Int J Earth Sci (Geol Rundsch)
DOI 10.1007/s00531-010-0557-7
ORIGINAL PAPER
Density variations in the thickened crust as a function of pressure,
temperature, and composition
Julia Semprich • Nina S. C. Simon
Yuri Yu. Podladchikov
•
Received: 30 October 2009 / Accepted: 25 April 2010
Ó Springer-Verlag 2010
Abstract Constraints on density as a function of pressure,
temperature, and composition are crucial to understand
isostatic movements during geodynamic processes. Here,
we provide a systematic series of density diagrams
extracted from thermodynamic calculations for a variety of
crustal compositions within a wide P–T range. We quantify
systematic density changes in collisional settings for relevant compositional variations and attempt to simplify the
density–composition relationships. Rock densities depend
strongly on pressure, temperature, and composition. Densities at some selected pressure–temperature conditions
increase linearly with increasing Al2O3 as well as MgO/
FeO contents in pelitic rocks. Al- and Fe-rich pelites yield
the highest densities, which is mostly due to the formation
of garnet but also depends on other minerals and changes
of reactions. The effect of loading on densities is investigated, and we show that for deep burial, a meta-pelite rich
in Fe and Mg yields much larger density changes than a dry
basalt and that the burial of such a rock with a composition
close to typical lower crust may result in significant negative buoyancy. Metamorphism of hydrous lower crust due
to pressurization and heating thus leads to densification of
thickened lower crust, while heating of dry crust leads to a
decrease in density. Hence, water-loaded isostatic subsidence due to metamorphism of water-saturated lower crust
is substantial and increases with the thickness and depth of
the reacting layer, while dry compositions show much less
or only transient densification and subsidence. The density
change due to thermal expansion, an extensively used
concept in geodynamic models, predicts uplift under the
J. Semprich (&) N. S. C. Simon Y. Yu. Podladchikov
Physics of Geological Processes, University of Oslo, Blindern,
P.O. Box 1048, 0316 Oslo, Norway
e-mail: julia.semprich@fys.uio.no
same P–T conditions and is an order of magnitude smaller
than the density variation calculated from petrologically
consistent diagrams.
Keywords Phase transitions Crustal densities Lower crust Basin formation Subsidence Mountain roots
Introduction
Crustal thickness commonly doubles in collisional settings
causing a topography rise and the formation of deep foreland basins (Beaumont 1981; DeCelles and Giles 1996).
The removal of topography by erosion does not necessarily
lead to an isostatic rebound of crustal roots and basin
basements (Kruse and McNutt 1988; Döring and Götze
1999). Based on analyses of gravity anomalies, mineral
reactions in the lower crust were recently identified as the
reason for the preservation of ancient crustal roots (Fischer
2002; James 2002). While past topography is difficult to
constrain quantitatively, basin stratigraphy provides a highprecision record of vertical movements in collisional settings and potentially reflects the progress of metamorphic
reactions in the lower crust.
Such compressional basins are found in the foreland of
mountain ranges (Beaumont 1981; DeCelles and Giles
1996), but may also be common in intra-continental settings, for example the Paleozoic intra-cratonic basins of
North America (Sloss 1988). Intra-cratonic basins that are
thought to be active today are the Hudson Bay, Chad, and
Congo basins (Downey and Gurnis 2009). The Congo basin
is currently under compressive stress (Ayele 2002) and is
characterized by thick crust (Pasyanos and Nyblade 2007),
as are for example the Williston basin in North America
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Int J Earth Sci (Geol Rundsch)
(Hamdani et al. 1994 and references therein) and the PreUralian Foredeep (Döring and Götze 1999). This implies
that the crust-mantle boundary in these basins has been
deepened due to thickening of the crust, and crustal
material is exposed to upper mantle conditions. In some
cases, this may lead to metamorphic phase transitions and
densification, enhancing basin subsidence.
Phase transitions have been suggested as a mechanism
for basin subsidence since the late 1950s. Their relevance
for basin formation has been extensively studied in a
simplified approximation as one reaction line with a fixed
density change Dq (Kennedy 1959; O’Connell and
Wasserburg 1967; O’Connell and Wasserburg 1972; Haxby
et al. 1976; Mareschal and Lee 1983; Mareschal 1987;
Hamdani et al. 1994; Artyushkov 2005; Artyushkov 2010).
However, phase transitions in natural rocks are complex
and gradual, and their slope and position as well as the
associated change in density depends on rock composition,
in addition to pressure and temperature. Detailed studies of
the influence of pressure, temperature, and composition
(P–T-X) on densities have been provided in the context of
extensional basins (Podladchikov et al. 1994; Yamasaki
and Nakada 1997; Petrini et al. 2001; Kaus et al. 2005;
Simon and Podladchikov 2008). In collisional settings,
complex petrogenetic grids have been used to acquire
density distributions in connection with the evolution of
mountain belts (Bousquet et al. 1997; Le Pichon et al.
1997). Similar studies have been undertaken by for
example Jull and Kelemen (2001), Tassara (2006),
Massonne et al. (2007) and Hetényi et al. (2007) using
thermodynamic calculations.
To better understand the formation of intra-cratonic
basins, foreland basins, and mountain belts, we need better
constraints on the evolution of lower crustal densities in
compressional settings as a function of pressure, temperature, and composition. Therefore, the main goal of this
paper is to provide a systematic series of density diagrams
extracted from thermodynamic calculations for a variety of
crustal compositions. In addition, we examine which
compositional changes are relevant, if they cause systematic density variations, and if and how we can simplify the
density–composition relationships. Compositional variations in mixes with pelitic compositions are studied first;
the results are compared to mafic rocks. We then demonstrate the relevance of the generated density diagrams by
calculating subsidence as a consequence of loading. We
discuss the application of our results to the preservation of
orogenic roots and the formation of basins in compressional settings, with the intra-cratonic East Barents basin
and the possibly related Uralian mountain range as examples. A more advanced model using fully dynamic 2-D
thermo-mechanical finite element calculations including
the realistic petrological P–T–density diagrams presented
123
here has been developed for the East Barents basin and will
be published elsewhere (Gac et al. 2008 and Gac et al.
manuscript in preparation).
Methods and results
Method of calculation
All phase diagrams and petrologic densities were
obtained with the Gibbs free energy minimization software Perple_X ‘07 (Connolly and Kerrick 1987; Connolly
1990; Connolly and Petrini 2002). Extensive documentation and downloads are provided by J. Connolly at
http://www.perplex.ethz.ch. Perple_X uses the thermodynamic data set of Holland and Powell (1998) for minerals
and aqueous fluids. Mineral abbreviations are listed in
Table 1, and the solid solutions used for pelitic rocks can
be found in Table 2. SiO2 polymorphs, aluminosilicate
polymorphs (Ky, Sil, And), Kfs, Pg, Lws, Zo, and H2O
are treated as pure phases. Solid solution models for
amphiboles that would cause slight variations in the
positions of the phase fields are ignored in the thermodynamic calculations for the pelitic compositions since the
effect on the densities of these rocks is negligible.
Pseudosections are calculated in the system K2O–Na2O–
CaO–MgO–FeO–Al2O3–SiO2–H2O. For reasons of simplification, we initially assume that all iron is divalent and
that all pelitic starting mixes are SiO2 and H2O saturated.
MnO is ignored in the calculations since the MnO contents in the rock compositions used for our calculations
are very low. However, increasing MnO would stabilize
manganese-bearing minerals such as e.g., garnet over a
wider P–T range (Symmes and Ferry 1992; Mahar et al.
