy
to reheat a given sample and test the hypothesis that the Longmen Shan was rapidly
cooled (by exhumation) sometime in the mid Cenozoic. This box spans 50 myr along the
time axis (from 50 to 0 Ma) with a temperature span of 80 °C (from 160 to 240 °C). We
admit that this size is somewhat arbitrary, but after iteratively testing a number of
options, we found that our Cenozoic box needed to be relatively confined to test the rapid
cooling hypothesis, but not too narrow to prevent HeFTy from locating good and
acceptable fits.
We note that the results from these models are non-unique solutions, and we
acknowledge that other tT constraint boxes could possibly explain the data. However,
these may not be plausible as several tT aspects of our models are likely inescapable. As
previously mentioned, date-eU correlations are only present in samples that have spent
appreciable amounts of time at relatively low temperatures (less than the PAZ of ZFTs).
More specifically, negative correlations that begin at relatively low eU concentrations
(like the correlations observed in our modeled samples—see the next section) require
zircons that have old U-Pb dates and little annealed damage. These conditions allow
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zircons to obtain substantial amounts of damage at low eU concentrations. Intuitively
then, the mere existence of negative date-eU correlations in the modeled samples
suggests that these zircons have spent prolonged periods of time (likely the entire
Phanerozoic) at temperatures below ~223 °C.
A final set of inputs includes the grain-specific information for individual zircons
in a given sample (i.e. measured He date, grain size, and eU concentration). Because of
the large number of individual He dates in each sample, some averaging of multiple
single grain inputs was required. This is partly a practical concern for inverse modeling
as the current version of HeFTy cannot run inverse models with greater than 7 individual
grains for a given thermal history. More importantly, some of the date irreproducibility in
each sample exceeds what would be predicted by grain size or radiation damage effects
alone. Heterogeneous intragranular distribution of U and Th is a likely cause of this
scatter. Without knowledge of each zircon’s intragranular U and Th zonation, date
inaccuracies up to ~35% could result from incorrect alpha ejection correction (Farley et
al., 1996; Hourigan et al., 2005). Larger degrees of dispersion are also possible due to the
effects of zoned radiation damage, which results in zoned diffusion domains (Guenthner
et al., 2013). For our modeled samples, some of the second order scatter along the
dominant date-eU trend is probably caused by zonation, but we lack the observations to
properly deal with this issue. We therefore adopt an approach for our various grainspecific inputs similar to the one used in modeling date-eU correlations in apatite (i.e.
Ault et al., 2009; Flowers and Kelley, 2011). This involves dividing the single grain
replicates into different bins based on eU concentrations. All of the zircons in each
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sample were divided into as many as five groups (depending on the full span of eU): 1)
grains less than 500 ppm eU, 2) grains with 500 to 1000 ppm eU, 3) grains with 1000 to
2000 ppm eU, 4) grains with 2000 to 3000 ppm eU, and 5) grains with greater than 3000
ppm eU. The HeFTy input for one of these groups consists of the mean date with the
standard deviation as the error, the mean grain size, and the mean eU concentration from
all of the grains in the group. This approach is not as ideal as considering each single
grain replicate as an independent thermochronometer. We note, however, that this
averaging does not exclude any data, and extracts more information from a given sample
than using a single mean date from every grain in the sample as the sole HeFTy input.
4. Model results
The zircon He dates for each sample or group of samples are plotted against eU in
figure 2. Results from our binning and averaging are shown as yellow circles in this
figure and served as the HeFTy inputs.
The date-eU trend for LME-18 is continuously negative with dates decreasing
from ~80 Ma to ~30 Ma between eU concentrations of ~280 ppm to ~1000 ppm. Dates
then remain relatively flat, decreasing slightly to ~22 Ma at almost 4000 ppm eU (fig.
2a). A similar, steeply negative then relatively flat trend is seen in the complete zircon He
dataset from Wang et al. (2012) with an oldest date of ~138 Ma at the lowest eU
concentration of 56 ppm (fig. 2a, inset).
The Wenchuan transect’s date-eU trend is also continuously negative, decreasing
from ~25 Ma at an eU of 174 ppm to ~9 Ma at an eU of 2352 ppm (fig. 2b). Interestingly,
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the grain with the highest eU concentration (2903 ppm) has an older date (~15 Ma)
compared to the next highest eU grain (2352 ppm). These highest eU grains are younger
than the grains with similar eU concentrations from sample LME-18 (dates of ~22 Ma).
Finally, the date-eU correlation for the WMF footwall sample is also continuously
negative, although the trend is less apparent at low eU concentrations (fig. 2c). Dates
decrease from ~20 Ma at the lowest amount of eU (78 ppm) to ~8 Ma at the highest
amount of eU (1274 ppm). Zircons from this sample have a narrower range of eU
compared to the other samples, with a majority of the grains possessing less than 500
ppm eU and no grain possessing an eU higher than 1274 ppm. Again, the highest eU
grains are younger than grains with similar eU concentrations from sample LME-18, but
are approximately the same as those from the Wenchuan transect.
The ZRDAAM results for all three datasets are also shown in figure 2. The
middle panels in figure 2 show envelopes for the good (dark grey) and acceptable (light
grey) tT paths that result from the various constraint boxes described above. In the panels
on the right, we show the same envelopes for paths that have passed through all of the
constraint boxes, but include only the portion of the model output from 250 Ma to the
present. We also include the best fit tT path in the middle panels and plot the resulting
date-eU correlation from these best fit paths in the panels on the left side. These model
generated date-eU correlations are projected beyond the model inputs (yellow points) to
lower and higher eU amounts, but we note that the inverse models were unconstrained
beyond these points. For all three samples, HeFTy finds good and acceptable tT paths that
155
are consistent with the geologic observations discussed above and the date-eU
correlations plotted on the left hand side of the figure.
4.1 LME-18
For each sample, the good and acceptable model results constrain: 1) the
maximum temperatures achieved in the Triassic-Jurassic orogenic event, 2) the maximum
temperatures achieved during the Cenozoic, 3) the timing for initiation of the Cenozoic
rapid cooling event, and 4) the duration of this rapid cooling event. An intuitive way to
think of good versus acceptable tT paths is that good paths are supported by the data,
while acceptable paths are simply not ruled out by the data. Assuming that the true tT
path for each sample lies somewhere within our constraint boxes, the good paths are
statistically the most likely tT paths for a given sample. If we focus on the good path
envelopes, then the LME-18 data best supports a Jurassic maximum reheating
temperature of 225 °C , a Cenozoic maximum reheating temperature of 185 °C, and a
rapid cooling event that began at 35 Ma and lasted until 20 Ma (see dashed horizontal and
vertical lines in fig. 2a). We can also estimate the amount of cooling during this event,
which is between ~140 and 120 °C. The maximum temperatures modeled for LME-18
during both the Late Triassic-Jurassic and Cenozoic are the lowest amongst the various
datasets (plots on right side of figure B2). The oldest dates at low eU prevent HeFTy
from finding good or acceptable paths and these dates therefore act as relatively tight
constraints on LME-18’s tT path. If the maximum temperatures were higher, then these
older dates would be reset closer to the age of rapid cooling, ~35-20 Ma. We also note
that the path envelopes for this sample are much narrower than the other modeled
156
datasets, despite the fact that the same constraint boxes are used in all of the models. The
greater spread in LME-18 data points, both in terms of eU and date, reduces the range or
degree of variability for good or acceptable tT paths that fit the data.
4.2 Wenchuan
The Wenchuan transect yielded good tT path envelopes for a Late TriassicJurassic maximum reheating temperature of 270 °C, a Cenozoic maximum reheating
temperature of 230 °C, and a Cenozoic rapid cooling event that began at 15 Ma (see
dashed horizontal and vertical lines in fig. 2b). The amount of cooling during the
Cenozoic event is ~210 °C. Because the maximum reheating temperatures for both the
Jurassic and Cenozoic are close to the bounds of our constraint boxes, we performed
additional model tests using a Triassic-Jurassic box (240-200 Ma) placed at temperatures
between 280 and 300 °C and a Cenozoic box (50-0 Ma) placed at 260 to 280 °C.
Acceptable paths were found at these higher temperatures, but the model did not generate
any good paths. The higher model reheating temperatures for the Wenchuan transect
relative to LME-18 result from the younger dates at low eU (the oldest date is ~30 Ma),
which lead to a flatter date-eU correlation. In other words, the samples in this transect
were heated to significantly higher temperatures and were more strongly reset for the
zircon He system than LME-18.
4.3 WMF footwall
The WMF footwall samples gave good path envelopes for a Late Triassic-Jurassic
maximum reheating temperature of 255 °C, a Cenozoic maximum reheating temperature
of 230 °C, and a Cenozoic rapid cooling event that began at 10 Ma. The amount of
157
cooling during the Cenozoic was ~210 °C. As with the Wenchuan transect, these
maximum reheating temperatures for the WMF footwall samples are close to the bounds
of our constraint boxes. We therefore ran additional models with a Triassic-Jurassic box
(240-200 Ma) placed at temperatures between 280 and 300 °C and a Cenozoic box (50-0
Ma) placed at 260 to 280 °C. Acceptable paths were found at these higher temperatures,
but the model did not generate any good paths. Like the Wenchuan transect, the high
model reheating temperatures for the WMF footwall samples are required by the
relatively young dates at low eU. The modeled date-eU correlation is interesting as it
shows a positive date-eU correlation at eU concentrations of less than 200 ppm, which
maybe expected in zircons with low amounts of damage. This positive date-eU
correlation captures some aspects of the real dataset, especially the observed young date
(~15 Ma) at relatively low eU (~100 ppm). However, the model date-eU trend does not
capture the old dates (~30 Ma) that are also at low eU (~100 ppm).
4.4 Summary
All of our models retrodict similar Phanerozoic thermal histories: reheating until
the Triassic, followed by cooling in the Late Triassic-Jurassic, subsequent reheating until
the Cenozoic, and final rapid cooling in the mid to late Cenozoic. For the Late TriassicJurassic event, similar model results are in part a consequence of using the same
constraint box design in all three simulations. But for the Cenozoic cooling event, our
design allowed HeFTy to model the cooling as either rapid or slow and all of the results
showed relatively rapid cooling (cooling occurred within a 15 to 10 my time span). This
style of cooling is therefore an important feature of each dataset’s thermal history and is
158
reflected in the date-eU correlations for each dataset. A common feature in all three
correlations is a pediment (analogous to a plateau) of relatively invariant He dates at high
eU concentrations. As discussed in a previous section, a flat date-eU correlation suggests
an episode of rapid cooling through or out of the PRZ at that time.
Each model has key differences as well. Our results suggest that the LME-18
zircons were reheated the least during both the Late Triassic-Jurassic (225 °C) and
Cenozoic (185 °C), began cooling the earliest (35 Ma), and cooled by the least amount
(~140 to 120 °C). The Wenchuan transect zircons, on the other hand, experienced the
highest reheating temperatures (270 °C in the Late Triassic-Jurassic, 230 °C in the
Cenozoic), and an intermediate timing for the Cenozoic cooling event (15 Ma), during
which they cooled by ~210 °C). The WMF footwall zircons show intermediate reheating
temperatures (255 °C in the Late Triassic-Jurassic, 230 °C in the Cenozoic) and a
Cenozoic cooling episode that started at roughly the same time as the one seen in the
Wenchuan transect samples (~15 Ma), although perhaps at a slightly later date (~10 Ma).
5. Discussion
5.1 Burial history and structural significance of date-eU correlations
Our models suggest that samples or groups of samples with negative date-eU
correlations have spent almost the entire Phanerozoic at temperatures less than ~223 °C.
Even with Triassic-Jurassic overthrusting associated with the Mesozoic Longmen Shan
orogenic event, from the Neoproterozoic to the Oligo-Miocene, the ZRDAAM results
show that each zircon He dataset supports relatively low amounts of reheating (middle
159
panels of figure 2). In general, the pre-Late Triassic reheating is consistent with limited
Neoproterozoic and Paleozoic deposits (~4-5 km) (Jia et al., 2006), and the model results
from each specific location are consistent with this sedimentary thickness pattern. LME18, the sample closest to the modern Sichuan basin (i.e. within ~5 km of the YBF, fig. 1),
only shows good ZRDAAM tT paths for maximum burial temperatures between 180 and
160 °C, while the Wenchuan and WMF footwall transects further towards the hinterland
show maximum temperatures between 210 to 180 °C and 240 to 200 °C respectively.
The WMF hanging wall and Xuelongbao samples are further still from the Sichuan
Basin-Longmen Shan margin (fig. 1) and show no date-eU correlation (fig. 2a). This
suggests that both datasets experienced higher temperatures than locations closer to the
modern basin and were likely buried to greater depths. In addition, both of these datasets
are in the hanging wall of the WMF, which has been interpreted as a late Miocene thrust
fault (Tian et al., 2013). The absence of date-eU correlations in these samples supports a
greater maximum burial depth than the WMF footwall and Wenchuan transects, and is
consistent with the WMF hanging wall coming from a greater structural depth than the
footwall.
5.2 Cenozoic exhumation history from date-eU correlations
The ZRDAAM results also give us the timing and spatial distribution of
exhumation following the maximum burial of each sample. Two distinct episodes of
exhumation for the central and southern Longmen Shan are seen in the good tT paths
from our models: 1) an event at the range front captured by LME-18 that began at 35 Ma
and lasted until 20 Ma, and 2) an event in the hinterland of the range captured by the
160
WMF footwall and Wenchuan transects that began most likely between 15 and 10 Ma.
This latter event is also consistent with the young (all <13.7 Ma) dates from the WMF
hanging wall and Xuelongbao transects. Both events are consistent with the original
findings of the previous authors (i.e. Godard et al., 2009; Wang et al., 2012; Tian et al.,
2013), but ZRDAAM allows us to reconcile the differences among these results as well
as those in Kirby et al. (2002) and to be more specific about the spatial distribution of
exhumation events within the orogen.
