Toasting the jelly sandwich: The effect of shear heating on
lithospheric geotherms and strength
Ebbe H. Hartz
Physics of Geological Processes, University of Oslo, 0316 Oslo, Norway, and Aker Exploration,
Haakon VII’s gt. 9, P.O. Box 580, Sentrum, NO, 4003 Stavanger, Norway
Yuri Y. Podladchikov Physics of Geological Processes, University of Oslo, 0316 Oslo, Norway
Strain rate (ε)
= 3 × 10–15
40
100
0
200 400 600 800
Temperature (°C)
P
o
e
80
w
r la
we
lur
60
Moho
fai
Depth (km)
20
B
le
DYNAMIC VERSUS STATIC MODELS OF LITHOSPHERIC
STRENGTH AND TEMPERATURE
The lithosphere encases the convecting, fluid-like silicate Earth. It
can be strong enough to resist deformation for billions of years, but it also
undergoes short phases (tens of millions of years) of rapid deformation.
Mechanical strength and temperature are key controls on magmatism
and lithospheric deformation. Lithospheric strength estimates from laboratory deformation experiments (Brace and Kohlstedt, 1980) or inferred
from natural observations (Jeffreys, 1970) are commonly summarized in a
global, one-dimensional model, the “Brace-Goetze lithosphere” or “BraceGoetze strength envelope” (Molnar, 1992). This model incorporates both
brittle rock strength, increasing with pressure (depth), and viscous rock
strength, which is a function of rock properties, strain rate, and temperature, and generally decreases with depth (Fig. 1). Rocks are assumed to
fail by the weaker of the two criteria, resulting in a branched strength
envelope with a strong, brittle (seismogenic) upper crust, and dry rock in
the lower crust or upper mantle, separated by a weak ductile middle crust
(Buck, 1991; Carter and Tsenn, 1987; Burov and Watts, 2006): the “jelly
sandwich” (Jackson, 2002). These traditional, one-dimensional mechanical models of lithospheric strength (the Brace-Goetze lithosphere) ignore
the thermal effects of deformation (Molnar, 1992). In such models, orogenic thickening would stretch the geotherm and thus cause a decay in
the geothermal gradient. However, high surface heat flow and magmatism
show that thick orogens are hotter than the stable continental lithosphere
at a given depth (Chapman and Furlong, 1992; Pollack et al., 1993). Had it
not been for this “orogenic heat”, Earth’s lithosphere would be ~20 times
too strong to deform under tectonic forces, and orogenic processes would
be violent and short-lived, affecting only narrow sutures between colliding
plates (Hyndman et al., 2005). Orogenic heat has been attributed to preorogenic or nonorogenic processes such as the rise of hot asthenospheric
material following delamination and sinking of relatively colder, denser
lithosphere from an orogenic root (Hyndman et al., 2005), or short-lived
tectonic wedges of highly radiogenic material (Jamieson et al., 1998).
.
A
0
itt
br
or
lee
er
By
Keywords: shear heating, lithosphere, strength, geotherm, rheology, heat
flow.
Shear heat (10–6 W m–3)
0
3
6
9
s
ition
ond g
ial c atin
Init r he
a
She
ting
ar hea
No she
ABSTRACT
We refine conventional continental-scale geodynamic models by
including conversion of mechanical work done by deformation into
heat. The intensity of the shear heating is extracted from the BraceGoetze strength envelope without any additional model parameters or
assumptions. Incorporation of this, certainly present, heating rate into
a model may result in up to tenfold stress reduction, which is exceeding
the effects of variation of common parameters within their uncertainty
limits. Shear heating with lithospheric thickening at high integrated
strength solves the puzzle of the heretofore-missing heat source
recorded by metamorphism, magmatism, and heat flow in mountain
building. However, the mechanism is self-limiting as the rising temperature reduces stress and thus the rate of heat production. Thus this is
a self-regulating mechanism maintaining a moderate integrated lithospheric strength consistent with results of model-independent forcebalanced calculations and with surface heat flow measurements.