1997; Tinkham et al. 2001). For a systematic discussion
of compositional effects on rock densities, the P–T range
is chosen between temperatures of 500–900°C and pressures of 0.05–3 GPa because we are mostly interested in
deeply buried lower crustal rocks. The P–T range of a few
selected compositions is then extended to a larger P–T
window for the kinematic model (300–1,300°C and
0.6–4.5 GPa).
Calculation of pelitic compositions
In order to investigate the compositional variations in
pelitic rocks, we calculate hypothetical pelitic mixes,
which are composed of the following minerals: Qtz, Fsp,
Ill, Chl, and Fe–Ti-oxides. The mineral compositions are
listed in Table 3 and are taken from Massonne et al.
(2007). Systematic variations of the whole rock compositions are generated by changing the proportions of these
five minerals.
Int J Earth Sci (Geol Rundsch)
Table 1 List of mineral abbreviations and end-members used in the
text
Density diagrams of pelitic rocks
Mineral
Abbreviation
Albite
Ab
Almandine
Alm
Amesite
Ames
Andalusite
And
Figure 2a shows the density distribution of mix1p (a pelitic
starting composition, see Table 4) in P–T space. Densities
vary between 2,600 and 3,300 kg/m3 at temperatures
between 500 and 900°C and pressures between 0.05 and
3 GPa. The density diagram shows several density jumps,
which are due to phase transitions (or reactions) in the
rock. In order to see which minerals and ultimately which
compositional variations are important for these differences in density, the major phase transitions and mineral
reactions are plotted (Fig. 2b). Three major types of reactions occur: (1) polymorphic transitions such as quartz–
coesite or sillimanite–kyanite, where the high-pressure
polymorph has the denser structure; (2) dehydration reactions such as chlorite reacting to form minerals with less or
no water in the structure, where the phases containing
water have lower densities; (3) water-free reactions like
Ab = Jd ? Qtz, which form minerals with higher densities
and are rather pressure than temperature dependent. Except
for the polymorphic transitions, many reactions are continuous, and the first appearance of a mineral does not
necessarily cause a large difference in density. Plotting
only the limits of mineral stability fields is not sufficient to
investigate the effect of phase transitions on the rock
density. Therefore, we plot the modal amounts of a mineral
in the rock as a function of pressure and temperature.
Figure 3 shows that continuous reactions can be easily
detected by variations in mineral modes. While garnet
(Fig. 3a) and phengite (Fig. 3c) are formed, biotite
(Fig. 3b) and kyanite (Fig. 3d) are consumed. This continuous reaction is important for the density of pelitic rocks
because it is a major garnet-forming reaction and can be
formulated in KFASH as follows:
Annite
Ann
Biotite
Bt
Carpholite
Celadonite
Cp
Cel
Chlorite
Chl
Chloritoid
Cld
Clinochlore
Clin
Clinopyroxene
Cpx
Cordierite
Crd
Daphnite
Daph
Eastonite
East
Feldspar
Fsp
Ferrosilite
Fs
Garnet
Grt
Illite
Ill
Jadeite
Jd
K-feldspar
Kfs
Kyanite
Lawsonite
Ky
Lws
Muscovite
Ms
Orthopyroxene
Opx
Paragonite
Pg
Phengite
Phe
Phlogopite
Phl
Plagioclase
Pl
Pyrope
Prp
Sanidine
San
Sillimanite
Sil
Staurolite
St
Talc
Tlc
Quartz
Qtz
Zoisite
Zo
See Kretz (1983) for most common minerals
The starting mix (mix1p) has the following weight
proportions: Qtz:Fsp:Ill:Chl:Fe–Ti-Ox = 25:12:40:20:3.
We exclude the oxides which are not considered in the
calculation and run a thermodynamic calculation with
excess water (i.e., not constraining the water content in the
rock). A pseudosection diagram of mix1p is shown in
Fig. 1. Finally, a density grid is generated for each pelitic
mix (see Connolly and Petrini 2002 for retrieval of rock
properties).
ðaÞ Ann þ 2Ky þ Qtz ¼ Alm þ Ms
ðbÞ KFe3 AlSi3 O10 ðOHÞ2 þ2Al2 SiO5 þ SiO2
¼ Fe3 Al2 Si3 O12 þ KAl3 Si3 O10 ðOHÞ2
ð1Þ
In addition, the modal variations (Fig. 3) show at which
P–T conditions a mineral has reached its maximum amount
in the rock, which implies that all reactions forming this
mineral have been completed.
Quartz–Illite variations
A systematic study of the effect of compositional variations
on densities requires a parameter which allows a gradual
change in the rock type. If we want to vary the composition
between pelagic clay (poor in Ca but rich in Al) and
sandstone, we mainly have to look at varying SiO2 and
Al2O3 contents in the rock. To achieve this, we vary only
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Int J Earth Sci (Geol Rundsch)
Table 2 Solid solution models for the phases used in the pelitic mixes and mafic compositions
Solid solution model
End-members
Formulas
References
Biotite (Bt)
Phlogopite
KMg2Mg[AlSi3O10](OH)2
Powell and Holland (1999)
Annite
KFe2Fe[AlSi3O10](OH)2
Eastonite
KMg2Al[Al2Si2O10](OH)2
Ordered biotite
KMg2Fe[AlSi3O10](OH)2
Carpholite (Cp)
Chlorite (Chl)
Chloritoid (Cld)
Clinopyroxene (Cpx)
Cordierite (Crd)
Garnet (Grt)
Phengite (Phe)
Plagioclase (Pl)
Staurolite (St)
Talc (Tlc)
Orthopyroxene (Opx)
Amphibole (Amp) (clino)
Magnesiocarpholite
MgAl2[Si2O6](OH)4
Ferrocarpholite
FeAl2[Si2O6](OH)4
Clinochlore
Mg4MgAl[AlSi3O10](OH)8
Daphnite
Fe4FeAl[AlSi3O10](OH)8
Amesite
Mg4AlAl[Al2Si2O10](OH)8
Holland et al. (1998)
Al-free chlorite
Mg4MgMg[Si4O10](OH)8
Magnesiochloritoid
Ferrochloritoid
MgAl2O[SiO4](OH)2
FeAl2O[SiO4](OH)2
White et al. (2000)
Green et al. (2007), Holland and
Powell (1996), Zeh et al. (2005)
Diopside
CaMg[Si2O6]
Hedenbergite
CaFe[Si2O6]
Jadeite
NaAl[Si2O6]
Ca-tschermaks
CaAl[AlSiO6]
Cordierite
Mg2[Al4Si5O18]
Ferrocordierite
Fe2[Al4Si5O18]
Hydrous cordierite
Mg2[Al4Si5O18] H2O
Pyrope
Mg3Al2[Si3O12]
Almandine
Fe3Al2[Si3O12]
Grossular
Ca3Al2[Si3O12]
Muscovite
KAlAl[AlSiSi2O10](OH)2
Celadonite
KAlMg[SiSiSi2O10](OH)2
Ferroceladonite
KAlFe[SiSiSi2O10](OH)2
Mahar et al. (1997)
Holland and Powell (1998)
Powell and Holland (1999)
Paragonite
NaAlAl[AlSiSi2O10](OH)2
High albite
Anorthite
Na[AlSi3O8]
Ca[Al2Si2O8]
Newton et al. (1980)
Holland and Powell (1998)
Magnesiostaurolite
Mg4Al18[Si7.5O44](OH)4
Ferrostaurolite
Fe4Al18[Si7.5O44](OH)4
Talc
Mg2Mg[SiSi3O10](OH)2
Ferrotalc
Fe2Fe[SiSi3O10](OH)2
Tschermaks talc
Mg2Al[AlSi3O10](OH)2
Enstatite
MgMg[SiSiO6]
Ferrosilite
FeFe[SiSiO6]
Magnesiotschermaks
AlMg[AlSIO6]
Tremolite
Ca2Mg3Mg2[Si2Si6O22](OH)2
Ferrotremolite
Ca2Fe3Mg2[Si2Si6O22](OH)2
Tschermakite
Ca2Mg3Al2[Al2Si6O22](OH)2
Pargasite
NaCa2Mg3MgAl[Al2Si6O22](OH)2
Glaucophane
Na2Mg3Al2[Si2Si6O22](OH)2
the proportions of Qtz and Ill. The amount of Qtz significantly influences the total amount of SiO2 in the rock,
while varying Ill proportions mainly has an effect on the
Al2O3 and K2O contents (see compositions in Table 2). In
addition, the Na2O, MgO, and FeO contents of the rock
will also vary slightly. Table 4 shows the compositions
123
Same model as Cld
Holland and Powell (1998)
Holland and Powell (1996)
Wei and Powell (2003)
used for our calculations; P–T–density diagrams of a few
of these theoretical mixes are shown in Fig. 4. The water
content is just high enough to ensure water saturation of the
rock under all conditions. Depending on the pressure and
temperature conditions as well as on compositions, the water
content in metapelites varies between 0.7 and 2.56 wt%.