The following discussion focuses on why each exhumation event is expressed
only in certain locations. We first offer several possible explanations for the absence of
the 35 Ma event in the WMF footwall and Wenchuan transects. In one scenario, we
propose that regional rock uplift occurred in the hanging wall of the YBF at 35 Ma, but
erosion (and therefore exhumation) was concentrated only at the front of the Longmen
Shan, near LME-18 (fig. 4). Samples further away from the YBF (e.g. the Wenchuan and
Xuelongbao samples) could have been uplifted as well, but because erosion was minimal
at these locations, their movement relative to the Earth’s surface (and the PRZ) was also
minimal. Alternatively, exhumation could have been orogen-wide but only expressed in
the zircon He dates of LME-18. In this scenario, prior to 35 Ma, the Wenchuan and WMF
footwall transects were at greater depths than the Wang et al. (2012) dataset. Following
the pulse of exhumation at 35 Ma, only samples in the Wang et al. (2012) transect, such
as LME-18, were exhumed above the PRZ; all other samples were exhumed as well but
remained either below or within the PRZ. Because these other samples remained at
relatively high temperatures, their dates do not record the 35 Ma episode of exhumation
161
and ZRDAAM’s ability to constrain such an event from these data is limited. Regardless
of whether or not exhumation at 35 Ma was orogen-wide, this event is at least clearly
captured by LME-18 and could be consistent with a central Tibetan plateau that was high
(4.5-5 km) by at least 26 Ma (DeCelles et al., 2007) and growing eastward as early as 45
Ma (Rohrmann et al., 2012). More work is required to describe the along-strike extent of
the 35 Ma event in the Longmen Shan though, as the ZRDAAM results from both the
WMF footwall and Wenchuan transects are inconclusive on this matter.
We can more definitively state that the later exhumation event at 15 Ma was
mainly concentrated in the range interior. Our model results show that sample LME-18
had to cool to a low temperature (~50 °C) by ~20 Ma, and the model does not allow for
much cooling (or exhumation) after that (approximately 30 °C from 20 to 0 Ma). We note
that this temperature constraint is relatively low, which suggests that the highest eU
grains (those with ~20 Ma dates) are heavily damaged and possess low closure
temperatures. Amounts of post-15 Ma cooling similar to what we observe for the WMF
footwall and Wenchuan transects (~180 °C) were unlikely for LME-18. As such, we
argue that a major shift in exhumation from the frontal YBF (near LME-18) to the
interior occurred between 20 and 15 Ma. The cause of this shift though is different
depending on sample location. For samples in the hanging wall of the WMF (Xuelongbao
and WMF hanging wall transects), out-of-sequence thrusting along the WMF since ~15
Ma may have caused increased relief across the fault that in turn resulted in an increase in
erosion (fig. 4). Evidence for greater recent activity along the WMF compared to the
YBF comes from a higher rate of recurrence intervals for recent earthquakes (Liu-Zeng et
162
al., 2009). Also, Miocene exhumation rates for the central Longmen Shan are highest in
the immediate hanging wall of the WMF, with a large disparity in rates across the fault
(low in the footwall) (Tian et al. 2013). Although out-of-sequence thrusting along the
WMF may explain the mid to late Miocene dates from the Xuelongbao and WMF
hanging wall transects, the WMF footwall and Wenchuan transects both sit in the
footwall of this fault and would likely have seen little increase in exhumation resulting
from differential uplift.
Increased erosion along river valleys in the Longmen Shan hinterland is perhaps a
better explanation for the 15 Ma exhumation of the Wenchuan and WMF footwall
transects. Several thermochronologic studies have documented a regional exhumation
event in eastern Tibet, predominantly expressed as increased incision into a relict
landscape along major river valleys, at either 15 to 10 Ma (Xu and Kamp, 2000; Clark et
al., 2005b; Wilson and Fowler, 2011; Duvall et al., 2012), or possibly as late as 5 Ma
(Kirby et al., 2002). Placing our model results in this context, initial uplift of the plateau
margin—possibly at 35 Ma as suggested by LME-18—led to river drainage
reorganization (Clark et al., 2004) and subsequent knickpoint migration (Richardson et
al., 2008). By 15 Ma, rivers penetrated into the orogen’s interior, exhuming the WMF
footwall transect (fig. 4). Modern denudation rates calculated from river sediment load
data are consistent with focused erosion along interior river valleys (Liu-Zeng et al.,
2011). Although the entire region between the YBF and WMF has higher denudation
rates relative to the plateau or Sichuan Basin, the highest rates are observed along the
trunk stream of the Min River, which follows the trace of the WMF (fig. 1).
163
6. Conclusions
The timing of major exhumation events in the Longmen Shan has broad
implications for the uplift history of the Tibetan Plateau. Despite the promise of zircon
He thermochronometry for constraining these events, He dates are irreproducible and
correlated with eU in some samples and groups of samples from different locations give
seemingly contradictory results. This has lead to ambiguous conclusions about the
Cenozoic exhumation history of the range. Using a new He diffusivity model that
accounts for the effect of radiation damage on He diffusion in zircon, we can both explain
the main cause of the date irreproducibility and model thermal histories from a sample’s
date-eU correlation. These histories are site-specific and contain information not only
about recent cooling events, but also aspects of the sample’s tT path since formation,
including the amount of Phanerozoic reheating. Our combined ZRDAAM results allow
us to place each dataset into a coherent exhumation history for the Longmen Shan and
constrain the timing and amount of Cenozoic exhumation at each location.
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171
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and symbols for previously published zircon He results, basement massifs, and major
faults (WMF = Wenchuan-Maowen Fault, YBF = Yingxiu-Beichuan Fault). The legend
divides those datasets whose model results are shown in figure 2, and datasets that were
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the Longmen Shan with respect to the greater Tibetan Plateau region.
172
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Figure B2: ZRDAAM results for the (A) LME-18 (inset is the entire Wang et al., 2012
dataset), (B) Wenchuan transect, and (C) WMF footwall datasets. Each sub-figure
contains three panels. The panel on the left shows individual aliquot (single grain for
LME-18 and WMF footwall, multiple grain for Wenchuan transect) zircon He dates
plotted against eU in the blue diamonds, and ZRDAAM input dates (see text for details)
in the yellow circles. The middle panel shows HeFTy constraint boxes and the ZRDAAM
result for the entire modeled thermal history with the envelope of good paths (in dark
grey) and acceptable paths (in light grey). Solid black line shows the best fit result. The
date-eU correlation predicted by this best fit path is plotted as a black curve in the left
panel. The right side panel shows HeFTy constraint boxes and envelopes resulting from
the same output shown in the middle panels, but from only 250 to 0 Ma and 0 to 300 °C.
The horizontal dashed lines in each panel highlight the maximum reheating temperatures
in the Triassic-Jurassic and Cenozoic (good path envelopes only), while the vertical
173
dashed lines highlight the timing (and duration in the case of LME-18) of the Cenozoic
rapid cooling event.
174
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Figure B3: Date-eU plots for the (A) Xuelongbao and (B) WMF hanging wall datasets.
Both plots show very little or no significant date dispersion and no trends between date
and eU.
175
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Figure B4: Temporal and spatial evolution of exhumation in the central Longmen Shan
shown schematically at (A) 35-20 Ma, and (B) 15-0 Ma. Solid black curves represent the
surface topography and symbols for data points are the same as shown in figure B1 (star
= LME-18, triangle = Wenchuan transect, square = Xuelongbao transect). Dashed subvertical line in (A) represents the Wenchuan-Maowen Fault (not yet active). Light grey
area in (A) represents material that is eroded away in (B).
176
APPENDIX C: SEVIER-BELT EXHUMATION IN CENTRAL UTAH
CONSTRAINED FROM COMPLEX ZIRCON (U-Th)/He DATASETS: RADIATION
DAMAGE AND He INHERITANCE EFFECTS ON PARTIALLY RESET DETRITAL
ZIRCONS
To be submitted to the professional journal: Geologic Society of America Bulletin
177
SEVIER-BELT EXHUMATION IN CENTRAL UTAH CONSTRAINED FROM
COMPLEX ZIRCON (U-Th)/He DATASETS: RADIATION DAMAGE AND He
INHERITANCE EFFECTS ON PARTIALLY RESET DETRITAL ZIRCONS
William R. Guenthner, Peter W. Reiners, Peter G. DeCelles, and Jerome Kendall
Abstract
Thermochronologic dates of detrital grains that have been partially reset after deposition
are difficult to interpret because of the potential variability of inherited pre-depositional
dates and kinetic behaviors of grains from diverse source terrains. In this study we
present several examples of complex detrital zircon (U-Th)/He date distributions from
sedimentary rocks that have been heated to temperatures near the zircon He partial
retention zone, leading to several types of date-eU correlations caused by relationships
between pre-depositional inherited age, radiation damage, and He diffusion kinetics.
These examples are from samples collected along three sub-vertical transects in mountain
ranges in central Utah: the Stansbury Mountains, Oquirrh Mountains, and the Wasatch
range near Provo, UT. Each range lies in the hanging wall of one of three major thrust
sheets that compose part of the Charleston-Nebo Salient, a segment of the Cretaceous
Sevier fold-and-thrust belt. Zircons from two of these transects (the Stansbury and
Oquirrh Mountains) show large date variation that can be at least partially understood
with a radiation damage-based model for He diffusion in zircon. We combine the output
from this model with a new approach for understanding partially reset datasets that relies
upon the concept of an “inheritance envelope.” For the Stansbury transect, this approach
yields inconclusive results; some aspects of the model generated inheritance envelopes
that match the real dataset, while others do not. But time-temperature (tT) constraints
178
from inheritance envelopes in the Oquirrh Mountains transect suggest a pulse of
exhumation beginning at either 110 or 100 Ma. The final transect from the Wasatch
Range is relatively simple and does not require an inheritance-based interpretation. Here
we document a pulse of exhumation at 100 Ma. Despite their complexity, we are
motivated to interpret the tT histories for these non-ideal datasets as they represent some
of the only in situ constraints on the timing of Cretaceous exhumation in the US
Cordillera. In the case of the Oquirrh and Wasatch Range datasets, these direct
measurements of thrust sheet tT histories offer some insight into the evolution of the
Sevier fold-and-thrust belt of central Utah.
1. Introduction
The (U-Th)/He system in zircon (zircon He dating) is widely used as a
thermochronometer and provenance tool, but zircon He dates from some samples often
show larger dispersion than expected from analytical precision and a single set of kinetic
parameters for He diffusion. In principle this dispersion could have several origins,
including effects arising from implantation (Spiegel et al., 2009; Gautheron et al., 2012;
Murray et al., in prep), anisotropic diffusion (Farley, 2007; Reich et al., 2007; Cherniak et
al., 2009; Saadoune et al., 2009), compositional influences on He diffusion, and
crystallographic defects. But one of the most important known influences on He
diffusivity in zircon is radiation damage. The effects of high radiation doses on He
diffusion in zircon have been recognized for more than half a century (e.g. Hurley, 1952;
Holland, 1954; Nasdala et al., 2004), but only recently have these effects been
179
quantitatively integrated with He diffusion models, and only recently has the effect of
damage at low dosages been recognized. Guenthner et al. (2013) showed that radiation
damage in zircon affects diffusivity in two distinct ways at opposite ends of the dose
spectrum. Depending on a sample's specific thermal history, these effects may produce
either positive or negative correlations (or both) between date and effective uranium
(eU), a proxy for relative radiation dose among grains from the same sample, which is
scaled for the relative alpha production rate in each zircon (eU = U + .235 × Th). These
authors constructed a zircon radiation damage and annealing model (ZRDAAM) that
parameterizes the relationship between damage and diffusivity and uses date-eU
correlations to constrain time-temperature (tT) paths. Instead of discarding dates from
grains with extreme eU concentrations or averaging dispersed dates into a single mean
date, ZRDAAM provides a possibility to describe the full range of single-grain dates
from individual rock samples through modeling of radiation damage effects on He
diffusivity as a function of potential tT paths. For sample thermal histories in which all of
the individual zircons have experienced the same tT path since their formation (i.e.,
igneous hand samples), ZRDAAM predicts eU-dependent He dates, through both forward
or inverse modeling, that are relatively straight-forward to interpret in the context of the
sample’s burial and exhumation history (e.g. appendix B of this dissertation).
Partially reset zircons from detrital hand samples, however, represent a more
difficult challenge for interpreting model results. In these samples, zircons share a
common post-depositional thermal history, but because each of these grains may be only
partially reset, their individual pre-depositional formation age and thermal histories will
180
also influence where they plot in date-eU space. Prior to deposition, each zircon will
possess its own unique amount of inherited radiation damage and He concentration and
therefore date (i.e. non-zero He dates at the time of deposition). Aside from maximum
limits deduced from U/Pb date and eU concentration, we cannot discern these a priori.
As a consequence, zircon He dates from these samples do not fall along a single date-eU
curve and instead plot within a region of date-eU space that we refer to as an “inheritance
envelope” (fig. 1).
An example of this inheritance envelope is shown in scenario 1 of figure 1. At the
lowest and highest amounts of eU, a zero-inheritance date-eU curve forms the lower and
upper bound of the envelope, respectively. This curve reflects either full resetting of
zircons in the detrital sample or near zero U/Pb dates at the time of deposition. This curve
acts as both an upper and lower bound due to the nature of the damage-diffusivity
relationship. Specifically, as damage accumulates in a newly formed crystal (as a
function of time and eU concentration), diffusivity initially decreases at relatively low
damage amounts, then increases once again at high damage (Guenthner et al., 2013). At
high eU, a zircon with any inherited, pre-depositional damage will have a high
diffusivity, and a younger date than the corresponding zero-inheritance zircon.
Conversely, at low damage, a zircon with inheritance will have more damage but low
diffusivity (because the switch-over from decreasing to increasing diffusivity has not yet
occurred) and an older date than the corresponding zero-inheritance zircon. In addition,
the lower diffusivities in these inheritance zircons allow them to retain more of their
inherited He. Examples of this behavior come from maximum inheritance date-eU
181
curves, which lie above or below the zero-inheritance curve, depending on eU
concentration. Each of these curves represents the date-eU trend for a group of zircons
with the same U/Pb dates and no He diffusion or annealing of damage following
formation but prior to deposition (i.e. pre-depositional residence at surficial temperatures
since formation). The zircons are then deposited in a sedimentary basin and have the
same post-depositional history as the zero-inheritance curve. In our scenario 1 example,
we imagine that the oldest U/Pb and predepositional He dates were 2500 Ma, and this
2500 Ma maximum inheritance curve therefore defines part of the lower bound of the
inheritance envelope from ~200 ppm to 5000 ppm eU. We can couple the 2500 Ma curve
with the maximum inheritance curves from a series of intermediate U/Pb dates (800,
1100, 1400, and 1700 Ma), and draw in a dashed line that defines the upper bound of the
inheritance envelope. Realistically, we do not expect many zircons to possess a tT history
characterized by residence at surface temperatures for a duration equal to the difference
between their formation age (U/Pb date) and depositional age, and this is probably
increasingly rare for grains with larger formation and depositional age differences. But
given a range of U/Pb dates, zircon He dates from a partially reset detrital sample should
fall between the various bounds created by the zero-inheritance and maximum
inheritance curves.