Shear heating
No shear heating
0
10
20 30 40
Strength (Δσ, kbar)
50
Figure 1. Lithospheric temperature and strength profiles with and
without shear heating. Geotherm (A) and Brace-Goetze strength
envelope (B) illustrating rock strength through the lithosphere
before and after thickening of an isostatically balanced three-layer
(wet quartz upper crust, dry mafic granulite lower crust, and dry
dunite mantle) lithosphere for 9 m.y., so that the Moho deepens from
40 to 80 km depth. Shear heating reduces the strength by a factor of
ten, which is well above all traditional modeling variables.
Other explanations invoke shear heating by viscous deformation in
two- or three-dimensional finite-difference or finite-element models of
a complexly deforming lithosphere (Regenauer-Lieb et al., 2001, 2006;
Roselle and Engi, 2002; Burg and Gerya, 2005; Doglioni et al., 2005;
Kaus and Podlachikov, 2006).
Here we consider the effects on a lithospheric scale of shear heating
in a deforming continent, using a comparatively simple one-dimensional
approach. Shear heating intensity (W m–3) is equal to strength (differential
stress to be more precise) times strain rate, thus having units Pa s–1 (Stüwe,
2002). Multiplying the Brace-Goetze strength envelope by the strain rate
used to produce it therefore quantifies shear heating intensity throughout the
lithosphere (Fig. 1B, upper scale). In comparison to the above-cited studies,
this method is general and easy to implement. It furthermore includes dissipation for both brittle and viscous irreversible deformation, and works for
both lithospheric thickening and thinning. In addition, the approach allows
calculations of both lithospheric strength and shear heating rate to be easily
compared to model-independent force-balanced calculations and measurements of surface heat flow. We use this facility to explore temperature and
strength of a thickening lithosphere, composed of a wet quartz upper crust
(0–30 km initial depth; Carter and Tsenn, 1987), dry mafic granulite lower
crust (30–40 km initial depth; Wilks and Carter, 1990), and dry dunite
mantle (>40 km initial depth; Chopra and Paterson, 1981). Other modeling
properties and numerical methods are given in the GSA Data Repository.1
1
GSA Data Repository item 2008076, numerical methods, and a case showing the effect of shear heating in an extending lithosphere, is available online at
www.geosociety.org/pubs/ft2008.htm, or on request from editing@geosociety.org
or Documents Secretary, GSA, P.O. Box 9140, Boulder, CO 80301, USA.
© 2008 The Geological Society of America. For permission to copy, contact Copyright Permissions, GSA, or editing@geosociety.org.
GEOLOGY,
April
2008
Geology,
April
2008;
v. 36; no. 4; p. 331–334; doi: 10.1130/G24424A.1; 4 figures; Data Repository item 2008076.
331
SHEAR HEATING AND STRENGTH DECAY IN MODELS
WITH HIGH-STRESS CREEP
The magnitude of shear heating in our first compressional example
is tied with the 25 kbar stress inherent to the common, simplified BraceGoetze strength envelope, in which power law creep is the only mode of
viscous, compressional deformation (Fig. 1B). This is inappropriate for
deep Earth or high stress (Tsenn and Carter, 1987), where the weaker,
nonexponential “Dorn creep law” or “Peierls creep law” should be used
(Brace and Kohlstedt, 1980; Molnar, 1992; Stüwe, 2002; Goetze, 1978;
Tsenn and Carter, 1987). Use of the Dorn creep law (Goetze, 1978) in
the Brace-Goetze strength envelope for stresses above 6 kbar gives a substantial reduction of the initial lithospheric strength (Fig. 3B, lower scale):
Initial upper-mantle strength is 11 kbar rather than 25 kbar, and the corresponding shear heating is 3 × 10 –6 W m–3 rather than 7.5 × 10 –6 W m–3
(Fig. 3B, upper scale). Nevertheless, once thermomechanical feedbacks
have been taken into account, the temperature and strength profiles predicted with and without the Dorn creep law are indistinguishable after the
lithosphere is thickened, illustrating how shear heating overshadows all
other modeling parameters (Figs. 1A, 1B, 3A, and 3B).
SHEAR HEATING AND STRENGTH DECAY IN MODELS
WITH VARIABLE STRAIN RATE
Conventional models of lithospheric deformation assume a constant
strain rate throughout the lithosphere, with strong and weak rocks deforming at the same rate. The typical strain rate in these models of 10 –15 s–1 is
332
40
60
800
800
600
600
400
400
200
200
0
m.y.