Int J Earth Sci (Geol Rundsch)
Table 3 Composition of
minerals used for the generation
of hypothetical pelitic mixes
(oxides in wt%)
Oxides
Quartz (Qtz)
Feldspar (Fsp), An15
Illite (Ill)
Chlorite (Chl)
Fe–Ti-Oxides
SiO2
100
67.5
47.5
26.0
–
TiO2
–
–
0.5
–
30.0
Al2O3
–
18.5
33.5
20.0
5.0
Fe2O3
–
0.5
–
5.0
40.0
FeO
–
–
2.0
20.0
16.0
MnO
–
–
–
–
3.0
MgO
–
–
1.5
16.0
2.0
CaO
–
3.0
–
–
4.0
Na2O
–
10.0
1.5
–
–
K2O
–
0.5
9.0
–
–
H2O
–
–
4.5
13.0
–
(2) Ky, Cpx, and additional Grt-forming reactions in the
high-pressure and high-temperature area, and (3) major
garnet-forming reactions at lower pressure and intermediate temperature. Figure 5 shows the density diagram of
mix1p with the most important reactions (see ‘‘Appendix’’
for detailed reactions).
This reaction list is not complete. Especially in the lower
temperature–lower pressure area, numerous reactions
involving staurolite, aluminosilicate, chlorite, and biotite
take place. For a complete petrogenetic grid, see Wei and
Powell (2003), Wei and Powell (2004), and Wei and Powell
(2006). Due to changes in composition, reactions might not
only change their position but may also be replaced completely by another reaction (discussed below in more detail).
Chlorite–Illite variations
Fig. 1 Pseudosections of a meta-pelitic rock calculated for mix1p
(see Table 4 for composition). For reasons of clarity, the small fields
are not labeled. Mineral abbreviations are given in Table 1
The quartz–illite variation is shown from top to bottom of
Fig. 4, where mix1p (pelagic clay or pelite composition
sensu stricto) has the highest Al2O3 and the lowest SiO2
content while mix3p (intermediate between pelite and
sandstone) has lower Al2O3 and higher SiO2 contents. The
P–T–density diagrams in Fig. 4 show several significant
density changes which are subject to varying composition
and caused by the following reactions: (1) polymorphic
transitions of quartz to coesite and sillimanite to kyanite,
As a next step, we vary the composition of a pelite with
less mafic to more mafic component which means changing
FeO and MgO contents in the rock (but ignoring Ca variations). Therefore, only the illite–chlorite ratios are varied.
Increasing chlorite and decreasing illite mainly results in an
increase in whole rock FeO and MgO and a significant
decrease in K2O, together with some reduction in Al2O3,
Na2O, and SiO2 (Table 4). Figure 4 shows the whole rock
FeO and MgO variation from left to right, with the lowest
whole rock FeO and MgO contents in mix1p (pelite) and
the highest in mix14p (FeO- and MgO-rich pelite).
Understanding the influence of compositional
variations on density
In order to quantify and compare variations in mineralogy
and consequently physical properties that are due to compositional changes, we compute mineral modes and densities at specific P–T conditions. The first point is chosen
well within the high-P, high-T area at 800°C and 2.5 GPa
123
Int J Earth Sci (Geol Rundsch)
Table 4 Starting compositions of hypothetical pelitic mixes (oxides
in wt%): mix1p-mix10p; mix11p-mix14p; mix21p-mix23p; mix31pmix33p; MORB and Fjørtoft gneiss (Massonne et al. 2007), lower
crustal Meta-pelite estimate (Schenk 1990) and average Lower Crust
estimate (Rudnick and Fountain 1995; Rudnick and Gao 2003)
mix1p
mix2p
mix3p
mix4p
mix5p
mix6p
mix7p
mix8p
mix9p
mix10p
mix11p
SiO2
61.07
63.83
66.58
69.33
72.08
74.70
76.96
58.31
55.54
52.78
60.44
Al2O3
21.07
19.27
17.47
15.69
13.89
12.07
10.24
22.87
24.67
26.48
20.53
FeO
5.62
5.52
5.41
5.30
5.19
5.06
4.93
5.74
5.85
5.95
6.64
MgO
CaO
4.11
0.51
4.03
0.51
3.95
0.52
3.86
0.51
3.79
0.51
3.70
0.51
3.59
0.50
4.20
0.51
4.28
0.51
4.36
0.51
4.93
0.52
Na2O
1.92
1.83
1.75
1.67
1.59
1.51
1.42
2.00
2.08
2.16
1.86
K2O
3.90
3.42
2.94
2.46
1.98
1.50
1.01
4.38
4.87
5.35
3.45
H2O
1.79
1.58
1.38
1.18
0.97
0.96
1.35
1.99
2.20
2.40
1.64
mix12p
mix13p
mix14p
mix21p
mix22p
mix31p
mix32p
MORB
Fjørtoft
Meta-pelite
Lower crust
SiO2
59.81
58.93
57.65
63.22
62.58
65.99
65.06
51.40
55.37
56.40
53.96
Al2O3
19.97
19.33
18.57
18.72
18.14
16.90
16.24
16.66
24.38
21.00
17.08
FeO
MgO
7.67
5.76
8.70
6.57
9.66
7.35
6.53
4.84
7.56
5.67
6.42
4.76
7.41
5.56
7.90
7.93
11.47
3.56
9.40
4.50
8.66
7.32
CaO
0.52
0.53
0.52
0.52
0.52
0.52
0.52
11.82
0.88
3.00
9.69
Na2O
1.79
1.72
1.63
1.78
1.71
1.69
1.62
2.84
0.41
2.00
2.68
K2O
2.99
2.52
2.02
2.96
2.51
2.48
2.00
0.09
2.53
2.50
0.62
H2O
1.49
1.70
2.59
1.43
1.31
1.23
1.58
1.37
1.39
Water contents are given at 500°C and 0.05 GPa; the water content varies with P and T. Water contents in Meta-pelite and Lower Crust
compositions were varied from dry to water saturated, see Fig. 10
Fig. 2 a P–T-density diagram
of mix1p (pelitic rock; densities
in kg/m3). b Important phase
transitions and mineral reactions.