As figure 1 suggests, we can compare date-eU variations in real suites of zircon
grains to these inheritance envelopes to test the viability of various post-depositional
thermal histories. If the inheritance envelope generated by a specific tT path and a
reasonable range of possible pre-depositional inheritance ages encompasses the full range
182
of a sample’s date variability, then this path is a plausible solution for the sample’s
thermal history. For example, assuming a maximum pre-depositional He date of 2.5 Ga,
the relatively low maximum reheating temperature (160 °C) of scenario 1 in figure 1
results in a broad inheritance envelope ranging from 0 to ~1750 Ma, whereas the only
slightly higher maximum temperature (180 °C) in scenario 2 results in a much narrower
envelope that ranges from 0 to ~600 Ma. A date that plots within the broad envelope
resulting from scenario 1 would support this post-depositional history, but not the tT path
in scenario 2. To illustrate this, we include in all of the scenarios a zircon He date of 750
Ma with an eU concentration of 190 ppm (red circles). This date only plots within the
envelope created by scenario 1’s tT path. Conversely, a zircon He date of 250 Ma at the
same eU concentration (yellow circle) falls outside the inheritance envelope of scenario
1, but does plot within scenario 2’s envelope. In scenario 3, this date plots on the
envelope and in scenario 4 it falls just above the envelope. We note that this approach is
similar to one used by Reiners et al. (2005), but is more sophisticated due to our new
understanding of how radiation damage affects He diffusion in zircon.
To demonstrate ZRDAAM’s utility for interpreting real zircons with varying
levels of He and damage inheritance, we present zircon He dates and ZRDAAM results
from the Sevier fold-and-thrust belt in central Utah. Our study area is the CharlestonNebo Salient (CNS, fig. 2), a region with a long history of exploration (e.g. Gilbert,
1890) and a well-understood basic geology—sedimentary unit thicknesses, relative ages
of structures, tectonic setting—that provides independent constraints on the likely
thermal histories experienced by our samples. In comparison, relatively little is known
183
about the timing of exhumation along particular thrust sheets within the CNS, especially
those west of the Wasatch hinge line (fig. 2). Such timing constraints are of particular
interest as this area is the focus of several long-standing debates about relationships
between exhumation in the CNS and the deposition of foreland basin units that are now
exposed in the eastward adjacent Book Cliffs during the Cretaceous. Topics of discussion
include the influence of thrust belt evolution on foreland basin architecture (DeCelles et
al., 1995; Yoshida et al., 1996; Houston et al., 2000; Miall and Arush, 2001; Currie,
2002), the relationship between thrust sheets and sedimentation (Heller et al., 1988;
Mitra, 1997; Willis, 2000; Horton et al., 2004; Adams and Bhattachayra, 2005), and how
these systems might in turn be affected by far-field changes in the magmatic arc
(DeCelles et al., 2009). The validity of different hypotheses for each of these topics rests
in part on having a solid timing framework for thrust activity.
Low-temperature thermochronology could constrain the timing of Cretaceous
exhumation in individual thrust sheets and, by inference, the timing of thrust activity. But
to our knowledge, no published thermochronologic datasets document in situ Sevier beltrelated exhumation in the CNS, and those thermochronology studies that have focused on
the greater Basin and Range province in Utah used apatite (U-Th)/He and fission track
(AFT) dates to document Miocene exhumation related mainly to Basin and Range normal
faulting (e.g. Stockli et al., 2001; Armstrong et al., 2003). Evidence for cooling due to
Cretaceous exhumation, possibly related to Sevier belt thrusting, is often not preserved in
the apatite He and AFT systems, most likely because Cretaceous exhumation involved
cooling through temperatures greater than either system’s partial retention or annealing
184
zones. Hence, our study relies upon the zircon He system to examine Sevier-related
exhumation and our results from three different thrust sheets in the CNS represent the
first in situ attempt at discerning the timing framework for Cretaceous thrust activity.
The variation in zircon He dates we present is complex, with significant date-eU
variability, so we discuss in detail the potential causes of this variation. To facilitate this,
we eschew an averaging approach and instead present all of the dates in a given sample
or transect, with the objective of understanding the range of dates in a ZRDAAM context.
This allows us to better assess the importance of factors that may influence date
dispersion. Thermal history modeling with ZRDAAM plays an important role in this
discussion; however, we also consider how grain size, He inheritance, and radiation
damage combine to influence a given He date. Taken together, these three factors explain
most of the date irreproducibility in each dataset, and can be used to constrain tT histories
and therefore the timing and rates of burial and exhumation that affected these thrust
sheets.
2. Geologic Setting
The CNS, referred to as the Provo Salient by some authors (e.g., Paulsen and
Marshak, 1998), is a classic thrust belt salient centered on Provo, UT in the central Utah
portion of the Sevier fold-and-thrust belt. Its northern and southern edges are defined by
the Charleston tranverse zone and Leamington zone respectively (Paulsen and Marshak,
1998; Kwon and Mitra, 2006). Tooker (1983) provided the first regional characterization
of the major contractional features of the CNS, which was subsequently modified by
185
Mitra (1997), Mukul and Mitra (1998), and DeCelles (2004). For the purposes of this
paper, we consider the CNS to comprise the following thrust faults (from west to east):
the Sheeprock, Tintic Valley, Stockton, Midas, and Charleston-Nebo thrusts (fig. 2). As
modified by Basin and Range normal faults, each of these thrusts carries a different
mountain range in its hanging wall, and we have focused our sampling efforts on the
Stansbury Mountains (Tintic Valley hanging wall), the Oquirrh Mountains (Midas
hanging wall), and the Mount Timpanogos area in the northern Wasatch Range
(Charleston-Nebo hanging wall). We also define the ranges and structures to the west of
the Wasatch Normal Fault (WNF) as being in the hinterland of the CNS, whereas features
to the east of the WNF compose the frontal part of the salient.
Constenius et al. (2003) documented in detail the structural style and history for
this frontal part of the CNS using erosional truncations and growth strata. These authors
described the most frontal portion of a large antiformal duplex called the Santaquin
Culmination centered above Thistle, UT. The culmination grew in two main phases, with
initial imbrication of the Nebo thrust from ~100-80 Ma, and internal duplexing from 8040 Ma. In subsequent sections, we use this relatively well constrained history to help
guide our tT modeling. Although the kinematic timing and thrust geometry for this frontal
portion is well understood, direct or in situ constraints on the exhumation history of
Sevier thrust sheets for the CNS hinterland (i.e. the Midas and Tintic Valley thrust sheets)
are non-existent. Inferences on the spatial-temporal pattern of thrust activity in the
hinterland come predominantly from provenance data in coarse-grained clastic sediments
east of the WNF (Mitra, 1997; Horton et al., 2004). This further underscores the geologic
186
value of our zircon He datasets, despite their inherent complexities. Other lowtemperature thermochronologic options (i.e. apatite He or AFT) are limited in the CNS
by poor apatite yields from the various sedimentary units that we sampled. Those few
apatites that were recovered had unusually low eU concentrations (less than 1 ppm in
most cases), and generally unreliable He dates with large uncertainties.
3. Methods
3.1 (U-Th)/He Dating
We sampled along three sub-vertical transects located in three different mountain
ranges (fig. 2). Each sub-vertical transect consisted of three to nine individual hand
samples (figs. 3, 4, and 5), which were collected in fine to medium grained quartzites of
either the Prospect Mountain Formation (Stansbury Mountains) or the Oquirrh Group
(Oquirrh Mountains, Mount Timpanogos). Zircon and apatite were separated from these
rocks by standard crushing, sieving, and magnetic and density separation procedures. Due
to extremely low apatite yields and poor quality (i.e., apatite grains with less than 1 ppm
eU), we report only the zircon (U-Th)/He results. These analyses were performed at the
University of Arizona following methods described in Reiners et al. (2004). Five or more
single-grain aliquots from each sample were analyzed using diode, Nd:YAG, or CO2
laser heating; cryogenic purification; and quadrupole mass-spectrometry for 4He analysis;
and isotope-dilution high-resolution inductively coupled plasma mass-spectrometry (HRICP-MS) for U and Th analysis. Alpha ejection corrections followed Hourigan et al.
(2005).
187
4. Results
4.1 Zircon (U-Th)/He
Single grain zircon He dates are reported in table 1 and plotted against elevation
for all three ranges in figure 6. We include these plots primarily to illustrate that no
obvious (or useful) trends exist between date and elevation for the Oquirrh and Stansbury
datasets, and that we must rely upon other relationships to properly interpret these data.
In order to better visualize the large spread in dates in some transects, we also include the
probability density plot of all of the grains in a given transect. For the Stansbury transect,
dates range from 48 Ma to 259 Ma with no obvious correlation with elevation. As the
probability plot shows (fig. 6a), a majority of these dates (40 out of 58) are late
Cretaceous (between 110 and 65 Ma) with the most prominent peak at ~105 Ma. The
Oquirrh Mountains data also show a wide spread with dates ranging from 283 to 90 Ma.
Like the Stansbury dataset, correlations between date and elevation are not readily
apparent. The probability density plot (fig. 6b) shows two prominent peaks at roughly
130 and 110 Ma, but the dates are more evenly distributed across the date spectrum than
they are in the Stansbury transect. Zircon He dates from Mount Timpanogos are the most
confined with a dominant peak at ~75-80 Ma and minor peaks at roughly 110 and 70 Ma.
A single zircon in this transect has a relatively old date of 164 Ma. The Mount
Timpanogos transect also shows a positive date-elevation relationship.
To better investigate the combined effects of radiation damage and inheritance on
the date irreproducibility in some samples, we plot all of the dates from the Stansbury,
188
Oquirrh, and Mount Timpanogos transects against eU in figure 7. We also examined
whether grain size—measured as the radius of a sphere with a surface-area-to-volume
ratio equivalent to that of each zircon—had any effect on date variability in our samples.
Because no correlations between grain size and date or grain size and eU are apparent, we
do not consider the grain size effect in the subsequent discussion. Interpreting these plots
in the context of thermal histories assumes that all of the zircons in a given transect share
a common post-depositional tT path. As such, we group them on the basis of their
stratigraphic proximity to one another. If a collection of samples comes from the same or
nearby stratigraphic horizons, then they presumably had a similar sedimentary burial
history. In the Stansbury dataset, samples 10UTSD1, 2, 3, 4, and 7 are all within ~400 m
of each other, while 10UTSD5 and 6 (fig. 3) are in roughly the same stratigraphic horizon
and are ~400 m below the next closest samples (10UTSD4 and 7). We therefore place
10UTSD1, 2, 3, 4, and 7 in one group (circles in figure 7a) and 10UTSD5 and 6 in the
other (triangles in figure 7a). The former group, with its large number of dates, will be
the main focus for the rest of this study. All of the Oquirrh transect samples are within
~250 m of one another, except for 10UTOO10, which is ~400 m stratigraphically below
the rest (fig. 4). Samples 10UTOO1 through 9 are placed in their own group (circles in
figure 7b), and sample 10UTOO10 is placed in its own group (triangles in figure 7b).
Because the group comprising samples 10UTOO1 through 9 contains many more dates
than sample 10UTOO10, we focus on this group in the following sections. The Mount
Timpanogos samples have the most stratigraphic separation with ~420 m separating
samples 10UTT6 and 7 and ~1360 m separating samples 10UTT1 and 7 (fig. 5). As such,
189
we consider the date-eU trends of 10UTT7 (circles in figure 7c), 10UTT6 (squares in
figure 7c), and 10UTT1 (triangle in figure 7c) separately.
5. Discussion
5.1 Interpretation of date-eU correlations
Both the Stansbury and Oquirrh datasets show a large degree of date variability
and it is difficult to discern any single correlation between date and eU. With the
potential effects of He and damage inheritance in mind (fig. 1), we emphasize here and in
the subsequent discussion the dates that could potentially constitute the zero-inheritance
curve. If both of these samples have inheritance envelopes that behave in a predictable
manner (i.e. similar to the inheritance envelopes in figure 1), then this curve should
provide the lower bound for the youngest grains at low eU, and the upper bound for the
oldest dates at high eU. For the Stansbury transect, the youngest grains at low eU (less
than ~1000 ppm), increase from 65 Ma at 90 ppm eU, to 110 Ma at 1036 ppm eU. Using
scenario 1 in figure 1 as a guide, we predict that the Stansbury zero-inheritance curve
switches over from being the lower bound to the upper bound of an inheritance envelope
at approximately 1000 ppm eU. The zero-inheritance curve should therefore sit at slightly
older dates as our observed dates decrease from 110 Ma at 1036 ppm eU to a youngest
date of 48 Ma at 1851 ppm eU. For the Oquirrh transect, the youngest grains increase
from 92 Ma at 159 ppm eU to 121 Ma at 424 ppm eU. Above roughly 500 ppm eU, the
trend for the youngest date at a given eU concentration becomes less obvious and we
postulate that this marks the approximate position for the zero-inheritance curve switch-
190
over. With the exception of two anomalously old dates ( 174 and 231 Ma) at relatively
high eU (790 and 1092 ppm, respectively), we predict that the zero-inheritance curve
should provide the upper bound for the inheritance envelope from ~500 to 1000 ppm eU.
In both transects, we observe a significant spread in dates above our proposed
zero-inheritance date-eU curve (and also below it in the Oquirrh dataset). This variability
is mostly confined to relatively low eU concentrations. For example, the oldest dates in
the Stansbury dataset (greater than 160 Ma, see peaks in date spectra in figure 6a) occur
at relatively low eU concentrations, with the oldest zircon He date (259 Ma) having an
eU concentration of only 151 ppm. Similarly, the Oquirrh transect has a large spread in
dates (91-283 Ma) between ~50 and 400 ppm eU. No obvious date-eU correlations exists
for this subset of the data, but we note that most of the oldest dates in the dataset occur at
relative low amounts of eU. This is a key observation and will be used in the subsequent
section, along with model-generated inheritance envelopes, in an attempt to constrain the
tT path for this transect.
Date-eU correlations for both 10UTT6 and 10UTT7 are nearly flat compared to
the Oquirrh and Stansbury datasets and appear to be much less complicated. Sample
10UTT7 may have a slight positive correlation at low eU concentrations (less than 500
ppm) as dates increase from 65 Ma to 77 Ma between 158 and 483 ppm eU (excluding
the single date at 113 Ma). Dates increase from 75 to 99 Ma between 60 and 1119 ppm
eU in sample 10UTT6; however, correlations in both of these samples are subtle. The
highest elevation sample (10UTT1) has the most dispersion, but lacks a clear correlation
between date and eU.