6
B
8
30
20
20
0
9
2
m.y.
6
D
8
10
8
Kbar
2
(10–6 W m–3 )
0
10
80
0
100
0
2
4
m.y.
6
8
2
Δσ
60
5
Shear heating
Kbar
40
0
0
0
2
4
m.y.
6
10
(10–6 W m–3 )
0
100
Shear heating
80
0
oC
C
Temperature
Temperature
Depth (km)
20
Δσ
SHEAR HEATING AND STRENGTH DECAY IN DYNAMIC
COMPRESSIONAL MODELS WITH POWER LAW CREEP
In our first example the lithosphere is thickened, neglecting, as is
conventional, the effects of shear heating. Then, rocks in the lower crust
and upper mantle retain their low initial temperature during thickening
(Fig. 1A), and stress remains almost constant within creeping sections
(Fig. 1B). In contrast, differential stresses increase within brittle parts of
the rock column due to their downward displacement (rising pressure)
(Fig. 1B, blue lines). If rocks near the Moho deform under a differential
stress of 2.5 × 109 Pa (25 kbar) (Fig. 1B, lower scale) at a strain rate of
3 × 10 –15 s–1, as in conventional models (e.g., Jackson, 2002) (Fig. 1B,
black line), the neglected corresponding rate of shear heating is
7.5 × 10 –6 W m–3 (Fig. 1B, upper scale). This is an order of magnitude
greater than the radiogenic heat production in highly radiogenic rocks
(Turcotte and Schubert, 2002) and would raise the temperature 755 K per
100% strain in rock with a lower crustal density (3300 kg m–3) and heat
capacity (1000 J kg–1 K–1) if deformation were fast enough that the
heat was contained. At realistic strain rates, the actual rise in temperature
will be lower because the actual heat production is suppressed by the conduction of heat during shearing and the thermal weakening of the rocks.
As a result, a two-way, thermomechanically coupled model predicts a temperature rise of ~100 K with respect to the case without shear heating for
100% strain (Figs. 1A and 2A). Such a rise would cause the strength of the
upper mantle to drop by a factor of ten (Figs. 1B and 2B).
oC
A
0
Depth (km)
Traditionally, the Brace-Goetze strength envelope is taken to be static
(e.g., Molnar, 1992). Instead, our computer code “LiToastPhere” allows
rock units to thicken or thin according to ambient strain rates, as described
in the Data Repository. Stresses and thus shear heating in extensional settings are roughly a third of compressional settings. Thus here we focus on
a compressional scenario, in which the crust thickens from 40 to 85 km
with a strain rate of 3 × 10 –15 s–1, as has happened during the India-Asia
collision. We compare results with and without shear heating, and three
different modes of viscous deformation and strain rates. For comparisons,
we present an example of the effects of shear heating in an extending lithosphere in the GSA Data Repository.
0
8
Figure 2. Temperature (A and C) and strength and shear heating
(B and D) plotted against time for a lithosphere thickened to twice
its original thickness. The panels to the left show the dramatic effect
of shear heating when standard power law rheologies and constant
strain rate (3 × 10–15 s–1) are implied. The panels to the right illustrate
the more stable scenario implementing Dorn creep at high stresses
and the concentration of deformation in the weak middle crust. Shear
heating balances the lithospheric strength by thermal weakening, so
that after thickening, rocks have about the same strength regardless
of initial assumptions.
many orders of magnitude too slow for high-strain zones, for example along
detachment faults, and too fast for rigid blocks between these zones (Stüwe,
2002). To test the effect of a variable strain rate, we have modeled deformation of a lithosphere with strong upper crust, lower crust, and mantle,
deforming ten times slower (strain rate 10–15 s–1) than the weak middle crust
(strain rate 10 –14 s–1), while keeping the overall thickening rate of the
crust the same as in previous models. The resulting stresses are more evenly
distributed throughout the lithosphere (Fig. 3C), and stress and strain rate
patterns agree well with fully dynamic models in which two strong layers
(i.e., upper crust and upper mantle) bend up and down rather than thicken
to accommodate overall shortening (Schmalholz et al., 2005).
For lower strain rates of 10 –15 s–1, our earlier estimate of shear heating in the upper mantle (strength 10.5 kbar), is reduced to 10 –6 W m–3.