The label ‘Grt in’ means that the
first garnet is formed at the
curve; ‘Bt out’ implies that the
last biotite breaks down. Large
density changes are caused by
hydration/dehydration reactions
(e.g., ‘Chl in/out’) in addition to
mainly pressure-dependent
reactions (e.g., ‘Cpx in’ and
quartz–coesite)
(point in Fig. 5a), the second one is at 700°C and 1.2 GPa
(point in Fig. 5b). Figure 6a shows the mineral modes in
volume percent versus the whole rock Al2O3 content in 10
hypothetical mixes (see Table 4) at 800°C and 2.5 GPa.
The stable phases at these conditions are Phe, Grt, Cpx
(mostly jadeitic), Ky, and Qtz. As expected, the amount of
Ky is decreasing with decreasing Al2O3 content in the rock.
Compositions with approximately 12 wt% Al2O3 and lower
(mix6p and mix7p) do not have enough Al2O3 to form
kyanite in addition to the Al-bearing phases (Phe, Grt,
Cpx). Since the density of Ky is quite high (&3,670 kg/
m3), the density of the rock is affected significantly. Cpx is
123
slightly increasing with Al2O3 (and Na2O), which also has
an effect on the whole rock density. In addition, the amount
of Phe is drastically increasing, while Qtz is decreasing.
Since Phe has a higher density than Qtz (Phe: 2,900 kg/m3;
Qtz: 2,690 kg/m3), this results in a higher rock density. The
amount of Grt, the mineral with the highest density, is
nearly constant over the whole compositional range.
Additional Grt can only form when there is a sufficient
amount of Al2O3 as well as FeO and/or MgO in the rock
(Jull and Kelemen 2001). Since the FeO and MgO contents
are almost constant, an increase in Al2O3 does not result in
the formation of more Grt.
Int J Earth Sci (Geol Rundsch)
Fig. 3 Modal amounts of
garnet (a), biotite (b), phengite
(c), and kyanite (d) in volume%
(varying scale). The ‘Grt in’ and
‘Bt out’ lines are added in order
to show the continuous reaction
as given by Eq. (1)
A list of rock densities at those specific conditions is
provided in Table 5. Figure 7a shows that there is a linear
density increase with increasing whole rock Al2O3 content.
If we compare the most silicic composition (mix7p, close
to a sandstone) with the most aluminous rock (mix10p,
pelagic clay), the density difference is 6.42% while the
difference in Al2O3 content is 16.22 wt%.
At 700°C and 1.2 GPa, the assemblage consists of
the phases Grt, Pl, Ky, Bt, Phe, and Qtz (Fig. 6b). In the
Al-poor mixes (mix6p and mix7p), Phe is not present at
the given conditions and will be formed at higher pressure. Due to the decrease in whole rock Al2O3, Al in the
Phe structure is gradually replaced by Si and Mg/Fe
(celadonitic substitution), which is strongly dependent on
pressure. Phe with a higher celadonitic proportion is
stable at higher P. The mineral densities also differ from
those at 800°C and 2.5 GPa, which is partly due to the
different P and T values and partly due to the compositional change in the minerals (e.g., Grt has a higher
Alm component, which is denser than Prp). All rock
densities at 700°C and 1.2 GPa are listed in Table 5 and
plotted in Fig. 7a. Again, an almost linear relationship
exists between the density and the Al2O3 content of the
rock. The difference in density between the most silicic
rock (mix7p) and the most aluminous composition
(mix10p) is 4.23%.
We plotted the densities of two more points in Fig. 7a:
500°C and 1.5 GPa and 500°C and 0.7 GPa (see Table 5
for whole rock density data). While the density still
increases linearly with aluminum content, the overall
density change is lowered to 3.7 and 3.8%, respectively.
The fact that Phe forms at higher pressure in Al-poor
compositions also has an effect on the mineral reactions
and the modes of the other minerals and therefore the
density (Grt increases, Bt and Ky decrease, Fig. 6b). In
Fig. 8, we plot the zero contour lines for these minerals
for mixes 1p-7p (pelagic clay to sandstone). At higher
temperatures, Bt decomposes at higher pressures with
decreasing Al2O3 content (Fig. 8b) while Grt forms at
lower pressures (Fig. 8a). Phe is also formed at higher
pressures (Fig. 8c), and the Ky stability field is drastically
reduced with decreasing Al2O3 in the whole rock
(Fig. 8d).
For Grt, we only consider reactions within the temperature interval from 600 to 900°C. In mixes 1p and 2p
(pelites with Al-rich compositions), the first appearance of
Grt on a prograde metamorphic path is due to reaction (1).
Grt is also formed by reaction of biotite with sillimanite or
cordierite (see reactions 10 and 11 in the appendix). In
mixes 3p, 4p, and 5p (less Al-rich compositions), most Grt
is formed by reaction (1). However, Grt is already formed
at lower metamorphic conditions by the breakdown of Crd
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Int J Earth Sci (Geol Rundsch)
Fig. 4 P–T-density diagrams of mixes with different compositions.
From top to bottom: increase in SiO2 and decrease in Al2O3; from left
to right: increase in FeO and MgO. Absolute densities and density
contrasts increase from lower left to upper right corner. Compositions
are given in Table 4
Fig. 5 Important reactions
responsible for significant
increase in density in the pelitic
composition (mix1p) at high P
(a) and lower P–T (b). Black
dots indicate the P–T conditions
used for the comparison of
modal amounts in Figs. 6 and 9.
Numbers refer to reactions
listed in the appendix except for
reaction 1 on b which is given
in the text
(reaction 12 in appendix). Reactions (1) as well as (12) are
also important Grt-forming reactions in mix6p and 7p
(most silicic compositions); however, at lower P and T, Grt
123
is formed by a reaction of Opx and Crd (reaction 13 in the
appendix). Although the first Grt is formed at lower
metamorphic conditions with decreasing Al2O3, the
Int J Earth Sci (Geol Rundsch)
Fig. 6 Mineral modes in vol% plotted versus Al2O3 content (in wt%)
in the hypothetical whole rock compositions mix1p-10p (pelitic to
quartzitic composition; Table 4) at 800°C, 2.5 GPa (a) and 700°C, 1.2
GPa (b). Mineral densities at these conditions are also added. Garnet
is the heaviest mineral but its modal amount is almost constant over
the whole range of whole rock Al2O3 contents, but more (relatively
dense) phengite and less (relatively less dense) quartz are stable in
Al2O3-rich compositions
Table 5 Densities in kg/m3 for hypothetical mixes at specified conditions (see Fig. 7)
q at 800°C, 2.5 GPa
mix1p
mix2p
mix3p
mix4p
mix5p
mix6p
mix7p
3100.80
3078.90
3057.30
3036.30
3015.50
2994.60
2977.30
q at 700°C, 1.2 GPa
2903.40
2888.80
2873.80
2859.40
2844.80
2834.30
2829.50
q at 700°C, 1.2 GPa dry
2960.60
2941.70
2923.10
2904.90
2887.00
2869.10
2852.40
q at 500°C, 1.5 GPa
2863.70
2851.70
2840.10
2828.30
2816.70
2805.10
2793.80
q at 500°C, 0.7 GPa
2767.70
2756.60
2745.30
2734.40
2723.30
2712.30
2701.80
mix8p
mix9p
mix10p
mix11p
mix12p
mix13p
mix14p
q at 800°C, 2.5 GPa
q at 700°C, 1.2 GPa
3122.90
2918.60
3145.30
2933.90
3167.80
2949.30
3139.60
2936.20
3180.90
2970.50
3223.00
3020.10
3268.50
3078.4
q at 700°C, 1.2 GPa dry
2979.60
2999.60
3020.90
3001.10
3043.60
3087.70
3134.3
q at 500°C, 1.5 GPa
2875.60
2887.50
2899.50
2773.10
2778.60
2784.10
2790.4
q at 500°C, 0.7 GPa
2779.10
2790.70
2802.00
2865.10
2866.20
2868.10
2869.3
Fig. 7 Density (in kg/m3) plotted versus whole rock Al2O3 content (in
wt%) for mixes 1p-10p (pelitic to quartzitic compositions) (a) and
versus whole rock FeO (in wt%) for mixes1p to 14p (FeO/MgO
variations) (b) calculated at different P–T points: 800°C, 2.5 GPa, dry
compositions at 700°C, 1.2 GPa, 700°C, 1.2 GPa, 500°C, 1.5 GPa,
500°C, 0.7 GPa. Note the difference in scales. Density increases almost
linearly with increasing Al2O3 as well as FeO content in the rock. Whole
rock densities at the specified P–T conditions are given in Table 5
amount of Grt in the rock is almost constant due to the lack
of FeO/MgO.