191
5.2 Overview of model inputs
The datasets presented above, specifically the Stansbury and Oquirrh transects,
are complicated and defy attempts to either average out date variability or match it with a
single date-eU trend, which we interpret to be the result of partial resetting of zircon
grains with a wide range of pre-depositional He dates and radiation-damage induced
kinetic behaviors. Still, because these datasets represent some of the only constraints on
the Cretaceous thermal history of the Sevier belt, and because they illustrate commonly
encountered thermochronologic challenges arising in sedimentary rocks heated to partial
resetting conditions, we attempt to explain their tT histories using the ZRDAAM kinetics
of Guenthner et al. (2013), which are incorporated into the HeFTy thermal modeling
software program (Ketcham, 2005). Our goals are to test both the amount of maximum
heating, which we assume to be due to burial, and timing of Cretaceous cooling, which
we assume to be due to exhumation, for each transect. We use a forward model-based
approach that involves inputting specific tT paths and comparing the output model dateeU curves to the real datasets. For each transect, we begin with a discussion of the model
tT inputs as calculated from the well-documented stratigraphic record. We then describe
how well certain forward model derived date-eU curves match our predictions about a
given transect’s zero-inheritance curve (dashed lines in fig. 7). Finally, sections of this
paper detail our attempts to match the large number of old dates at low eU concentrations
in the Stansbury and Oquirrh transects with an inheritance envelope. Because the Mount
Timpanogos data show relatively little date variability, we do not include an inheritance
section when discussing this dataset.
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Although the tT paths used for each transect depend on the specific local
stratigraphy and structural setting, in general the geology at each location is consistent
with sample burial (heating) in sedimentary basins throughout the Paleozoic and into the
early Cretaceous, and then exhumation (cooling) as a result of Sevier-belt related
thrusting in the late Cretaceous. The CNS also experienced a final pulse of Basin and
Range related exhumation (cooling) in the middle to late Cenozoic (Constenius et al.,
2008), which we include in our model tT paths. The main geologic events associated with
burial or exhumation for each transect are summarized in figure 8. The zircon He
thermochronometer may not be sensitive to every tT segment shown in this figure, but we
include many of these events in order to honor the relatively well established preCretaceous geologic history of each location. The maximum Phanerozoic temperatures
achieved at each location prior to late Cretaceous exhumation are a function of the
estimated thickness of sedimentary cover, and can be calculated using observed unit
thicknesses and a simple 1D crustal geotherm.
For this geotherm, we rely upon the equation for steady-state, depth-dependent
temperature with an additional term for uniform radiogenic heat production throughout
our modeled crust (Turcotte and Schubert, 2002). An advection term is also included
when modeling the effects of exhumation on this geotherm. Typical values of 25 km2 *
m.y.-1 for thermal diffusivity, 1°C/m.y. for heat production, 20 °C for surface
temperatures, and 30 km for layer thickness were used. In our modeled tT paths, we
calculate burial temperatures using a cold (20 °C/km), average (25 °C/km), and warm (30
°C/km) geothermal gradient. Each gradient is assigned by fixing the temperature at the
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base of the layer to a specific value (e.g., 600 °C at the base of the layer gives an average
gradient of 20 °C/km). We note that the layer thickness and basal temperature are not
necessarily representative of any particular boundary layer within the lithosphere. Rather,
they are used simply to produce the geothermal gradient of interest. Furthermore, the
general form and structure of the upper part of our modeled geotherm (i.e., the region
encompassing the zircon He closure depth), is relatively insensitive to changes in the
layer thickness or the type of basal boundary condition (Reiners and Brandon, 2006).
The other main input for our modeled date-eU correlations is crystal radius, more
specifically the radius of a sphere with an equivalent surface-to-volume ratio for each
zircon. For ease of visualization, we use a single value for the crystal radius of all of the
individual zircons during each model run. This allows us to calculate the resulting dateeU trend as a continuous curve and isolates the date dispersion caused by varying crystal
size from the dispersion that results from radiation damage effects. Because there is no
clear relationship between crystal size and date, we use the mean crystal radius of all
zircons in a given sample as our primary input. But we also consider the standard
deviation of the mean in order to capture some of the variance in grain size. Each specific
tT path therefore has three modeled date-eU trends, the mean grain size plus or minus two
standard deviations. The mean grain size plus/minus the standard deviation used for each
dataset is as follows: 54 ± 22 µm for the Stansbury transect, 43 ± 18 µm for the Oquirrh
transect, and 40 ± 10 µm for the Mount Timpanogos transect.
5.3 Stansbury Mountains
5.3.1 tT inputs
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Our HeFTy models for the Stansbury dataset include three major phases of
sedimentary burial: 1) Cambrian through early Mississippian burial by predominantly
miogeoclinal sediments, 2) latest Mississippian through Permian burial by sediments of
the Oquirrh Basin, and 3) Triassic through Aptian burial by sediments mainly associated
with the Cordilleran foreland basin system (fig. 8). We focus our discussion on the burial
and exhumation history of the samples in the upper stratigraphic portion of our transect
(circles in figure 7a). An equivalent style and timing of burial and exhumation is
expected for samples 10UTSD5 and 10UTSD6, but because these two samples are ~450900 m stratigraphically below the rest (fig. 3), the maximum burial temperatures
experienced by the two could be ~10-15 °C warmer (depending on the geothermal
gradient).
For Cambrian through upper Mississippian sedimentary thicknesses, we use the
measured sections and maps of Rigby (1958), Hintze and Kowallis (2009), and Clark et
al. (2012). Where disagreements about unit nomenclature exist, we rely upon the most
recent description of the given unit. Mapping relationships and cross-sections (fig. 3)
show that our Stansbury transect samples come from the upper part of the lower
Cambrian Prospect Mountain Formation. Initial deposition is therefore placed at 521 Ma
(beginning of Stage 3) with another ~400 m of Prospect Mountain Formation overlying
our samples. Above the Prospect Mountain Formation, an additional 670 m of Cambrian
sediments (Pioche through Orr Formations) were conformably deposited at our location
(fig. 3). The next overlying units are of latest Devonian and earliest Mississippian and
consist of the Stansbury Formation, Pinyon Peak Limestone, Fitchville Formation, and
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Gardison Limestone (370 m total). In the Stansbury Range, these units are an eastern
expression of the late Devonian Antler Orogeny (Rigby, 1959; Silberling et al., 1997),
and were either deposited during deformation (Stansbury Formation) or immediately after
deformation (Pinyon Peak Limestone, Fitchville Formation, Gardison Limestone). In our
HeFTy models, we represent this event as a period of rapid cooling in the late Devonian.
For the thicknesses of the missing units (uppermost Cambrian Ajax Dolomite through
early Devonian Simonson Dolomite), we rely upon the Stansbury Range composite
stratigraphic chart of Hintze and Kowallis (2009) that gives a total missing thickness of
1020 m. The end of Simonson Dolomite deposition brackets the beginning of this
exhumation event and is thought to be early Givetian in age (~390 Ma, Sandberg et al.,
1982). The upper bound on this event is marked by deposition of the middle Famennian
(~370 Ma) Pinyon Peak Limestone (Sandberg and Gutschick, 1979). Another 1230 m of
conformable Mississippian strata from the Deseret Formation to the Manning Canyon
Shale overlies the Gardison Limestone.
The next major phase of sedimentary burial is represented by the thick succession
of early Pennsylvanian through early Permian rocks of the Oquirrh Group. In the
Stansbury Range, the beginning of Oquirrh Group deposition is marked by the Butterfield
Peaks Formation, which is 1800 m thick and Moscovian in age (Armin and Moore, 1981;
Stevens and Armin, 1983). An additional 3500 m of Oquirrh Group strata consisting of
the Bingham Mine, Freeman Peak, and Curry Peak Formations, were deposited on top of
the Butterfield Peaks Formation. Oquirrh Group deposition ended during the late
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Wolfcampian (Jordan, 1979; Hintze and Kowallis, 2009). This brings the total Oquirrh
Group thickness to 5300 m.
The final phase of sedimentary burial occurred from the late Permian until the late
Cretaceous and is the most enigmatic in terms of the units deposited and their
thicknesses. Jordan and Allmendinger (1979) described 780 m of lower Permian (~280
Ma) Kirkman Limestone through Lower Triassic (~245 Ma) Thaynes Limestone exposed
in the Martin Fork syncline of the eastern Stansbury Mountains. The remaining Mesozoic
section is completely absent throughout much of western Utah and the total extent and
thicknesses of the Chinle Formation and Glen Canyon Group in this area—the units that
overlie the Thaynes in other parts of Utah—are speculative. Hintze and Davis (2003)
reported 230 m of Chinle Formation in the Pahvant Range, which represents some of the
westernmost exposures of this unit. These authors also described well-logs near Sevier
Lake in western Utah that contained 450 m of Lower Jurassic Navajo Sandstone.
Restoration along the Sevier Desert Detachment placed this well against the western
flank of the Pahvant Range (DeCelles and Coogan, 2006), which is still some distance
away from our transect. Regardless, these thicknesses represent perhaps the best estimate
of missing equivalent strata in the Stansbury Mountains. Regional isopachs suggest at
least an additional 1000 m of Early to middle Cretaceous (140-110 Ma) foredeep strata
were deposited over our transect (DeCelles, 2004) and we include these numbers in all
models.
The remaining modeled tT segments for the Stansbury dataset are designed to test
our hypotheses about the timing and amount of Cretaceous and Cenozoic exhumation in
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the range. To help guide these inputs and narrow the range of tested paths, we considered
several factors. An upper bound on the age of exhumation in the Stansbury range comes
from the timing of movement along the Sheeprock thrust. Various authors (Mitra, 1997;
DeCelles, 2004) have described this structure as both the oldest and westernmost of the
major thrusts composing the CNS. Given that the thrust places the upper Proterozoic Otts
Canyon, Dutch Peak, and Kelly Canyon Formations (units that are absent in the
Stansbury Mountains) on top of the lower Cambrian Prospect Mountain Formation
(Mukul and Mitra, 1998), it seems likely that the Sheeprock thrust was active before the
Tintic Valley thrust, which carries the Stansbury Mountains in its hanging wall. Based on
similar hanging wall and footwall units, geometry, and position relative to the WNF,
DeCelles (2004) placed movement of this thrust in the same 140-110 Ma timeframe as
the Canyon Range thrust to the south and the Willard thrust to the north. A major pulse of
thrust-related exhumation was therefore unlikely much earlier than ~110 Ma in the
Stansbury range. The lower age bracket for Tintic Valley thrust activity (and thus
Stansbury exhumation) comes from the age estimates of Constenius et al. (2003) for
movement along the frontal (and presumably younger) Charleston-Nebo fault system. As
previously mentioned, these authors described a major phase of slip along the Nebo thrust
as occurring between 100 and 80 Ma. This age span suggests that movement along the
Tintic Valley thrust was likely minimal after ~100 Ma; however, it does not necessarily
preclude exhumation of the Stansbury Mountains at this time. The range could have
continued to be passively uplifted (and subsequently exhumed) along the more deeply
rooted Nebo thrust. As such, we also examine the date-eU correlations that result from a
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phase of rapid exhumation younger than 100 Ma. Finally, the dataset itself gives us some
hint as to what the appropriate age brackets are for our tT inputs. The large number of
Albian through Cenomanian (~110 to ~90 Ma) zircon He dates in this dataset (fig. 6a)
suggest that many of these zircons likely record an episode of rapid exhumation around
this time. With these constraints in mind, we test for three different time periods of rapid
exhumation: 1) 120-110 Ma, 2) 110-100 Ma, and 3) 100-90 Ma. Within each time period,
we also test whether 3, 4, 5, or 6 km of total exhumation best reproduces the observed
date-eU trends.
The last segment of our model tT histories includes a pulse of Cenozoic cooling
related to Cordilleran collapse and Basin and Range extension. Some ambiguity exists,
however, as to the timing of extension-related exhumation in the Stansbury Mountains.
At this latitude, Consentius et al. (2003) described half-grabens and associated basin fill
that indicated the frontal part of the CNS in the Wasatch Range began to collapse and
extend at ~39 Ma. Although this phase of orogenic collapse possibly affected the
Stansbury Range as well, structures and stratigraphy similar to those in the Wasatch
Range are absent. Furthermore, the most prominent extensional feature in the Stansbury
Mountains, the range-bounding Stansbury normal fault on the west side of the range, has
long been recognized as a Basin and Range style fault (Gilbert, 1890) with several
kilometers of total slip (Rigby, 1958). This suggests that the majority of Cenozoic
exhumation in the Stansbury Mountains occurred during Basin and Range deformation.
The timing of displacement along the Stansbury normal fault is unknown, but AFT and
apatite He dates from nearby ranges provide some constraints. Stockli et al. (2001)
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documented exhumation along the Sevier Desert Detachment in the Canyon Range at ~19
Ma, whereas Armstrong et al. (2003) showed that a major phase of exhumation began in
the Wasatch Range at 12-10 Ma. Due to the similarity in their positions relative to the
WNF, we argue the beginning of Basin and Range exhumation in the Stansbury Range
likely occurred at the same time as in the Canyon Range. In our models, the total amount
of this exhumation (or cooling) corresponds to the remaining rock thickness following
our Late Cretaceous episode of exhumation. That is, it is equal to the amount necessary to
bring the rocks to the surface at the present day.
5.3.2 Model results—zero-inheritance curve
Figure 9a shows model date-eU trends and corresponding tT paths that best
capture certain traits of the real dataset’s expected zero-inheritance date-eU trend (i.e.,
fig. 7a). No single model reproduces every aspect of dataset, so we focus our discussion
on a number of possibilities. We also stress that the following discussion is aimed at
explaining only certain aspects of the dataset (i.e. possible zero-inheritance dates) and not
the date variability seen in the entire dataset. Of the various models tested, tT paths
calculated with an average geothermal gradient of 20 °C/km and exhumation beginning at
120 Ma give a range of date-eU trends that, if combined, define a zero-inheritance curve
for the Stansbury data. Specifically, the tT path with these inputs and 4 km of exhumation
gives a date of 47 Ma at 50 ppm eU, which then increases to 75 Ma at 150 ppm and 84
Ma at 250 ppm (dotted line in fig. 9a). Compared to real dates of 65 Ma at 90 ppm and 87
Ma at 242 ppm, the model curve resulting from 4 km of exhumation at 120 Ma provides a
lower bound to the real dataset at low eU and could be interpreted as a zero-inheritance
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envelope. Unfortunately, this model curve decreases to a date of 66 Ma at 1000 ppm and
is too young to bound the data at high eU. A better match to these real dates is the tT path
that results from 5 km of exhumation at 120 Ma (solid line in fig. 9a). This scenario gives
a date of 107 Ma at 500 ppm (several zircons clustered around 500 ppm have dates
between 102 and 108 Ma) and then decreases to 74 Ma at 1500 ppm (real date of 72 Ma
at 1498 ppm). Despite being an upper bound to high eU dates, this model curve has dates
that are too old at low eU (81 Ma at 50 ppm) and fails to provide the expected lower
bound to the zero-inheritance curve. We also consider a tT path calculated from 6 km of
exhumation at 120 Ma (dashed line in fig. 9a). Like the 5 km at 120 Ma scenario, the 6
km of exhumation scenario may define the upper bound of a zero-inheritance curve at
high eU, but the rest of the curve is relatively flat and gives old dates at low eU (105 Ma
at 50 ppm). The tT paths in which exhumation begins at 120 Ma therefore give several
model outputs that collectively constitute a zero-inheritance curve, but because these
model curves do not result from a single path, our ability to constrain the thermal history
for this transect is limited.