The corresponding rise in temperature could be as much as 315 K per
100% strain, but in our model, the upper mantle is thickened by only
33% during 9 m.y. of deformation. With two-way, thermomechanical
coupling, this gives an estimated temperature rise of only 50 K. Meanwhile, higher strain rates of 10 –14 s–1 in the middle crust do not contribute
significantly to shear heating due to weakness of the rocks (Figs. 3C
and 3D). Overall, this geologically more realistic model shows less
shear heat production than equivalent models with uniform strain rate
(Fig. 3D) and thus presents the strongest upper mantle of all shear heating scenarios discussed here (Fig. 3C).
GEOLOGY, April 2008
0
0
Va
ria
Shear heat (10–6 W m–3)
3
6
9
A
s
le
itt
Br
tr
p
ree
nc
ial c
ond
rate
Dor
–14
10
D
_
_
Variable strain rate
Constant strain rate
Before
thickening
on
si
es
pr
Init
ain
t str
10
ition
Depth (km)
10–15
–15
.
Shear-strain rate (γ) = 10–1
for 0.1 second
s
80
Shear heat (10–6 W m–3)
1
2
3
C
om
rc
fo
stan
60
Strain rate (ε)
(intial depth)
Strain rate (ε)
= 3 × 10–15
re
ilu
fa
te
ra
Con
40
in
a
20
.
B
.
bl
e
0
No shear heating
Shear heating = 108 W m–3
After
thickening
100
0
200 400 600 800
Temperature (°C)
0
10
20 30 40 50
Strength (Δσ, kbar)
0
10
20
30
40
Strength (Δσ, kbar)
Figure 3. Profiles of temperature, strength, and shear heating at variable modes of lithospheric deformation. Geotherm (A), Brace-Goetze
strength (B and C), and shear heating (D) profiles before and after thickening of the same lithosphere as in Figure 1. The two models both
include shear heating and high-stress creep laws for stresses above 6 kbar, but A applies constant strain rate, and B infers variable strain
rate and a simple shear (fault) zone just below the Moho at 80 km depth. Notice how the variable strain rate has little effect on the strength
(B and C) but a large effect on the shear heating (D) and thus temperature (A).
INTEGRATED LITHOSPHERIC STRENGTH COMPARED
TO FORCE-BALANCED MODELS
Notably, all our shear heating models yield integrated lithospheric
strengths of ~1013 Pa m after 100% thickening, regardless of the highly
different assumptions of strain rate and creep laws. This balance occurs
because high-strength models also produce more shear heat (Figs. 1, 2,
and 3). Thus, within 30% strain, the integrated lithospheric strength is
balanced at a steady state of ~1013 Pa m (e.g., Figs. 1B and 2B). This
contrasts models that neglect shear heating, in which compression
without shear heating results in continuous rise in lithosphere strength,
reaching ~1014 Pa m by the end of the numeric experiment (Fig. 1B, blue
line). Interestingly, the forces in an orogen can be calculated using only
gravity, without any rheological or thermal input (Jeffreys, 1970; Molnar
and Lyon-Caen, 1989), and cap the strength integrated over depth in the
Brace-Goetze strength envelope at 1013 Pa m, or an average of 1 kbar
GEOLOGY, April 2008
strength over 100 km depth (Stüwe, 2002). Thus only models with shear
heating return realistic estimates of long-term quasi-steady-state lithospheric strength (Fig. 2D).
THE EFFECT OF SHEAR HEATING ON SURFACE HEAT FLOW
Another important difference between lithospheric deformation
models with and without shear heating is the predicted surface heat flow.
In stable continents, the average surface heat flow is 0.07 W m–2, with
approximately equal contributions from conduction of asthenospheric
heat and from radiogenic heat from within the lithosphere (Turcotte and
Schubert, 2002). In the model without shear heating, surface heat flow
drops from ~0.07 to ~0.05 W m–2 due to stretching of the geotherm
during lithosphere thickening (Fig. 4). Instead, shear heating elevates the
surface heat flow: Multiplying a lithospheric strength (stress) of 1013 Pa m
by a strain rate of 3 × 10 –15 s–1, we obtain a depth-integrated heat flow of
0.03 W m–2. However, shear heating is faster than the conduction of heat
toward Earth’s surface. Accounting for this, our models with shear heating
yield a transient surface heat flow rise to ~0.08 W m–2 (Fig. 4).