Changes in the Bt-forming reactions are mostly taking
place in the range between 700 and 900°C. Ky and Bt
breakdown according to reaction (1) in the pelitic compositions (mixes 1p and 2p). Ky is not stable anymore in
intermediate compositions (mix3p to mix5p), and Bt breaks
down according to reaction 14 (see ‘‘Appendix’’). This
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Int J Earth Sci (Geol Rundsch)
Fig. 8 Zero contour lines
indicating the first or last
formation of Grt (a), Bt (b), Phe
(c), and Ky (d) in mixes mix1p7p. Compositional variations in
the rock have a strong influence
on the position of the mineral
stability fields
Fig. 9 Mineral modes in vol%
plotted versus whole rock FeO
content (in wt%) in the
hypothetical compositions
mix1p-14p at 800°C, 2.5 GPa
(a) and 700°C, 1.2 GPa (b).
Mineral densities at these
conditions are also added. The
modal amount of dense garnet
increases significantly with
increasing whole rock FeO,
while phengite decreases
reaction is displaced toward higher pressures with
decreasing Al2O3 content in the rock. Figure 8 shows the
complexity of the metamorphic reactions and the consequences for rock properties. A reduction of Al2O3 in the
rock composition clearly reduces the amount of any additional aluminosilicate phase, which then has an influence
on other mineral-forming reactions. Nevertheless, the first
appearance of a mineral will not necessarily change the
density significantly because the amount of the mineral
may be small.
We also compare the mineral modes at the two reference points at 800°C and 2.5 GPa and at 700°C and
1.2 GPa for the compositions with chlorite–illite variations. Here, whole rock FeO is plotted versus the modal
amount of minerals in Fig. 9. At 800°C and 2.5 GPa
(Fig. 9a), Qtz and Cpx modes are almost constant while
kyanite and phengite decrease. Ky is not stable as a
123
phase in the compositions with low whole rock Al2O3,
and Grt forms instead. Grt takes up the majority of FeO
and MgO in the rock and yields the highest densities.
From mix1p to mix14p, the FeO content increases by 4.2
wt% and the MgO content by 3.4 wt%, resulting in a
density increase of 5.42% (see also Fig. 7b; Table 5). At
700°C and 1.2 GPa (Fig. 9b), Phe breaks down while the
amounts of Qtz and Pl do not vary that much. Grt and
Ky, however, increase at the expense of Bt after complete Phe breakdown, which is again caused by a change
in reactions. The increase in density is 6.03% with whole
rock FeO and MgO increasing by 4.2 wt% and 3.4%,
respectively (Fig. 7b; Table 5). Figure 7b shows that
densities increase approximately linearly with increasing whole rock FeO at higher temperatures, while the
density is almost constant at 500°C, 1.5 GPa and 500°C,
0.7 GPa.
Int J Earth Sci (Geol Rundsch)
Fig. 10 P–T-density diagrams for meta-pelite (mix1p), Fe–Mg-rich
meta-pelite (mix14p), and MORB (all compositions given in
Table 4). Compositions are becoming more mafic from left to right,
and water content is decreasing from top to bottom from water
saturated to 1.5 wt% H2O to dry. The classical, mainly pressuredependent phase changes from gabbro to granulite to eclogite leading
to large Dq are clearly visible in the dry MORB composition (lower
right panel). However, water-saturated composition (upper panels)
produce significant densification upon heating, and also the density
distribution of the mafic compositions with just 1 wt% water is
strongly influenced by temperature-dependent reactions (not shown)
In summary, even small changes in whole rock composition can lead to significant changes in mineralogy and
hence the density of the rock. Variations in the Al2O3
content of the rocks lead to an almost linear increase in
density that is mostly due to the additional formation of
aluminosilicates, while the amount of Grt is almost constant. This density increase is larger at higher P and T.
An increased amount of FeO and MgO in the rock
composition, however, significantly increases the amount
of Grt. Grt also takes up most of the Al2O3 in the rock (Jull
and Kelemen 2001). The formation of other Al-bearing
phases is therefore suppressed with increasing FeO and
MgO content. Since Grt is the densest mineral, only a few
wt% of increase in FeO and MgO in the whole rock significantly increases the whole rock density.
Varying water content
In all calculations above, we assumed water to be an excess
phase, which might be a good assumption for rocks in the
upper crust. Lower crustal rocks, however, contain less
water or may even be completely dehydrated (Austrheim
1991). In order to investigate the effect of H2O on density,
we use the water-saturated mix1p (1.79 wt% H2O at 500°C
and 0.05 GPa) as a starting point and compare it with the
same composition containing approximately 1.5 wt% H2O
and a dry mix1p. The density diagrams of the three mixtures are shown in Fig. 10. We also compare the densities
at the two chosen P–T conditions. At 800°C and 2.5 GPa,
the dry rock is 0.52% denser than the water-saturated rock.
At 700°C and 1.2 GPa, the density difference is much
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Int J Earth Sci (Geol Rundsch)
higher (2.17%). The water content can change the density
significantly at certain P–T conditions, especially at lower
P and T, while the effect in the higher P, higher T field is
not that pronounced. This is due to the fact that most
hydrous phases decompose at relatively low temperatures,
and the only water-bearing mineral in a water-saturated
meta-pelite at high temperature and pressure is Phe.