Although the zero-inheritance curve constraints for our preferred timing of
exhumation (120 Ma) do not capture all aspects of the date variability, we can still use
zero-inheritance curves to rule out some thermal histories. As an example, in figure 9b
we show the model curves generated from the same set of inputs described above, with
the same exhumation amounts (4, 5, and 6 km), but a later start date of exhumation (100
Ma). In these thermal histories, the dates at each eU concentration are slightly younger
than their counterparts shown in figure 9a. Because none of the 100 Ma curves appear to
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act as either lower or upper bounds, the Stansbury transect dataset is slightly better
explained by a pulse of exhumation at 120 Ma as opposed to one at 100 Ma. Similarly,
trends modeled with an average geothermal gradient of 25 °C/km and exhumation
starting at 120 Ma (fig. 10) can also be ruled out. These model trends are shifted to much
younger dates compared to the ones shown in figure 9a. The date-eU curves for the 4 and
5 km exhumation scenarios do not match any of the real dates, while the 6 km scenario
curve passes through some of the data, but does not act as an upper or lower bound. We
note that none of the thermal histories discussed above reproduces any of the oldest dates
at eU concentrations between ~150 and 500 ppm, and we discuss the potential of
inheritance envelopes for explaining this date variability in detail below.
5.3.3 Model results—inheritance envelopes
In order to test the potential effect of inheritance on the Stansbury dataset, we
append an additional tT step to each of our model inputs. This step consists of either 1100
or 1700 Ma at 20 °C prior to deposition and simulates varying degrees of He and damage
inheritance prior to a given zircon being deposited in the Prospect Mountain. These dates
represent commonly found U/Pb dates in the Paleozoic stratigraphy of the western U.S.
(Gehrels et al., 2011; 1100 Ma = Grenville and 1700 Ma = Yavapai-Mazatzal). Also,
because we are attempting to simulate a maximum/minimum envelope, we chose the full
retention of He and damage at surface conditions for each inheritance curve. We included
extra tT steps in all of the various exhumation scenarios described in the previous two
sections and results from a representative tT path (5 km of exhumation at 120 Ma) with
each additional step are shown in figure 11a. Although the inheritance date-eU trends
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may explain some of the date dispersion between 80 and 100 Ma (fig. 11a inset), these
trends do not exceed ~105 Ma and fall far short of reaching the oldest date of 259 Ma. In
all of the models tested (i.e., 3, 4, 5, and 6 km of exhumation at 120, 110, and 100 Ma),
dates from the inheritance date-eU curves never exceeded those from the zero-inheritance
curves. That is, the temperatures are high enough to fully reset each zircon at some point
during burial and no inherited He is retained. Some amount of inherited damage remains
as the inheritance curves drop to near zero dates at high eU.
Inheritance curves with older dates are possible though in certain thermal
histories. To demonstrate this, we explored other model tT options that, at a minimum,
retained the same amounts of sedimentary burial and Sevier belt-related exhumation, but
had lower geothermal gradients and a later date of Cretaceous exhumation. The
geothermal gradient was lowered in order to achieve lower temperatures, and hence less
resetting, throughout a zircon’s tT history. Because the temperatures are lower in these
additional tests, the model lowest eU dates more directly reflect the timing of the
Cretaceous pulse of exhumation. In other words, a 120 Ma exhumation event of 4, 5, or 6
km at a low geothermal gradient (lower than 20 °C) gives zero-inheritance dates of ~120
Ma at low eU, which is too old to match the Stansbury dataset. As such, we made the
timing of exhumation younger so that the dates for zero-inheritance zircons at the lowest
eU concentrations (i.e. zircons with some of the lowest diffusivities) would reflect those
in the dataset at similar eU concentrations (e.g. 73 Ma at 45 ppm eU).
We show a representative inheritance envelope from one of these additional tT
paths in figure 11b. The specific path consists of 5 km of exhumation beginning at 80
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Ma, and the resulting inheritance curves reproduce much of the date variability in the
Stansbury dataset. In particular, the oldest inheritance curve (1700 Ma) captures some of
the oldest dates at low amounts of eU (e.g. 259 Ma at 151 ppm), whereas the combined
zero-inheritance and inheritance curves bound the dates at high eU. Almost all of the
young dates at low eU are also bounded by the various curves (fig. 11b insert). One
problem with this explanation is that changing the thermal history so that the inheritance
envelope bounds nearly all of the data leads to an unexpected and counter-intuitive zeroinheritance curve. In other words, the zero-inheritance curve increases rapidly from 80
Ma at 50 ppm eU to 124 ma at 250 ppm eU and does not reflect the apparent (or
expected) date-eU correlations at low and high eU (dashed line in fig. 7a). That is, if this
scenario reflects the true tT path for the Stansbury transect, then the correlations that
appear to define a zero-inheritance envelope in figure 7a are merely coincidental. Several
other aspects of the tT history are also not geologically likely. An average geothermal
gradient of 15 °C/km might be too cool for a basin that has undergone several episodes of
extension and compression. Perhaps more problematic, a several km pulse of exhumation
at 80 Ma this far into the CNS hinterland, goes against many established ideas pertaining
to thrust fault progression, uplift, and erosion in the Sevier belt (DeCelles, 2004, see
below for further discussion).
Attempts to fully understand all aspects of this complex dataset are therefore
difficult and fraught with inconsistencies. In part, this may result from an incomplete
understanding of all of the variables that affect a zircon He date (both the known
unknowns and unknown unknowns). Heterogeneous distribution of U and Th within a
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zircon is a good example of one such variable. For certain thermal histories, large U and
Th concentration differences between the rim and core of a zircon (or vice versa) can lead
to differences of up to 100 m.y. between zoned and unzoned grains with the same bulk
eU concentration (Guenthner et al., 2013). The 120 Ma scenario inheritance envelope
(fig. 11a) might fail to reproduce several aspects of the Stansbury data because some of
the oldest dates in this dataset are heavily zoned. Also important is that the ZRDAAM
presently assumes that the annealing of radiation damage that affects He diffusivity
follows the kinetics of zircon fission-track annealing. In reality this annealing may be
more complicated, and possibly dependent on the level of radiation damage in a given
zircon (Garver et al., 2005). This may explain why no single zero-inheritance curve
provides a lower and upper bound to the dates at low and high eU, respectively. If
damage annealing in high eU zircons occurs at temperatures lower than those modeled in
ZRDAAM, then the 4 km at 120 Ma zero-inheritance curve could be shifted to older
dates at high eU and its corresponding tT path might be more viable. Unfortunately,
resolving these issues is beyond the scope of the current study and is the focus of ongoing
work. Instead, we turn our attention to the other two datasets from the CNS region, which
provide more straightforward interpretations.
5.4 Oquirrh Mountains
5.4.1 tT inputs
We use some of the same tT inputs for sedimentary burial in the Oquirrh
Mountains as in the Stansbury Mountains, with the obvious exception of the Cambrian
through Mississippian phase (fig. 8). Maps by Clark et al. (2012) place all of our samples
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in the middle of the Butterfield Peak Formation of the Oquirrh Group, and most within
roughly the same stratigraphic horizon (fig. 4). Sample 10UTOO10 is the lone exception
and sits approximately ~500 m stratigraphically below the rest of our Oquirrh transect.
We therefore exclude it from our tT modeling. The Butterfield Peak Formation has a total
thickness of 2770 m (Tooker and Roberts, 1970; Clark et al., 2012), and we estimate that
our transect sits in the middle with approximately 1390 m of additional Butterfield Peak
overlying it. Above this formation is the Moscovian Bingham Mine Formation (1980 m,
Hintze and Kowallis, 2009) and the Wolfcampian Oquirrh units: the Freeman Peak
Formation, Curry Peak Formation, and the Kirkman Limestone (1550 m). Bissell (1959)
also described rocks of the Diamond Creek Sandstone and the lower Park City Group in
the Oquirrh Mountains, which are Leonardian in age (~270 Ma) and 760 m thick. This
brings the total thickness of the Pennsylvanian-Permian stratigraphy in the Oquirrh
Mountains to 5680 m.
The next youngest units that crop out in the Oquirrh Mountains are Oligocene age
volcanic and igneous units (Moore, 1973). Like the Stansbury Mountains, Mesozoic
strata are completely absent from this range, but we assume that units similar in age and
thickness to those used in our Stansbury tT paths were also deposited on top of our
Oquirrh transect. These include the Thaynes Limestone and our conjectural Chinle
through Navajo sequence. The Thaynes Limestone crops out both to the west of our
Oquirrh transect in the Stansbury Range and also to the east, in the vicinity of Salt Lake
City, where it is more than twice as thick—700 m as opposed to 340 m (Solien, 1979).
We use the same thickness for Thaynes deposition in the Oquirrh Mountains as in the
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Stansbury Mountains, but note that this unit could have been thicker. Finally, we include
1000 m of Early Cretaceous (140-110 Ma) foredeep strata (DeCelles, 2004) in our model
thermal histories.
For the timing of exhumation, we again test three different time periods: 1) 120110 Ma, 2) 110-100 Ma, and 3) 100-90 Ma. These models are designed to see whether
the Midas thrust (which has the Oquirrh Mountains in its hanging wall) was active
contemporaneously with the Tintic Valley thrust (i.e., 120-110 Ma), was active soon after
the Tintic Valley thrust (i.e. 110-100 Ma), or was involved in initial stages of the growth
of the Santaquin Culmination (i.e., 100-90 Ma). Within each time period, we test
exhumation amounts of 3, 4, 5, or 6 km.
The final segments of the tT paths for our Oquirrh models are also similar to the
Stansbury models and consist of a pulse of Cenozoic exhumation related to Basin and
Range normal faulting. We use the same timing and magnitudes (given the amount of
Cretaceous exhumation) for this segment in the Oquirrh transect as in the Stansbury
transect. This is appropriate given that the west side of the range is bounded by a series of
normal faults, many of which have long been classified as Basin and Range style
(Gilbert, 1890).
5.4.2 Model results—zero-inheritance curve
In order to distinguish between the various models for our Oquirrh dataset, we
again focus first on the model generated zero-inheritance curves and attempt to match
these with our expected curve from the real dataset (fig. 7b). No single model curve can
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explain all of the date variability, but we leave a discussion of the influence of He and
radiation damage inheritance on Oquirrh dates to the next section.
Figure 12 shows date-eU results from the two tT paths that come closest to
reproducing the expected zero-inheritance curve for the Oquirrh dataset (i.e., dashed line
in fig. 7b). A tT path with 3 km of exhumation beginning at 110 Ma and a 20 °C/km
geothermal gradient results in a date-eU trend that acts as lower bound at low eU,
capturing many of the youngest dates between 50 and 500 ppm eU (fig. 12a). For
example, this curve rises from a date of 82 Ma at 50 ppm eU to 107 Ma at 250 ppm and
123 Ma at 500 ppm. Real dates of 92 Ma at 159 ppm, 103 Ma at 237 ppm, and 121 Ma at
424 ppm fall along the model curve. The model curve levels out at a date of 132 Ma at
750 ppm eU before decreasing slightly to 124 Ma at 1250 ppm. At these higher eU
concentrations, the zero-inheritance curve either passes directly through (within error)
real dates of 135 Ma at 865 ppm eU, or provides an upper bound to other high eU dates
such as 114 Ma at 778 ppm. This curve fails to reproduce only two anomalously old dates
(174 Ma at 790 ppm, and 231 Ma at 1092 ppm). A different tT path with 6 km of
exhumation beginning at 100 Ma and a 20 °C/km geothermal gradient gives a zeroinheritance model curve that also provides a good upper bound at high eU, but is a
slightly worse lower bound at low eU (fig. 12b). Despite a younger date of exhumation,
the zero-inheritance curve in figure 12b is shifted to slightly older dates than the curve
shown in figure 12a. Model zircons are cooled to lower temperatures more quickly (6 km
of exhumation as opposed to 3 km), which leads to dates that increase from 99 Ma at 50
ppm eU to 133 Ma at 500 ppm. The curve continues to rise, reaching a maximum of 143
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Ma at 750 ppm and bounding all of the high eU dates except for the two anomalous dates
that were previously mentioned. Although this zero-inheritance curve is less ideal than
the one generated from the 3 km at 110 Ma scenario, the relevance of showing this model
output will become apparent in the next section on inheritance envelopes.
5.4.3 Model results—inheritance envelopes
Like our Stansbury transect, we use supplemental tT steps to simulate inherited
zircon He dates of 1100 Ma and 1700 Ma for the Oquirrh transect. Although the
inheritance curves for both the 3 km of exhumation at 110 Ma and 6 km of exhumation at
100 Ma scenarios captures nearly all of the oldest Oquirrh dates (fig. 13), we argue that
the 3 km of exhumation at 110 Ma scenario has a combined zero inheritance curve and
inheritance envelope that encompasses more of the Oquirrh transect data. We admit that
the distinction between these two plots is subtle, and it may be too difficult to constrain
slight differences in exhumation timing with the Oquirrh inheritance envelopes. Perhaps
more definitively, we can use these envelopes to constrain this maximum burial
temperature. For example, figure 14 shows the 6 km at 100 Ma scenario with a
geothermal gradient of 20 °C/km (maximum temperature=173 °C) and 25 °C/km
(maximum temperature=212 °C). The zero-inheritance date-eU trend is too flat in this
latter scenario and not a good match to the data. Of equal importance though, the high
temperatures in this tT path prevent both inheritance curves from exceeding the oldest
date in the zero-inheritance curve (~90 Ma). This suggests that the maximum burial
temperature for the Oquirrh transect was closer to 173 °C than 212 °C.