This finding may go toward resolving the puzzle of “orogenic heat”
(Hyndman et al., 2005), and where the heat source is in orogenic (Barrovian) metamorphism (Jamieson et al., 1998), and may support results
from more complex finite-element models (Burg and Gerya, 2005). Common orogenic processes cool the lithosphere. For example, melting of
rocks absorbs heat, and crustal thickening and thrusting stretch or stack
the geotherm. Yet magmatism inverts metamorphic gradients, and a high
surface heat flow (0.07–0.09 W m–2) is common in orogens (Chapman and
Furlong, 1992; Pollack et al., 1993; Beaumont et al., 2001). It has been
Surface heat
flow (W m–2 )
Generally earthquakes in the deep crust or upper mantle are considered as brittle or Byerlee-type failure. In our first model, neglecting
shear heating (Fig. 1B), such earthquakes would occur near the Moho
of a thickened orogen, as predicted by, e.g., Jackson (2002). In contrast,
none of the shear heating models present such high stresses at depth
(e.g., Figs. 2B and 2D). Conversely one could argue that this is an artifact
of all deformations being modeled as pure shear thickening at modest
strain rates. Earthquakes in contrast occur along faults, which are local
high-strain zones. Thus, potentially, brittle failure could occur by rapidly
raising the strain rate in a narrow zone. We test this hypothesis by raising
the strain rate exponent 10% every 0.1 s, reaching a maximum of 10 –1, in
a meter-scale subhorizontal simple shear zone. Initially the differential
stresses in the shear zone rise proportional to the increase in strain rate.
As both strain rate and stresses increase, the subsequent shear heating
becomes intense, thereby weakening the rocks, so that stresses decrease
despite the continuous rise in strain rate. In the example presented in
Figure 3C, differential stresses peak at ~35 kbar, utilizing a strain rate of
10 –1 s–1 (Figs. 3A and 3C). By then shear heating is intense (108 W m–3),
causing frictional melting within 0.1 s (Fig. 3D). Shear heating thus provides a plausible alternative to traditional models of deep brittle earthquakes that neglect the effect of thermomechanical feedback (Kelemen
and Hirth, 2007), through a positive feedback between shear heating and
rising strain rates at stresses below brittle failure.
0.08
with shear heating
0.06
0.04
without shear he
ating
0
2
Time (m.y.)
6
8
Figure 4. Surface heat flow in models with and without shear heating
(power law rheology) (Fig. 1). Notice that only when shear heating is
included does the heat flow rise, as observed in nature.
333
proposed that this extra “orogenic heat” is inherited from the preorogenic
setting, caused by (1) the rise of hot asthenosphere following delamination
of the lower lithosphere, (2) enhanced heat transport due to circulating
fluids, or (3) an increase in radiogenic heat production below mountain
belts (Hyndman et al., 2005; Jamieson et al., 1998; Jiménez-Munt and
Platt, 2006). Acknowledging the potential role of these processes, we
note that even our most conservative estimates of the rise in heat flow of
0.03 W m–2 during mountain building match the missing orogenic heat.
CONCLUSIONS
We have devised a simple, easily reproducible and universally
applicable method to modify the Brace-Goetze strength envelope to calculate shear heating. Using this simple one-dimensional method, and
despite our use of minimum estimates of strain rate and stress, we have
shown that shear heating represents a first-order control on the distribution of strength and temperature in Earth’s lithosphere, and therefore has
a dramatic effect on patterns of deformation, particularly during continental collision. While others utilize the Brace-Goetze strength envelope
to explore two- to threefold variations in strength dependent on choice
of creep law (Tsenn and Carter, 1987), rock parameters (Buck, 1991),
wetness of rocks (Burov and Watts, 2006; Jackson, 2002; Afonso and
Ranalli, 2004), rheological strain softening (Huismans and Beaumont,
2003), or strain rate (Cloetingh and Burov, 1996), our calculations indicate that shear heating can change strength in deep Earth by as much
as a factor of ten, and in some important cases, conclusions of strength
models directly reverse when shear heating is considered.