Comparison with the density of mafic rocks
We also computed P–T–density diagrams for a mid-ocean
ridge basalt (MORB, Table 4, composition from Massonne
et al. 2007) to compare densities of a mafic rock with
densities of different pelitic compositions (Fig. 10). Pseudosections are calculated in the system K2O–Na2O–CaO–
MgO–FeO–Al2O3–SiO2–H2O as before, and all thermodynamic calculations involve divalent iron only. Most solid
solutions used in the pelitic mixes are also relevant for the
mafic rock; additional solid solutions, e.g., for amphibole
and orthopyroxene, are given in Table 2. At 800°C and
2.5 GPa, the MORB yields a density of 3,427 kg/m3. The
basalt only needs 0.04 wt% of water to be saturated at those
conditions. If we compare this value to the density of
mix1p, pelagic clay (3,101 kg/m3), the difference in density is 10.5%. However, if the basalt is compared to a more
Fe- and Mg-rich composition, e.g., mix14p, the difference
in density is reduced to 4.8%. Massonne et al. (2007)
showed that pelitic rocks can get very dense at high to
ultrahigh pressures, which is confirmed by our results. We
also compute densities for a Fe- and Al-rich natural rock,
the Fjørtoft gneiss (Fig. 11; Table 4), which was found to
be the densest meta-pelite by Massonne et al. (2007) at
ultrahigh-pressure conditions. The Fjørtoft gneiss yields
3,304 kg/m3 at 800°C and 2.5 GPa, and the density
Fig. 11 P–T-density diagram of the Fjørtoft gneiss (Table 4)
123
difference between mafic and pelitic rocks is reduced to
3.7%. At 700°C and 1.2 GPa, the MORB has a density of
3,111 kg/m3 and a water content of 0.81 wt%. The MORB
density is 7.17% higher than that of mix1p, while the
density difference between the MORB and mix14p is only
1.07%. The Fjørtoft gneiss, however, is 3.54% denser than
the MORB at these conditions.
In accordance with the results of Massonne et al. (2007),
we conclude that at certain conditions, a meta-pelitic rock
can become denser than a meta-mafic rock if the metapelite has a significant amount of Al2O3 and FeO.
The average lower crust is expected to be a mixture of
felsic and mafic rocks as numerous xenolith analyses (e.g.,
Rudnick and Taylor 1987; e.g., Downes 1993; Rudnick and
Fountain 1995) as well as exposed lower crustal sections
(e.g., Fountain and Salisbury 1981; Schenk 1984; e.g.,
Schenk 1990) indicate. An extensively used representative
average composition of the lower crust has been derived by
Rudnick and Fountain (1995) on the basis of xenolith data
and geophysical observations. Due to the fact that a
majority of xenoliths is mafic, the calculated average
composition yields phase relations and densities very
similar to a MORB, yet with slightly higher silica and a
lower CaO content and somewhat lower densities.
Uncertainties of the density diagrams
All calculated physical rock properties will be approximations of real rock properties due to the fact that we have
to simplify the system, and some mineral solid solution
models are not formulated with certain elements e.g., Ti or
Fe3?. The same also holds true for the thermodynamic data
since some minerals are thermodynamically less well
known and stability fields might be under- or overestimated
e.g., for biotite (Massonne and Schreyer 1989; Massonne
et al. 2007). In addition, thermodynamic calculations imply
perfect equilibrium, whereas metamorphic rocks do not
always equilibrate instantly during prograde metamorphism (e.g., mineral zonation) and hardly during retrogression (metastability; Spear 1995). In the thermodynamic
calculation, however, instant equilibrium is assumed.
Another factor of uncertainty is the water content in the
rock, which changes during metamorphism. In our calculations, we have to assume a certain water content of the
initial rock, which will then be constant over the whole
pressure and temperature range. Wherever H2O is present
as an excess phase, however, it will not be included in the
calculation of physical rock properties. Another simplification is the assumption that the fluid phase is only composed of H2O. The fluid may contain other components,
and the amount as well as the composition of the fluid may
change during different stages of metamorphism and may
influence phase equilibria.
Int J Earth Sci (Geol Rundsch)
Despite the simplifications, the calculated phase diagrams and extracted densities correlate quite well with
phase relations and densities of natural rocks (for discussions about the thermodynamic data and correlation with
natural rocks see e.g., Sobolev and Babeyko 1994; Gerya
et al. 2001; Tinkham et al. 2001; Wei and Powell 2003,
2004, 2006; Zeh and Holness 2003; Massonne et al. 2007).
Our obtained density values are, within a 1% tolerance,
very close to those calculated by Massonne et al. (2007) for
a psammopelitic rock composition, the Fjørtoft gneiss, and
a MORB at high to ultrahigh-pressure conditions and a
meta-pelite at lower P–T conditions calculated by Gerya
et al. (2001).
In addition, the calculated P–T-dependent densities are a
much more realistic approximation of the actual density
distribution in the crust than the commonly used layers of
constant, and P–T independent, average density, or densities that only depend on temperature via thermal expansion. In fact, feedback between tectonic processes and
reactions that influence physical properties is expected, and
P–T-dependent densities should therefore be incorporated
in dynamic models (e.g., Gerya et al. 2001; Goffe et al.
2003; Gac et al. 2008; Simon and Podladchikov 2008).
Partial melting
Continental crust can melt by adding water to rocks at
temperatures above their water-saturated solidi, by
decompression due to dehydration-melting reactions and
by an increased heat supply (Thompson and Connolly
1995). At temperature conditions of crustal orogenesis,
water is required to generate melt, but the small amount of
free water in lower crustal rocks will only produce negligible amounts. Dehydration-melting of muscovite and
biotite at higher P–T conditions can produce up to 25 vol%
of melt in meta-pelitic rocks (Thompson and Connolly
1995). Mafic compositions, however, produce an insignificant portion of melt.
Independent of the amount of melt generated, partial
melting of lower crustal rocks will remove the more felsic
and less dense components of the crustal rocks and leave
the more mafic and denser minerals as restite. According to
Massonne (2009), Grt becomes a restite phase in granitic
and dioritic rocks with rising temperature, and a significant
increase in Grt content to more than 20 vol% is caused by
the breakdown of Bt, Lws, and Phe. In fact, compositions
such as the Fe- and Mg-rich pelite (mix14p) could represent such a restite. This is also in accordance with exposed
crustal cross sections where the restitic Fe- and Mg-rich
rocks constitute a significant and dense part of the lower
crust while granites and granodiorites are found in the
upper crust (Fountain and Salisbury 1981; Schenk 1984,
1990).
Therefore, despite some expected melting in the pressure–temperature range of interest, we do not consider the
formation of a silicate melt (melting is suppressed in the
phase diagram calculations), and the phase relations calculated for the high-temperature field are metastable.
Density along a continental shield geotherm
We have shown here that phase transitions in natural rocks
are complex and gradual, and their slope and position as
well as the associated changes in density depend on rock
composition. With our calculated density diagrams, more
realistic densities can be extracted along a geotherm, and
we are able to test the effect of phase transitions as a
response to loading. Since the exact composition of the
lower crust is not known, we cover a large range of possible compositions by using densities of meta-pelitic as
well as meta-mafic rocks.
We choose a linear geotherm for the lower crust and
upper mantle which results in a temperature of approximately 300°C at 20 km and 1,300°C at 200 km depth, in
accordance with reconstructed geothermal gradients for
old continental shields (Jaupart and Mareschal 2007). In
Fig. 12, this geotherm is plotted on top of the density
diagram of the Fe- and Mg-rich pelitic rock (mix14p) to
show that the chosen geotherm will pass through several
significant density jumps. The densities for six different
rock compositions are extracted along this continental
shield geotherm: (1) the pelitic composition (mix1p), (2) a
Fe- and Mg-rich pelite (mix14p), (3) the Fjørtoft gneiss as
an Al- and Fe-rich end-member and representative of a
naturally occurring rock, (4) a dry MORB, (5) a dry pelite
Fig. 12 Continental shield geotherm (300°C at 20 km and 1,300°C at
200 km) plotted on top of the P–T-density diagram of mix14p
(Fe–Mg-rich meta-pelite, Table 4). Arrows indicate the final P–T path
that results for crustal burial from the steps of pressurization (DP = 1.2
GPa) and heating as described in the text for one point in the crust
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Int J Earth Sci (Geol Rundsch)
(mix1p), (6) a hydrated (water saturated) MORB, and (7) a
hydrated lower crustal composition (Rudnick and Fountain
1995; Rudnick and Gao 2003). Figure 13 shows the densities of those seven compositions with increasing pressure
along the geotherm. We chose the starting point to be well
within the crust at approximately 20 km, which roughly
corresponds to 0.6 GPa lithostatic pressure, and extend the
density curves up to 4 GPa for completeness. As expected,
there is a large variation in density depending on the rock
type, with the more silicic compositions starting significantly lighter than the mafic rocks. Figure 13 also shows
that phase transitions and therefore density jumps for the
various compositions are not located at the same P–T
conditions (except for the Qtz-Cs transition at approximately 3 GPa which is the same for all rock compositions).