5.5 Mount Timpanogos
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5.5.1 tT inputs
Our tT models for the Mount Timpanogos transect focus on the two samples
collected at the base of the transect (10UTT6 and 10UTT7). These samples are
stratigraphically separated by ~420 m and we model them separately. Based on mapping
by Constenius et al. (2011) and our own field observations, sample 10UTT7 was
collected in the upper part of the Bridal Veil Limestone member of the Oquirrh Group,
~230 m below the contact with the Bear Canyon Formation, while sample 10UTT6 was
collected ~190 m above this contact. The Bridal Veil Limestone member is Morrowan in
age (312 Ma, Maxfield, 1957) with an estimated 6320 m of additional Oquirrh group
strata overlying it in the vicinity of Mount Timpanogos (Larson and Clark, 1979;
Konopka and Dott, 1982; Hintze and Kowallis, 2009). These units include the Bear
Canyon Formation, Shingle Mill Limestone, Wallsburg Ridge Formation, and Granger
Mountain Formation and range in age from Atokan (312 Ma) to Wolfcampian (280 Ma).
Above the Oquirrh Group, composite stratigraphic charts for this area document 1050 m
of Permian Kirkman Limestone through Park City Group (Hintze and Kowallis, 2009).
Mesozoic rocks are absent from this location and we estimate their missing
thicknesses. Due to our transect’s relative proximity to Salt Lake City, we use Solien’s
(1979) 700 m of Thaynes Formation for the thickness of Lower Triassic rocks at Mount
Timpanogos and add our conjectural Chinle-Navajo thicknesses to complete the Upper
Triassic-Lower Jurassic sequence. To the north and south of Mount Timpanogos, Imlay
(1967) measured 390 m and 880 m of Twin Creek Limestone-Arapien Shale at Thistle
and Salt Lake City, respectively. We average these two numbers together and use 635 m
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as a representative thickness for Middle Jurassic (160 Ma) rocks deposited on top of our
transect. Finally, we estimate that roughly 1000 m of additional Early Cretaceous
foredeep units were deposited above Mount Timpanogos prior to exhumation (DeCelles,
2004).
We again test three different phases of exhumation in the Timpanogos transect: 1)
100-90 Ma, 2) 90-80 Ma, and 3) 80-70 Ma. The timing of thrust-related, Cretaceous
exhumation in the Wasatch Range is predicted by the two stages of growth for the
Santaquin Culmination (100-80 Ma, 80-40 Ma, Constenius et al., 2003) and our models
are designed to see which stage includes exhumation at Mount Timpanogos. Also, the
majority of zircon He dates in our transect are between 70 and 90 Ma (fig. 6c), further
suggesting that a major pulse of exhumation occurred sometime during the Late
Cretaceous. Varying amounts of exhumation (3, 4, 5, and 6 km) are tested for each phase.
The final step in our model tT paths includes a pulse of extension related
exhumation during the mid-Cenozoic. Constenius et al. (2003) described extensional
features near Mount Timpanogos that preceded Basin and Range style normal faulting
and are related to low-angle, normal displacement along the Deer Creek detachment.
Movement along this detachment began at 39 Ma (Constenius et al., 2003), and we
therefore begin our final phase of extension-related exhumation at this time. Basin and
Range style extension is also obvious at Timpanogos (i.e., the Wasatch Front), and the
amount of time separating the two stages of extension appears to be brief (~5 Ma,
Constenius et al., 2003). As such, we model a continuous cooling event from 39 to 0 Ma
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and give it a magnitude of cooling which is equivalent to the amount necessary to bring
our transect to surficial temperatures.
5.5.2 Model results
Our preferred tT path for 10UTT7 consists of 5 km of exhumation starting at 100
Ma with a geothermal gradient of 20 °C/km (fig. 15a). Only two dates at ~750 ppm eU
are slightly too young for the resulting model curve, and one date is anomalously old at
~400 ppm eU. Otherwise, our model date-eU curve captures the steady increase in dates
between 150 and 500 ppm eU and the subsequent date plateau that we see in the real
dataset. The model curves generated by 4 and 6 km of exhumation at 100 Ma (fig. 15b)
maintain this basic shape, but are shifted to either younger or older dates respectively. We
also rule out a younger date for exhumation at Mount Timpanogos on the basis of the
model results for 5 km at 90 and 80 Ma (fig. 15c). The date-eU trend is too young for the
5 km at 80 Ma scenario, missing almost all of the real dates, and we argue that the same
is true for the 5 km at 90 Ma scenario, although here the differences are more subtle. As a
further constraint, we show the model results for both the 10UTT7 and 10UTT6 (420 m
stratigraphically above 10UTT7) tT paths in figure 16. In the 5 km at 90 Ma scenario, the
10UTT6 curve is too young relative to the data, whereas the 5 km at 100 Ma model dateeU curve provides a better match.
Compared to the other datasets discussed above, both of the Mount Timpanogos
date-eU correlations are flatter with less dispersion. This matches our predictions about
the burial depths and temperatures experienced by this dataset relative to the other two.
Our preferred tT path for 10UTT7 is calculated from a burial history that includes over 10
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km of sedimentary units and has a maximum temperature of 231 °C (13 °C hotter than
the Stansbury Range, 58 °C hotter than the Oquirrh Range). This temperature is high
enough to anneal significant amounts of damage, which causes most of the grains in this
sample to have similar diffusivities regardless of eU concentration. It also eliminates any
inherited He or damage in these zircons, hence there is no need to model inheritance
envelopes for these samples.
5.6 Summary of tT results
To summarize, our preferred thermal histories for each transect are: 4, 5, or 6 km
of exhumation beginning at 120 Ma in the Stansbury Mountains, 3 km of exhumation
beginning at 110 Ma in the Oquirrh Mountains, and 5 km of exhumation beginning at 100
Ma at Mount Timpanogos. All of these are calculated with an average geothermal
gradient of 20 °C/km. We are relatively confident of the model-derived timing constraints
for the Mount Timpanogos transect as this dataset is the most straightforward. Despite its
date variability, we also have some confidence in our constraints for the Oquirrh transect,
for which ZRDAAM produces plausible inheritance envelopes. The timing of
exhumation could have started at 110 Ma or 100 Ma, but a rapid cooling event within this
timeframe seems likely. The Stansbury dataset is complex and our conclusions for its
thermal history are speculative at best. We argue that this dataset supports an exhumation
event sometime in the Late Cretaceous, but more specific constraints are lacking. We
caution that our preferred scenario of exhumation at 120 Ma for the Stansbury transect is
far from ideal and any geologic conclusions drawn from it are likewise.
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In the remaining sections, we focus our discussion on the significance of these
results for the evolution of the Sevier fold-and-thrust belt and foreland basin system. In
general, our ZRDAAM-derived exhumation constraints are consistent with other indirect
measures of thrust belt exhumation, which demonstrates that ZRDAAM results for
complicated datasets like the Oquirrh transects are at least geologically plausible. Also
important though, our new findings represent the first in situ constraints for exhumation
in the hinterland of the central Utah Sevier belt (i.e., Stansbury and Oquirrh Ranges), a
region whose uplift and erosion history has been previously inferred mainly on the basis
of provenance data from sedimentary units located 10s or 100s of km from the Tintic
Valley or Midas thrust sheets (e.g. DeCelles et al., 1995; Mitra, 1997; Horton et al.,
2004). This motivates us to attempt to place our datasets (even the Stansbury transect) in
some geologic context.
5.7 Geologic significance of tT results
In order to interpret our tT constraints in a geologic context, we first assume that
the main pulse of cooling in each range caused by erosional exhumation that is directly
related in both space and time to rock uplift in hanging walls of active thrust faults.
Although this is clearly an oversimplification, because each transect represents a
relatively confined location within the Sevier belt, and because these locations lie in the
hanging walls of major thrust sheets (fig. 2), this assumption seems appropriate. Zircon
He dates from thrust sheet hanging walls in other orogens have also been interpreted in
this manner, and these dates are consistent with other constraints of thrust timing (e.g.,
Metcalf et al., 2009; Pearson et al., 2012). If we use this assumption, then our data
214
suggest that thrusting in the CNS hinterland moved progressively eastward with time (fig.
17). This process was initiated with movement along the Tintic Valley thrust at 120 Ma
followed by activation of the Midas Thrust at either 110 Ma or 100 Ma and movement
along the Nebo thrust beginning at 100 Ma (fig. 17). A 120-100 Ma period of thrust
propagation at the rear of the CNS has implications for the broader thrusting history in
central Utah, the dynamics of the evolving orogenic wedge, and the deposition of
foreland basin units.
Placed in a regional context, our results are consistent with several previous
interpretations of deformation in the central Utah Sevier belt. Mitra (1997) inferred early
Aptian exhumation of the Sheeprock thrust sheet from paleocurrents and clast counts in
the Pigeon Creek Formation at Thistle (fig. 2, Schwans, 1988), and our date of 120 Ma
for the Tintic Valley thrust fits this timing. Either the Tintic Valley and Sheeprock thrusts
were active coevally at ~120 Ma, or our new constraints push back the timing of
Sheeprock activity into the Neocomian. Regardless, the Stansbury tT paths agree with
arguments that thrusting was ongoing in this area since at least the mid Early Cretaceous
(DeCelles, 2004). The ZRDAAM results for exhumation in the Tintic Valley thrust sheet
are also roughly coeval with orogen-parallel extension in northern Utah (Wells et al.,
2008), which suggests that hinterland extension and frontal contraction may have been
linked at this time. Mid Cretaceous (40Ar/39Ar date on phlogopite of 105 ± 6 Ma) collapse
and extension of a large hinterland culmination in the Raft River, Albion, and Grouse
Creek Mountains core complexes could have transferred stress towards both the north
and south, resulting in congruent shortening of the adjacent fold-and-thrust belt (Wells et
215
al., 2008). Our constraints for exhumation of the Stansbury Mountains—ranges that are
located to the southeast of the Raft River complex—agree with this hypothesis.
At the front of the CNS, the Mount Timpanogos transect tT paths, and possibly
the Oquirrh tT paths as well, fit within Constenius et al.’s (2003) framework for the
structural evolution of the Santaquin Culmination. On the basis of growth strata and
erosional truncations, these authors proposed that the Santaquin Culmination grew in two
main phases: 1) initial movement along the Nebo thrust and triangle zone formation
(~100-90 Ma), and 2) a period of internal shortening and growth of an antiformal stack
(~90-40 Ma). The tT results for Timpanogos match the timing for establishment of the
triangle zone, and—with the results from the Stansbury and Oquirrh Mountains—suggest
a change in the style of thrusting in the CNS from translational between 120 and 100 Ma
to initial internal duplexing between 100 and 90 Ma.
A switch in thrusting style that occurred between 100 and 90 Ma might have
implications for the Cretaceous evolution of critical taper in the CNS orogenic wedge.
Because of its relatively continuous advance towards the foreland, we speculate that the
CNS wedge was supercritical from at least 120 Ma to 100 Ma, and possibly earlier
depending on the timing of movement along the Sheeprock thrust. Following initial
movement on the Nebo thrust and exhumation of Mount Timpanogos, the wedge entered
a subcritical phase as propagation ceased and growth of the culmination commenced. The
transition from relatively thick miogeoclinal units west of the WNF, to much thinner
miogeoclinal units east of the hinge line (Hintze and Kowallis, 2009) may explain the
change in wedge criticality. Because our transects are either directly on or to the west of
216
the Wasatch hinge line, the Tintic Valley, and we expect the Midas and Nebo thrusts as
well, carry thick sequences of siliciclastic and massive carbonate units in their hanging
walls. Wedge taper (equal to the sum of the surface slope plus the angle of the basal
decollement) can remain critical at relatively low angles if thrusts propagate into these
types of sedimentary units (DeCelles and Mitra, 1995), and little internal deformation
was therefore required between 120 and 100 Ma to increase the surface slope and
maintain critical taper. However, once the basal décollement ramped up into the thinner
strata east of the hinge line (ca. 100-90 Ma), the angle of taper necessary for criticality
increased, forcing the wedge to deform internally via duplexing.
Regardless of the cause, growth of the Santaquin Culmination between 100 and
40 Ma may have focused erosion at the front of the CNS, decreasing exhumation in the
hinterland. Prior to the rise of the culmination, exhumation of the Sheeprock and perhaps
the Midas and Tintic Valley thrusts contributed coarse-grained detritus to the Pigeon
Creek (or Cedar Mountain) Formation (Mitra, 1997). On the basis of PrecambrianMesozoic clast counts, Horton et al. (2004) suggested that rocks continued to be derived
from these hinterland thrust sheets until the Santonian-Campanian, and were deposited in
the Blackhawk Formation of the Upper Indianola Group (fig. 17). Another major pulse of
exhumation occurred during the late Campanian, contributing Oquirrh Group clasts to
Castlegate Sandstone-equivalent units at the front of the CNS. Although we agree with
the assessment that Precambrian clasts originated west of the hinge line, we argue that
they were likely recycled and exhumed along thrust sheets located in the Santaquin
Culmination proper. Our preferred tT scenarios for Mount Timpanogos and the Oquirrh
217
have almost no exhumation occurring in the Campanian and it seems unlikely that they
were being significantly eroded at this time. A Campanian exhumation event is consistent
with the inheritance envelope for the 5 km at 80 Ma scenario in the Stansbury transect
(fig. 11b), but the tT path required for this envelope has no Early Cretaceous exhumation,
which is inconsistent with the geologic framework as detailed above. Within the
Santaquin Culmination, these recycled clasts may have come from wedgetop or foredeep
units east of Mount Timpanogos, as our thermal histories also preclude a major pulse of
Santonian-Campanian exhumation for this location. To explain the absence of Late
Cretaceous hinterland exhumation that matches Horton et al.’s (2004) observations in at
least the Mount Timpanogos and Oquirrh datasets, we suggest that the Santaquin
Culmination served as an orographic barrier focusing erosion along its front and
preventing erosion in the hinterland. The windward side of this barrier would have been
facing towards the east with moisture coming off of the Cretaceous interior seaway. With
the initial rise of the Santaquin Culmination after 100 Ma, the Oquirrh Mountains were
left isolated behind a growing orographic barrier that halted continued exhumation. In
this context, we propose that all three transects may have been sitting high and dry on the
so-called Nevadaplano (DeCelles, 2004) during the Late Cretaceous.