Lithosphere deformation models without shear heating have
yielded estimates of total lithospheric strength that are 5–20 times higher
(Jackson, 2002; Hyndman et al., 2005) than force-balanced calculations
(Stüwe, 2002). These strength estimates have been presented as evidence for extreme stresses and brittle earthquakes in deep orogenic roots
(Jackson, 2002). Shear heating and thermomechanical coupling in our
models yield steady-state lithospheric strengths that are close to forcebalanced estimates, and well below those needed for brittle earthquakes
in deep orogenic roots. Furthermore, shear heating causes a rise in
modeled surface heat flow, similar to measured data. The effects of shear
heating on lithospheric deformation are profound, and no geodynamic
model is complete without it.
ACKNOWLEDGMENTS
Research is funded by the Norwegian Science Council through the Petromaks
program and a “Centre of Excellence” grant to Physics of Geological Processes.
N. Hovius, S. Medvedev, S. Bræck, and E. Jettestuen are thanked for discussions, and
S. Schmalholz, T. Gerya, and C. Doglioni are thanked for constructive comments.
REFERENCES CITED
Afonso, J.C., and Ranalli, G., 2004, Crustal and mantle strengths in continental lithosphere: Is the jelly sandwich obsolete?: Tectonophysics, v. 394,
p. 221–232, doi: 10.1016/j.tecto.2004.08.006.
Beaumont, C., Jamieson, R.A., Nguyen, M.H., and Lee, B., 2001, Himalayan tectonics explained by extrusion of a low-viscosity crustal channel
coupled to focused surface denudation: Nature, v. 414, p. 738–742, doi:
10.1038/414738a.
Brace, W.F., and Kohlstedt, D.L., 1980, Limits on lithospheric stress imposed by
laboratory experiments: Journal of Geophysical Research, B, Solid Earth
and Planets, v. 85, p. 6248–6252.
Buck, W.R., 1991, Modes of continental lithospheric extension: Journal of Geophysical Research, B, Solid Earth and Planets, v. 96, p. 20,161–20,178.
Burg, J.P., and Gerya, T.V., 2005, The role of viscous heating in Barrovian metamorphism of collisional orogens: Thermomechanical models and application to the Lepontine Dome in the central Alps: Journal of Metamorphic
Geology, v. 23, p. 75–95, doi: 10.1111/j.1525-1314.2005.00563.x.
Burov, E.B., and Watts, A.B., 2006, The long-term strength of continental lithosphere: ”Jelly sandwich” or “crème brûlée”?: GSA Today, v. 16, no. 1,
p. 4–10, doi: 10.1130/1052-5173(2006)016<4:TLTSOC>2.0.CO;2.
Carter, L.M., and Tsenn, M.C., 1987, Flow properties of continental lithosphere:
Tectonophysics, v. 136, p. 27–63, doi: 10.1016/0040-1951(87)90333-7.
334
Chapman, D.S., and Furlong, K.P., 1992, Thermal state of the continental crust,
in Fountain, D.M., et al., eds., Continental lower crust: Development in geotectonics, volume 23: Amsterdam, Elsevier, p. 179–199.
Chopra, P.N., and Paterson, M.S., 1981, The experimental deformation of dunite:
Tectonophysics, v. 78, p. 453–473, doi: 10.1016/0040-1951(81)90024-X.
Cloetingh, S., and Burov, E.B., 1996, Thermomechanical structure of European continental lithosphere: Constraints from rheology profiles and EET
estimates: Geophysical Journal International, v. 124, p. 695–723, doi:
10.1111/j.1365-246X.1996.tb05633.x.
Doglioni, C., Green, D., and Mongelli, F., 2005, On the shallow origin of hotspots
and the westward drift of the lithosphere, in Foulger, G.R., et al., eds., Plates,
plumes, and paradigms: Geological Society of America Special Paper 388,
p. 735–749.
Goetze, C., 1978, The mechanism of creep in olivine: Royal Society of London Philosophical Transactions, ser. A, v. 288, p. 99–119, doi: 10.1098/
rsta.1978.0008.
Huismans, R.S., and Beaumont, C., 2003, Symmetric and asymmetric lithosphere
extension: Relative effects of frictional-plastic and viscous strain softening:
Journal of Geophysical Research, B, Solid Earth and Planets, v. 108, p. 1–22.