The most striking feature of Fig. 13 is that all water-saturated rocks show a larger density variation (Dq) along the
P–T path than the dry compositions and that the Fe- and
Mg-rich meta-pelitic rock has the largest Dq. While the dry
MORB certainly yields the highest absolute densities under
all conditions, the increase in density is small compared to
all other compositions.
Isostatic response to crustal phase transitions
A simple 1-d isostatic model is developed to investigate the
effect of loading or burial on densities and subsidence in a
reacting crustal layer. The results are evaluated as a function of the pressure and temperature increase, the initial
Fig. 13 Densities for seven different rock compositions extracted
along the continental shield geotherm as shown in Fig. 12 and plotted
against P and the approximate corresponding depth. Hydrated Fe–
Mg-rich pelitic rocks show the highest density increase while MORB
yields the highest density but only a small Dq. Dry rocks show a first
step of densification around 0.5–1 GPa. The largest densification
starts at slightly lower pressures in mafic compositions compared to
meta-pelites, with the Fjørtoft gneiss being intermediate
123
depth and the thickness of the reacting layer, and the initial
geotherm or thickness of the lithosphere. The water-loaded
isostatic subsidence S is related to the density changes by
the simple equation
S ¼ z1 ðhq2 i hq1 iÞ qm
hq2 i ðqm qw Þ
ð2Þ
where qm is the constant density of the mantle (3,300 kg/
m3), qw is the density of water (1,000 kg/m3), and z1 is the
initial thickness of the reacting layer. hq1 i and hq2 i are
the average densities of the reacting layer before and after
the reaction, respectively. Since this paper is on the effect
of crustal phase transitions, we assume that mantle density
is constant. Hence, subsidence depends on the thickness of
the reacting layer (z1) and the densities before and after
reactions (Dq = hq2 i - hq1 i) scaled by hq2 i. In a simplified
geometric approach, Dq depends on the rock type, the
initial depth of the reactions, which is determined by
the initial slope of the geotherm, and the angle between the
slope of the geotherm and the phase transitions (Mareschal
and Lee 1983; Simon and Podladchikov 2008). As shown
above, however, reactions in crustal rocks are complex and
cannot easily be reduced to single reaction lines and rigorously analyzed as done for mantle phase transitions in
Simon and Podladchikov (2008).
The burial and pressure increase may arise due to sediment or thrust loading, horizontal compression and lithospheric flexure and crustal thickening, or a combination of
these processes, or by subduction or delamination. However, a discussion on the mechanism for pressure increase
is beyond the scope of this paper, and we will merely
investigate the density changes and subsidence due to some
preset burial of the crust. Some discussion on the application of our results to common tectonic settings is provided below. Temperature rises in this model because the
deepened lower crust heats back to the initial geothermal
gradient. Additional heating may occur due to sediment
blanketing, radiogenic heat production, or shear heating
would increase the effect of thermal re-equilibration.
An example for a schematic P–T path consisting of
burial (pressurization) and thermal re-equilibration is given
in Fig. 12 for one point in the crust.
Figure 14 shows the density change Dq of a crustal layer
with fixed initial thickness and position as a response to
pressure (DP) and temperature increase (DT) for different
bulk compositions with different water contents (see
Fig. 10). The reacting layer is initially located at 20–40 km
depth, corresponding to a lithostatic pressure interval of
0.56–1.2 GPa and a temperature of 300–476°C for an initially 140-km-thick lithosphere.
Dq varies from -200 to ?350 kg/m3 in a complex and
non-linear way, in particular for burial of wet lower
crust. For the given conditions, these density variations
Int J Earth Sci (Geol Rundsch)
approximately correspond to water-loaded isostatic uplift
or subsidence of -2,000 and 3,500 m, respectively.
In dry or nearly dry rocks, the average density of the
reacting layer generally increases as a consequence of
increasing pressure and decreases due to heating for all
compositions and conditions (Fig. 14d–i), with the most
pronounced Dq increase caused by the granulite to eclogite
facies transition (densely spaced contours in Fig. 14d–i).
This transition is at lower absolute pressures for more
mafic compositions (compare Fig. 14g, h and i; see also
Fig. 10). In mafic wet lower crustal rocks, pressurization
without significant heating may not affect densities or even
lead to slightly decreasing average densities at some conditions (Figs. 14c, 10c).
Heating of a completely dry lower crustal layer leads to
a decrease in density and hence negative Dq. Hydrated
crust, in contrast, may contract as a response to heating at
pressures equivalent to or higher than those at normal
continental Moho (Fig. 14a–c). In mafic rocks, significant
heating-related densification occurs for water contents as
low as 1 wt% (Fig. 14f). For DP and DT equivalent to a
doubling of the crustal thickness (upper right corner of
panels in Fig. 14), Dq is largest for the wet Fe–Mg-rich
meta-pelite (up to 350 kg/m3). This is evident already from
Fig. 13, where the densities along the continental geotherm
are shown, and the Fe–Mg meta-pelite displays the largest
density contrast of all compositions at around 2 GPa. The
Fjørtoft gneiss and wet average lower crust behave
similarly to the Fe–Mg-rich meta-pelite and wet MORB,
respectively (not shown).
Dq due to reactions in the lower crust and the waterloaded isostatic response depend critically on a range of
parameters that will not be explored here. Figure 15 shows
two examples for Dq and subsidence for two different P–T
paths (i.e., trajectories through Fig. 14) and different initial
lithosphere thicknesses (i.e., thermal states) for a set of
rock compositions and pressurization and heating of a 20km-thick reacting layer initially located at 20–40 km
depth. The density change and subsidence calculated
using the widely used expression q ¼ q0 ð1 aDTÞ
(q0 = 2,900 kg/m3, a = 3.28 9 10-5; McKenzie 1978) to
obtain the Dq of this lower crustal layer are also shown for
comparison. The cold and thick lithosphere (200 km) and
moderate pressure increase (0.1 GPa; Fig. 15a) may be
more relevant for cratonic interiors, whereas the large
pressure increase (0.95 GPa) and hotter lithosphere
(120 km, Fig. 15b) may describe the situation at a continental margin, e.g., in a foreland basin. All rock types
densify when pressure increases, but while Dq is similar for
wet and dry rocks with the same composition in a cold
lithosphere (Fig. 15a), it is significantly larger for dry rocks
than for wet rocks in a thinner and hotter lithosphere
(Fig. 15b). After the 0.1 GPa pressure increase, the densities of all rock types except the wet average lower crust and
wet MORB decrease as a response to heating, which would
result in uplift. The wet mafic rocks have almost constant
Fig. 14 Density contrast (Dq
[kg/m3]) contoured as a result of
pressurization (DP) and heating
(DT) of a 20-km-thick lower
crustal layer initially located at
20–40 km depth
(Pinitial = 0.56–1.20 GPa,
Tinitial = 300–476°C). Initial
lithosphere thickness: 140 km,
temperature at the base of the
lithosphere: 1,300°C. For these
model, parameters density
contrasts of 351 and
-197 kg/m3 correspond to
a maximum isostatic waterloaded subsidence of 3,162 m
and maximum uplift (no
erosion) of 1,813 m,
respectively.
a hydrated meta-pelite,
b hydrated Fe–Mg pelite,
c hydrated MORB, d metapelite with 1.5 wt% water,
e Fe–Mg pelite with 1.5 wt%
water, f MORB with 1.5 wt%
water, g dry meta-pelite, h dry
Fe–Mg pelite and i dry MORB
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Int J Earth Sci (Geol Rundsch)
Fig. 15 Calculated mean Dq of the reacting layer and resulting
water-loaded isostatic subsidence curves for selected compositions.