6. Conclusions
Because of the method’s inherent challenges, practitioners of zircon (U-Th)/He
thermochronology can often be dissuaded from making accurate geologic conclusions in
partially reset, detrital settings. However, with an understanding of the coevolution of
218
radiation damage, He diffusion kinetics, and He date in zircon through time, coupled with
detailed information about a region’s geologic history, we can place some constraints on
a sample’s thermal history in these settings. Our samples from three sub-vertical transects
in the CNS are good examples of datasets that match these criteria. In an attempt to
interpret the tT histories for these transects, we considered the full date spread in a given
sample or transect and explored how the combined factors of He inheritance and
radiation damage influenced specific dates. Our approach relied upon a new radiation
damage and annealing model for He diffusion in zircon (Guenthner et al., 2013) and both
explained some of the sources of date dispersion and demonstrated this model’s utility.
Guenthner et al. (2013) previously showed how radiation damage influences zircon He
dates, manifesting as positive and negative date-eU correlations, which we have used to
constrain tT paths for each of our sample locations. A new finding from this study though
is that radiation damage and He inheritance can interact in partially reset samples to
produce an “inheritance envelope” that expands to older dates at progressively lower eU
concentrations. In the case of our Oquirrh Mountains transect, these envelopes were used
to help constrain the thermal history of this particular range.
Although the Stansbury dataset is perhaps too complex to fully constrain, we can
rule out certain thermal histories for this dataset and tentatively assign a date of 120 Ma
for the beginning of Cretaceous exhumation. The tT results from the Oquirrh and Mount
Timpanogos transects are more conclusive and also offer some insight into the
Cretaceous thrusting history of the CNS. Specifically, they provide a timing framework
for the transition from a phase of continuous eastward progradation (at least 120 to 100
219
Ma) to one of initial internal deformation and growth of the Santaquin Culmination (10040 Ma). This timing in turn supports previous hypotheses about the changing nature of
the orogenic wedge throughout the Sevier orogeny, but also provides new information
about the evolving pattern of erosion in the CNS during the Cretaceous. Because the
ZRDAAM results from all three transects conform to many past inferences about
thrusting in this region, we have some confidence that this new and relatively untested
model can explain zircon He date variability in a manner consistent with a sample’s
regional geologic setting. These dates represent some of the first in situ measurements of
exhumation related to the Cretaceous Sevier fold-and-thrust belt, and could be used in the
future to tie the exhumation of particular thrust sheets in the Sevier belt to the deposition
of specific units in the adjacent foreland basin.
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Silberling, N.J., Nichols, K.M., Trexler, J.H. Jr., Jewell, P.W., and Crosbie, R.A., 1997,
Overview of Mississippian depositional and paleotectonic history of the Antler foreland,
eastern Nevada and western Utah, in Link, P.K., and Kowallis, B.J., editors, Mesozoic to
Recent geology of Utah: Brigham Young University Geology Studies, v. 42, part 2, p.
161-198.
Solien, M.A., 1979, Conodont biostratigraphy of the Lower Triassic Thaynes Formation,
Utah: Journal of Paleontology, v. 53, p. 276-306.
Spiegel, C., Kohn, B., Belton, D., Berner, Z., Gleadow, A., Apatite (U-Th-Sm)/He
thermochronology of rapidly cooled samples: The effect of He implantation: Earth and
Planetary Science Letters, v. 285, p. 105-114.
Stevens, C.H., and Armin, R.A., 1983, Microfacies of the Middle Pennsylvanian part of
the Oquirrh Group, central Utah, in Miller, D.M., Todd, V.R., and Howard, K.A., editors,
Tectonic and stratigraphic studies in the eastern Great Basin: Geological Society of
America Memoir 157, p. 83-100.
230
Stockli, D., Linn, J.K., Walker, J.D., and Dumitru, T.A., 2001, Miocene unroofing of the
Canyon Range during extension along the Sevier Desert detachment, west central Utah:
Tectonics, v. 20, p. 289-307.
Tooker, E.W., 1983, Variations in structural style and correlation of thrust plates in the
Sevier foreland thrust belt, Great Salt Lake area, Utah, in Miller, D.M., Todd, V.R., and
Howard, K.A., editors, Tectonic and stratigraphic studies in the eastern Great Basin:
Geological Society of America Memoir 157, p. 61-74.
Tooker, E.W., and Roberts, R.J., 1970, Upper Paleozoic rocks in the Oquirrh Mountains
and Bingham mining district, Utah: U.S. Geological Survey Professional Paper 629-A, 76
p.
Turcotte, D.L., and Schubert, G., 2002, Geodynamics: New York, Cambridge University
Press, 456 p.
Wells, M.L., Spell, T.L., Hoisch, T.D., Arriola, T., and Zanetti, K.A., 2008, Laser-probe
40
Ar/39Ar dating of strain fringes: Mid-Cretaceous synconvergent orogen-parallel
extension in the interior of the Sevier orogen: Tectonics, v. 27, doi:
10.1029/2007TC002153.
231
Willis, A., 2000, Tectonic control of nested sequence architecture in the Sego Sandston,
Neslen Formation and Upper Castlegate Sandstone (Upper Cretaceous), Sevier Foreland
Basin, Utah, USA: Sedimentary Geology, v. 136, p. 277-317.
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architecture in the Castlegate Sandstone (Upper Cretaceous), Book Cliffs, Utah: Journal
of Sedimentary Research, v. 66, p. 737-748.
40 27.571
40 27.571
40 27.571
40 27.571
40 27.571
40 27.571
40 27.821
40 27.821
40 27.821
40 27.821
40 27.821
40 27.821
40 28.025
40 28.025
40 28.025
40 28.025
40 28.025
40 28.025
40 28.795
10UTSD2_1
10UTSD2_2
10UTSD2_3
10UTSD2_4
10UTSD2_5
10UTSD2_6
10UTSD3_1
10UTSD3_2
10UTSD3_3
10UTSD3_4
10UTSD3_5
10UTSD3_6
10UTSD4_1
Lat.
10UTSD1_1
10UTSD1_2
10UTSD1_3
10UTSD1_4
10UTSD1_5
10UTSD1_6
Stansbury
Mountains
Sample
Name
-112 37.757
-112 37.757
-112 37.757
-112 37.757
-112 37.757
-112 37.757
-112 37.625
-112 37.687
-112 37.687
-112 37.687
-112 37.687
-112 37.687
-112 37.687
-112 37.580
-112 37.580
-112 37.580
-112 37.580
-112 37.580
-112 37.580
Long.
3074
3074
3074
3074
3074
3074
2872
3207
3207
3207
3207
3207
3207
3361
3361
3361
3361
3361
3361
3.15
7.85
11.0
27.0
6.12
5.07
5.96
10.0
9.59
14.6
4.84
5.50
4.53
14.3
9.02
3.60
4.29
6.63
13.8
41
51
52
71
44
44
54
62
54
61
50
54
39
59
53
37
44
50
62
534
471
157
1307
705
257
259
50.1
129
170
434
869
286
1339
151
112
61.0
130
184
131
147
172
1104
212
712
175
47.1
92.0
127
281
712
231
675
139
157
38.9
72.1
348
241
224
93.7
577
322
204
117
25.5
173
97.8
351
495
145
481
103
102
26.3
65.7
163
0.74
0.80
0.81
0.86
0.77
0.76
0.80
0.83
0.81
0.83
0.79
0.80
0.75
0.83
0.80
0.73
0.76
0.78
0.83
4
Elevation Mass Halfwidth
U
Th
He
Ft
(m)
(µg)
(ppm) (ppm) (nmol/g)
(µm)
TABLE C1. ZIRCON (U-Th)/He DATA
106
102
108
79.2
102
117
89.5
93.0
259
108
164
110
105
71.6
128
172
90.7
105
137
Corr.
Age
(Ma)
4.0
4.3
4.1
3.0
4.4
3.9
3.5
3.5
11
3.9
5.7
3.9
3.6
2.6
4.9
6.2
3.8
4.1
4.7
Analyt. ±
(2σ)
232
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.795
40 28.784
40 28.784
40 28.784
40 28.784
10UTSD4_2
10UTSD4_3
10UTSD4_4
10UTSD4_5
10UTSD4_6
10UTSD4Pb_1
10UTSD4Pb_2
10UTSD4Pb_9
10UTSD4Pb_10
10UTSD4Pb_11
10UTSD4Pb_12
10UTSD4Pb_13
10UTSD4Pb_14
10UTSD4Pb_16
10UTSD4Pb_23
10UTSD4Pb_24
10UTSD4Pb_29
10UTSD4Pb_30
10UTSD4Pb_31
10UTSD4Pb_34
10UTSD4Pb_35
10UTSD5_1
10UTSD5_2
10UTSD5_3
10UTSD5_4
-112 37.289
-112 37.289
-112 37.289
-112 37.289
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
-112 37.625
2699
2699
2699
2699
2872
2872
2872
2872
2872
2872
2872
2872
2872
2872
2872
2872
2872
2872
2872
2872
2872
2872
2872
2872
7.11
4.85
2.86
9.06
4.57
6.99
9.00
17.7
8.24
9.00
7.19
6.19
8.89
4.14
3.65
5.6
5.05
17.6
8.48
3.51
14.3
15.2
4.67
5.65
46
42
35
64
41
58
63
70
68
67
59
58
69
50
47
47
50
85
52
49
59
78
50
52
493
330
506
206
278
62.5
150
38.4
162
81.9
96.6
76.7
228
107
159
211
190
79.3
135
82.9
90.5
182
260
222
TABLE C1 (CONTINUED)
2872
6.51
56
388
352
364
93.2
553
338
41.1
197
26.7
115
41.4
61.3
43.2
94.8
67.8
134
155
89.6
46.4
64.8
64.5
44.5
123
187
88.6
171
406
183
214
324
140
25.8
87.0
14.9
73.1
44.1
43.0
33.0
106
50.9
97.5
125.4
95.3
28.1
65.8
40.2
47.1
91.3
125
96.4
183
0.78
0.76
0.72
0.82
0.75
0.81
0.82
0.85
0.86
0.87
0.86
0.85
0.87
0.83
0.82
0.81
0.84
0.89
0.83
0.82
0.86
0.89
0.83
0.84
0.81
166
107
104
215
95.2
81.3
98.8
72.6
82.8
103
83.8
82.9
90.4
92.7
116
115
99.9
64.8
97.3
92.4
101
90.2
91.2
87.2
97.3
6.3
3.7
4.2
7.0
3.3
3.1
3.5
2.6
4.5
4.0
2.8
2.5
3.3
2.7
3.3
4.7
3.1
2.2
4.4
2.7
4.4
6.4
3.7
4.5
4.2
233
-112 36.784
-112 36.784
-112 36.784
-112 36.784
-112 36.784
-112 36.784
112 12.115
112 12.115
112 12.115
112 12.115
112 12.115
112 12.115
40 28.799
40 28.799
40 28.799
40 28.799
40 28.799
40 28.799
40 25.198
40 25.198
40 25.198
40 25.198
40 25.198
40 25.198
40 25.539
40 25.539
10UTSD7_1
10UTSD7_2
10UTSD7_3
10UTSD7_4
10UTSD7_5
10UTSD7_6
Oquirrh
Mountains
10UTOO1_1
10UTOO1_2
10UTOO1_3
10UTOO1_4
10UTOO1_5
10UTOO1_6
10UTOO3_1
10UTOO3_2
112 11.925
112 11.925
-112 37.104
-112 37.104
-112 37.104
-112 37.104
-112 37.104
-112 37.104
40 28.425
40 28.425
40 28.425
40 28.425
40 28.425
40 28.425
10UTSD6_1
10UTSD6_3
10UTSD6_4
10UTSD6_5
10UTSD6_6
10UTSD6_7
-112 37.289
-112 37.289
40 28.784
40 28.784
10UTSD5_5
10UTSD5_6
3226
3226
2850
2850
2850
2850
2850
2850
2425
2425
2425
2425
2425
2425
2557
2557
2557
2557
2557
2557
5.47
4.58
3.07
2.02
3.07
3.77
3.28
1.79
9.06
6.50
3.61
6.78
4.91
4.32
13.7
6.63
7.64
5.89
11.1
5.47
41
50
35
32
36
49
36
31
69
45
40
59
46
42
60
53
55
42
70
42
184
67.8
266
374
734
198
665
611
144
556
491
260
192
319
1006
110
292
1814
182
840
TABLE C1 (CONTINUED)
2699
8.66
53
102
2699
6.61
53
252
139
87.3
171
165
237
240
482
77.4
116
370
123
306
200
300
1156
92.0
190
157
182
398
3.28
199
144
62.9
129
175
544
197
350
265
92.6
455
228
185
111
145
611
48.8
113
370
98.9
246
53.2
238
0.83
0.81
0.79
159
167
108
113
174
183
114
113
120
167
108
126
112
91.0
106
85.3
77.2
47.9
96.3
63.5
118
185
5.6
5.0
3.5
4.0
6.2
5.3
3.6
4.0
3.7
5.5
4.0
3.9
3.6
2.8
4.4
2.7
2.6
1.8
3.1
2.1
5.0
8.1
234
40 25.539
40 25.539
40 25.539
40 25.539
40 25.636
40 25.636
40 25.636
40 25.636
40 25.636
40 25.636
40 25.746
40 25.746
40 25.746
40 25.746
40 25.746
40 25.746
40 25.510
40 25.510
40 25.510
40 25.510
40 25.510
40 25.510
40 25.510
10UTOO3_3
10UTOO3_4
10UTOO3_5
10UTOO3_6
10UTOO4_1
10UTOO4_2
10UTOO4_3
10UTOO4_4
10UTOO4_5
10UTOO4_6
10UTOO5_1
10UTOO5_2
10UTOO5_3
10UTOO5_4
10UTOO5_5
10UTOO5_6
10UTOO6_1
10UTOO6_2
10UTOO6_3
10UTOO6_4
10UTOO6_5
10UTOO6_6
10UTOO7_1
112 12.537
112 12.537
112 12.537
112 12.537
112 12.537
112 12.537
112 12.537
112 12.730
112 12.730
112 12.730
112 12.730
112 12.730
112 12.730
112 12.156
112 12.156
112 12.156
112 12.156
112 12.156
112 12.156
112 11.925
112 11.925
112 11.925
112 11.925
2612
2757
2757
2757
2757
2757
2757
2894
2894
2894
2894
2894
2894
3111
3111
3111
3111
3111
3111
1.44
2.03
1.40
4.89
3.16
2.09
5.32
2.03
4.23
12.0
8.83
4.76
11.4
10.8
8.95
42
32
31
35
37
43
42
48
39
32
51
37
41
58
61
43
67
57
61
159
827
210
232
562
538
336
216
486
295
1032
199
182
338
813
351
131
122
600
TABLE C1 (CONTINUED)
3226
2.71
35
270
3226
2.31
33
190
3226
2.05
33
289
3226
2.56
40
176
138
655
78.6
60.1
71.9
196
372
93.4
352
131
257
129
99.7
247
378
78.0
72.2
111
57.6
205
116
104
91.6
134
476
136
84.9
292
283
197
103
222
272
1095
110
137
256
536
268
149
132
412
174
115
159
89.5
181
134
159
91.3
137
124
121
103
98.1
221
231
123
163
144
133
173
219
202
152
141
139
134
113
4.8
4.5
6.2
3.5
4.0
3.5
3.1
3.7
3.5
7.5
8.4
4.4
6.2
4.6
4.5
6.4
7.4
6.5
5.6
4.6
4.7
4.5
3.8
235
40 25.510
40 25.510
40 25.510
40 25.510
40 25.510
40 25.261
40 25.261
40 25.261
40 25.261
40 25.261
40 25.261
40 24.918
40 24.918
40 24.918
40 24.918
40 24.918
40 24.918
40 24.283
40 24.283
40 24.283
40 24.283
40 24.283
40 24.283
10UTOO7_2
10UTOO7_3
10UTOO7_4
10UTOO7_5
10UTOO7_6
10UTOO8_1
10UTOO8_2
10UTOO8_3
10UTOO8_4
10UTOO8_5
10UTOO8_6
10UTOO9_1
10UTOO9_2
10UTOO9_3
10UTOO9_4
10UTOO9_5