Hyndman, R.D., Currie, C.A., and Mazzotti, S.P., 2005, Subduction zone backarcs, mobile belts, and orogenic heat: GSA Today, v. 15, no. 2, p. 4–10.
Jackson, J., 2002, Strength of the continental lithosphere: Time to abandon the
jelly sandwich?: GSA Today, v. 12, no. 9, p. 4–9, doi: 10.1130/1052-5173
(2002)012<0004:SOTCLT>2.0.CO;2.
Jamieson, R.A., Beaumont, C., Fullsack, P., and Lee, B., 1998, Barrovian regional
metamorphism: Where’s the heat? in Treloar, P., and O’Brien, P., eds., What
controls metamorphism and metamorphic reactions?: Geological Society
[London] Special Publication 138, p. 23–51.
Jeffreys, H., 1970, The Earth: Cambridge, UK, Cambridge University Press, 300 p.
Jiménez-Munt, I., and Platt, J.P., 2006, Influence of mantle dynamics on the topographic evolution of the Tibetan Plateau: Results from numerical modelling: Tectonics, v. 25, TC6002, doi: 10.1029/2006TC001963.
Kaus, B.J.P., and Podlachikov, Y.Y., 2006, Initiation of localized shear zones in
viscoelastioplastic rocks: Journal of Geophysical Research, B, Solid Earth
and Planets, v. 111, p. 1–18.
Kelemen, P.B., and Hirth, G., 2007, A periodic shear-heating mechanism for
intermediate-depth earthquakes in the mantle: Nature, v. 446, p. 787–790,
doi: 10.1038/nature05717.
Molnar, P., 1992, Brace-Goetze strength profiles, the partitioning of strike-slip
and thrust faulting at zones of oblique convergence, and the stress–heat
flow paradox of the San Andreas fault, in Evans, B., and Wong, T.-F., eds.,
Fault mechanics and transport properties of rocks: A Festschrift in honor of
W.F. Brace: London, Academic Press, p. 435–459.
Molnar, P., and Lyon-Caen, H., 1989, Some simple physical aspects of the support, structure, and evolution of mountain belts, in Clark, S.P., Jr., Burchfiel,
B.C., and Suppe, J., eds., Processes in Continental Lithospheric Deformation: Geological Society of America Special Paper 218, p. 179–207.
Pollack, H.N., Hurter, S.J., and Johnson, J.R., 1993, Heat flow from the Earth’s
interior: Analysis of the global data set: Reviews of Geophysics, v. 31,
p. 267–280, doi: 10.1029/93RG01249.
Regenauer-Lieb, K., Weinberg, R.F., and Rosenbaum, G., 2006, The effect of
energy feedbacks on continental strength: Nature, v. 442, p. 67–70, doi:
10.1038/nature04868.
Regenauer-Lieb, K., Yuen, D.A., and Branlund, J., 2001, The initiation of subduction: Criticality by addition of water?: Science, v. 294, p. 578–580, doi:
10.1126/science.1063891.
Roselle, G.T., and Engi, M., 2002, Ultra high pressure (UHP) terrains: Lessons
from thermal modeling: American Journal of Science, v. 302, p. 410–441,
doi: 10.2475/ajs.302.5.410.
Schmalholz, S.M., Podladchikov, Y.Y., and Jamtveit, B., 2005, Structural softening of the lithosphere: Terra Nova, v. 17, p. 66–72, doi: 10.1111/
j.1365-3121.2004.00585.x.
Stüwe, K., 2002, Geodynamics of the lithosphere: An introduction: Berlin,
Springer, 449 p.
Tsenn, M.C., and Carter, N.L., 1987, Upper limits of power law creep of rocks:
Tectonophysics, v. 136, p. 1–26, doi: 10.1016/0040-1951(87)90332-5.
Turcotte, D.L., and Schubert, G., 2002, Geodynamics: Cambridge, UK, Cambridge University Press, 456 p.
Wilks, K.R., and Carter, L.M., 1990, Rheology of some lower crustal rocks: Tectonophysics, v. 182, p. 57–77, doi: 10.1016/0040-1951(90)90342-6.
Manuscript received 3 October 2007
Revised manuscript received 7 December 2007
Manuscript accepted 1 January 2008
Printed in USA
GEOLOGY, April 2008