10UTOO9_6
10UTOO10_1
10UTOO10_2
10UTOO10_3
10UTOO10_4
10UTOO10_5
10UTOO10_6
112 13.484
112 13.484
112 13.484
112 13.484
112 13.484
112 13.484
112 12.690
112 12.690
112 12.690
112 12.690
112 12.690
112 12.690
112 12.834
112 12.834
112 12.834
112 12.834
112 12.834
112 12.834
112 12.537
112 12.537
112 12.537
112 12.537
112 12.537
2189
2189
2189
2189
2189
2189
2432
2432
2432
2432
2432
2432
2553
2553
2553
2553
2553
2553
41
38
39
40
49
41
59
43
42
40
52
46
44
58
53
49
43
48
439
202
554
632
76.8
427
170
785
199
272
137
112
140
143
354
320
321
265
TABLE C1 (CONTINUED)
2612
37
612
2612
41
258
2612
41
272
2612
42
196
2612
37
332
237
105
82.6
122
28.5
51.6
64.0
343
88.1
85.5
70.9
77.9
82.6
48.5
205
83.6
96.4
77.4
305
92.2
162
85.8
189
244
201
281
266
45.2
245
84.7
459
145
204
85.9
51.4
57.8
190
203
182
267
131
226
146
134
82.4
161
128
235
129
106
132
144
107
135
170
183
134
98.5
92.4
283
121
131
197
114
90.3
136
113
98.9
116
3.3
6.2
3.7
2.8
3.4
4.0
3.0
3.8
4.7
5.1
3.6
2.5
2.5
8.0
3.3
3.8
5.7
3.3
2.5
3.9
3.1
2.8
3.2
236
40 23.451
40 23.451
40 23.451
40 23.451
40 23.451
40 23.451
40 23.942
40 23.942
40 23.942
40 23.942
40 23.942
40 23.942
40 24.258
40 24.258
40 24.258
40 24.258
40 24.258
40 24.258
40 24.258
40 24.258
40 24.258
40 24.258
40 24.258
Mount
Timpanogos
10UTT1_1
10UTT1_2
10UTT1_3
10UTT1_4
10UTT1_5
10UTT1_6
10UTT6_1
10UTT6_2
10UTT6_3
10UTT6_4
10UTT6_5
10UTT6_6
10UTT7_1
10UTT7_2
10UTT7_3
10UTT7_4
10UTT7_5
10UTT7_6
10UTT7_7
10UTT7_8
10UTT7_9
10UTT7_10
10UTT7_11
111 37.704
111 37.704
111 37.704
111 37.704
111 37.704
111 37.704
111 37.704
111 37.704
111 37.704
111 37.704
111 37.704
111 37.811
111 37.811
111 37.811
111 37.811
111 37.811
111 37.811
111 38.757
111 38.757
111 38.757
111 38.757
111 38.757
111 38.757
2414
2414
2414
2414
2414
2414
2414
2414
2414
2414
2414
2757
2757
2757
2757
2757
2757
3579
3579
3579
3579
3579
3579
35
36
37
39
43
43
35
37
42
38
37
42
41
42
35
37
36
36
43
44
42
41
40
1099
390
542
669
130
195
449
749
205
265
333
166
327
54.3
1040
388
422
439
294
255
279
836
745
TABLE C1 (CONTINUED)
70.4
121
185
183
117
29.7
148
132
125
93.7
102
48.0
124
22
334
160
254
43.4
160
89.1
124
65.7
361
303
112
171
185
39.7
54.5
134
190
69.1
79.9
112
54.8
108
17.3
399
140
142
135
135
121
88.3
389
517
75.2
73.8
79.1
69.1
64.9
68.9
77.4
66.0
76.3
74.8
85.2
79.6
79.1
75.1
99.5
89.5
81.3
82.1
104
111
74.0
118
164
2.5
2.0
2.1
1.9
1.6
1.9
2.4
2.8
2.3
2.4
2.7
2.6
2.5
2.4
3.7
2.9
2.5
2.3
2.6
3.2
2.0
3.6
5.3
237
10UTT7_12
40 24.258
111 37.704
TABLE C1 (CONTINUED)
2414
52
349
227
187
113
3.4
238
239
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Figure C1: Model date-eU curves and inheritance envelopes generated from the five
different thermal histories shown in the top right panel. These thermal histories simulate
burial and exhumation of a detrital sample in a sedimentary basin and consist of slow
heating to a maximum temperature (in parenthesis) starting at 500 Ma and ending at 250
Ma, followed by slow cooling to surficial temperatures ending at the present. Six date-eU
curves are modeled in each scenario, consisting of a zero-inheritance curve, which is the
240
date-eU curve that results from each tT path as shown in the top right, and five maximum
inheritance curves resulting from the same post-depositional tT path as the zeroinheritance curve, plus an additional pre-depositional tT step. For example, the thermal
history for the 800 Ma curve has an additional point placed at 20°C and 800 Ma, which
creates a single temperature step that holds each zircon at 20 °C for 300 m.y. (from 800
Ma to 500 Ma). Heavy dashed lines represent the full extent of the envelope in each
scenario. In scenarios 1 through 4, temperatures are not high enough to anneal significant
amounts of damage and so a strong negative correlation exists at high eU. The
temperatures in scenario 5 (320 °C), however, do cause significant annealing and no
negative correlation is produced. This scenario also has temperatures high enough to
eliminate all inherited damage or He, which makes all of the maximum inheritance
curves identical to the zero-inheritance curve. Two data points are included in all date-eU
plots, one with an eU of 190 ppm and a date of 250 Ma (yellow circles), the other with an
eU of 190 ppm and a date of 750 Ma. These points illustrate the utility of inheritance
envelopes for constraining thermal histories (see text for details).
241
Figure C2: Regional geologic map for Charleston-Nebo Salient with key thrust faults,
mountain ranges, and towns annotated. Inset shows map location within the state of Utah.
Faults are dotted where location is inferred. Dashed lines represent transverse faults.
Yellow circles denote sub-vertical transect locations.
242
Figure C3: Geologic map of the Stansbury transect with cross-section. Sample symbols
(circles vs. triangles) are consistent with the symbols used in figures 7-11.
Cpm=Cambrian Prospect Mountain, Cum=upper and middle Cambrian strata undivided,
MDgs=Devonian-Mississippian Stansbury Formation through Gardison Limestone,
Md=Mississippian Deseret Formation, Qg=Quaternary glacial deposits. Dashed and
dotted lines in cross-section denote stratigraphic horizons that are approximately
equivalent. Adapted from Clark et al. (2012).
243
Figure C4: Geologic map of the Oquirrh transect with cross-section. Sample symbols
(circles vs. triangles) are consistent with the symbols used in figures 7 and 12-14.
Pobp=Pennsylvanian Butterfield Peak Formation (Oquirrh Group). Dashed and dotted
line in cross-section denote stratigraphic horizons that are approximately equivalent.
Adapted from Clark et al. (2012).
244
Figure C5: Geologic map of the Mount Timpanogos transect with cross-section. Sample
symbols (circles vs. squares vs. triangle) are consistent with the symbols used in figures
7, 15, and 16. Pobc=Pennsylvanian Bear Canyon Formation (Oquirrh Group),
Pobv=Pennsylvanian Bridal Veil Limestone (Oquirrh Group), Qal=Quaternary alluvium.
Adapted from Constenius et al., 2011.
245
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246
Figure C6: Date-elevation plots for the (a) Stansbury, (b) Oquirrh, and (c) Mount
Timpanogos transects. Probability density function plots for each location are included as
well.
247
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Figure C7: Date-eU plots for the a) Stansbury, b) Oquirrh, and c) Mount Timpanogos.
The shape of each point (circle, triangle, or square) matches the symbols used in figures
3-5 to denote the various samples (see text for details).
248
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Figure C8: Summary of tT paths used in the forward models of each transect. The major
geologic events that led to each episode of burial or exhumation are annotated (see text
for details).
249
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Figure C9: Forward model results for the Stansbury Mountains transect using a
geothermal gradient of 20 °C/km. Because we are not matching samples 10UTSD5 and 6
to our model curves, the triangles that represent these samples have been made
transparent. Corresponding tT paths are shown in the panels below each date-eU plot.
Black curves are for a grain size of 54 microns (mean), and the dashed grey curves are for
grain sizes of 75 and 33 microns (2 standard deviations). (a) Results from tT paths with 4,
5, and 6 km of exhumation at 120 Ma. (b) Results from tT paths with 4, 5, and 6 km of
exhumation at 100 Ma.
250
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!5#")*6&Figure C10: Forward model results for the Stansbury transect using a geothermal gradient
of 25 °C/km. Symbols and plots are similar to figure 9. Scenarios consist of 4, 5, and 6
km of exhumation starting at 120 Ma.
251
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252
Figure C11: (a) Stansbury transect model curve from tT path with 5 km of exhumation at
120 Ma (as shown in figure 9a) and two inheritance date curves (labeled 1100 and 1700
Ma). Inset shows the same plot from 0 to 500 ppm eU and 0 to 150 Ma. The tT path for
these inheritance curves is the same as shown in figure 12, but with an additional step at
20 °C and either 1100 or 1700 Ma. (b) Stansbury transect model curve from tT path with
5 km of exhumation at 80 Ma and two inheritance date curves (labeled 1100 and 1700
Ma). Inset shows the same plot from 0 to 500 ppm eU and 0 to 150 Ma. Corresponding tT
path is shown just below the date-eU plot. This path was appended with additional steps
of 20 °C at either 1100 or 1700 Ma.
253
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Figure C12: Forward model results for the Oquirrh transect using a geothermal gradient
of 20 °C/km. Symbols and plots are similar to figure 9. (a) Model curve resulting from 3
km of exhumation at 110 Ma. (b) Results for model tT paths with 6 km of exhumation at
100 Ma.
254
8
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Figure C13: Inheritance date-eU curves (labeled 1100 and 1700 Ma) for Oquirrh transect
tT paths with (a) 3 km of exhumation at 110 Ma and (b) 6 km of exhumation at 100 Ma
(both with a 20 °C/km geothermal gradient). The tT paths for these inheritance curves are
the same as shown in figure 12, but with an additional step at 20 °C and either 1100 or
1700 Ma.
255
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Figure C14: Inheritance date-eU curves (labeled 1100 and 1700 Ma) for the Oquirrh
transect. Both tT paths have 6 km of exhumation at 100 Ma, but the curve in (a) was
calculated with a 20 °C/km geothermal gradient, whereas the curve in (b) was calculated
with a 25 °C/km geothermal gradient.
256
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Figure C15: Forward model results for sample 10UTT7 from the Mount Timpanogos
transect using a geothermal gradient of 20 °C/km. Symbols and plots are similar to figure
9. (a) Model curve resulting from 5 km of exhumation at 100 Ma. (b) Results for model
tT paths with 4 and 6 km of exhumation at 100 Ma. Curve from panel a is in grey. (c)
Results from model tT path with 5 km at 90 Ma and at 80 Ma. Curve from panel a is in
grey.
257
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Figure C16: Forward model results for samples 10UTT6 (squares) and 10UTT7 (circles)
from the Mount Timpanogos transect with 5 km of exhumation at 100 Ma and 5 km of
exhumation at 90 Ma (both with a 20 °C/km geothermal gradient). Solid black line is the
date-eU curve for 10UTT7, while the dashed black line is the date-eU curve for 10UTT6.
258
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Figure C17: Kinematic history of thrusting in the CNS from previous authors and
constraints presented in this study. The grey area represents Constenius et al.’s (2003)
timing for growth of the Santaquin Culmination. For reference, a schematic composite
stratigraphic chart from the neighboring Book Cliffs (fig. 2) is included on the right.
Adapted from Schwans (1988), Mitra (1997), Constenius et al., (2003), and DeCelles
(2004).
259
APPENDIX D: PERMISSIONS
260
American Journal of Science
217 Kline Geology Laboratory Yale University
P.O. Box 208109
New Haven, Connecticut 06520-­8109 E.mail: ajs@yale.edu
Campus address: Kline Geology Laboratory
210 Whitney Avenue Telephones: 203 432-­3131 203 432-­5668 FAX: 203 432-­5668 April 18, 2013
William Guenthner Department of Geosciences University of Arizona 1040 E. 4th Street Tucson, AZ 85721 Dear Mr. Guenthner, We understand that you are preparing your Ph. D. thesis titled Zircon (U-­
Th)/He dates from radiation damaged crystals: A new model for the zircon (U-­Th/He thermochronometer and you would like to include the following paper in your thesis: Guenthner, W. R., Reiners, P. W., Ketcham, R. A., Nasdala, L., and Giester, G., 2013, Helium diffusion in natural zircon: Radiation damage, anisotropy, and the interpretation of zircon (U-­‐Th)/He thermochronology, v. 313, p. 145-­‐198, doi 10.2475/03.2013.01. We understand that credit will be given to the American Journal of Science for the
original work and permission for its use.
PERMISSION GRANTED.
Sincerely,
Danny M. Rye, Editor