Solely temperature-dependent density (q = q0 (1 - aDT)) model is
shown for comparison. Reacting layer thickness and initial depth as in
Fig. 14. a Typical cratonic conditions: initial lithospheric thickness = 200 km, small pressure increase by 0.1 GPa which may be
caused by e.g., intra-plate stresses, flexure, or loading. Subsequent
thermal re-equilibration follows the timescale of thermal conduction
([ 100 Ma). All compositions produce subsidence due to loading, but
dry rocks expand and uplift upon heating. Dry MORB expands more
than 5 times more than predicted by the commonly used thermal
expansion coefficient over the temperature range of 173°C. Hydrated
compositions contract or expand depending on P–T conditions. b
Initially, 120-km-thick lithosphere and large pressure increase (0.95
GPa), which may be expected for large burial (orogeny, subduction)
and/or strong compression (over-pressure). Dry rocks contract more
during pressurization, but expand during heating, while wet compositions show protracted densification during heating, in particular the
Fe–Mg-rich pelite. Near-linear scaling of subsidence with Dq breaks
down for large Dq
densities and expand slightly at DT [ 120°C. The solely
temperature-dependent density approximates the density
evolution of the wet pelites, but strongly underestimates the
thermal expansion of dry MORB (Fig. 15a). The large
pressure increase applied in Fig. 15b results in significant
(500–1,350 m) water-loaded subsidence. Upon heating,
the dry rocks then expand and uplift as predicted by
123
q ¼ q0 ð1 aDTÞ, while all hydrous compositions continue to contract and subside. The largest densification and
subsidence (2,850 m) is reached by the Fe–Mg-rich pelitic
composition for the given conditions (Fig. 15b). These
results are remarkable given that most previous phase
change models are based on reactions in dry basalt. If
thermodynamic equilibrium is assumed, however, a dry
basaltic layer at 20–40 km depth will already be very dense
(in the garnet granulite and eclogite fields). The average
density will increase significantly during burial, but
decrease again during thermal equilibration, so subsidence
is transient and not permanent. A wet meta-pelite that has
lost a bit of silicic melt densifies due to pressure- and
temperature-dependent reactions and may be a more suitable candidate for subsidence related to reactions. Moreover, our Fe–Mg-rich pelite composition is close to some
estimates for average middle and lower crust and may
constitute a large part of normal continental crust (Schenk
1984, 1990).
Schenk (1990) calculated an estimated bulk composition for the meta-pelite unit as well as for the whole lower
crust of the exposed lower crustal section in Calabria
based on rock compositions and detailed mapping (both
estimates are added to Table 4 for comparison). The lower
crust is expected to be very heterogeneous with metabasic
units as well as highly restitic pelitic rocks (Schenk 1990).
The Fe–Mg-rich composition (mix14p) that we used for
our calculation is close to the composition of these pelitic
restites and may therefore be a good representative for a
lower crustal bulk composition. Although most studies
based on the composition of rare lower crustal xenoliths
and seismic data suggest that the average composition of
the lower crust is mafic (Pakiser and Robinson 1966;
Rudnick and Fountain 1995; Rudnick and Gao 2003), we
have to keep in mind that it is lithologically heterogeneous (Rudnick and Fountain 1995; Rudnick and Gao
2003). Furthermore, studies of exposed crustal cross sections reveal that the lower crust can be intermediate to
silicic (Gray 1977; Fountain and Salisbury 1981) and that
a major part of the lower crust may consist of meta-pelitic
rocks with only the lowermost part being metabasic
(Schenk 1990).
In summary, we show that crustal phase transitions
cause a significant densification of the crust as a response
to burial. In contrast to expectations, the largest density
changes are not caused by pressurization of (dry) basalts,
but by heating (and pressurization) of initially hydrated
meta-pelites. Negative buoyancy of a hydrous lower crust
buried to approximately twice its initial depth will be
significant (Dq * 300 kg/m3) and may result in 1–5 km of
water-loaded subsidence, depending on initial depth and
thickness of the reacting layer. Density change predicted by
density as a function of thermal expansion only, in contrast,
Int J Earth Sci (Geol Rundsch)
shows the opposite behavior to our realistic density calculations (density decreases as a response to heating), and
Dq is an order of magnitude smaller (*20–30 kg/m3,
Fig. 15).
Discussion and application
Recently, Massonne et al. (2007) stated that our knowledge about precise density data as a function of rock
composition and P–T conditions is very scarce. We are
aware of only five previous studies on the density of
crustal rocks at typical P–T and fluid conditions of crustal
metamorphism computed by energy minimization methods. Jull and Kelemen (2001) investigated dry, mafic
compositions at high temperatures ([800°C) only. Gerya
et al. (2001) presented models using densities of fully
hydrated crustal rocks at low pressure (\1 GPa). More
recently, Hetényi et al. (2007) considered an averaged
lower crustal bulk composition at three hydration levels:
dry, with 1 wt% H2O and fully hydrated. Massonne et al.
(2007) compared density diagrams of ten rock compositions at fully hydrated conditions, excluding the average
lower crust composition studied by Hetényi et al. (2007).
Although the studies of Hetényi et al. (2007) and Massonne et al. (2007) are complimentary, they are conducted
using different software packages and solution models.
Tassara (2006) compared extensive density calculations
for anhydrous rocks using the approach of Sobolev and
Babeyko (1994) and densities for three compositions
characteristic of the lower crust under fully hydrated
conditions computed by Perple_X. We presented here a
more systematic comparison of the densities of lower
crustal rocks at lithospheric P–T conditions and constructed ‘‘four-dimensional’’ P–T-q-X diagrams (Figs. 4,
10). The results of our calculations can be used to
improve the interpretation of geophysical data (particularly gravity) and in kinetic and dynamic numerical
models of basin formation, dynamics of mountain ranges
and gravitational instabilities.
In the following sections, we will discuss some geodynamic applications of our modeling results to settings
where the lower crust is buried into the mantle, namely
mountain ranges and intra-cratonic basins.
Application to the preservation of orogenic roots
The simplest model of mountain building involves thickening of the crust in a compressional setting, where the
high topography of the mountain range is maintained
because the density of the crustal root is lower than that of
the surrounding mantle. With time, topography is removed
by erosion, but the buoyant root leads to further uplift until
the mountains are worn flat and the root is leveled again
(e.g., James 2002). Alternative models propose eclogitization and delamination of the root, leading to collapse of
the mountain range and eventually also to leveling of the
topography and the crust-mantle boundary (e.g., Bird
1979). However, some old mountain ranges preserve their
thick crustal root. Fischer (2002) argued that this preservation is due to metamorphic reactions that reduce the
density contrast between the lower crust and the mantle.
An alternative explanation based on the eclogitization and
delamination model was provided by Leech (2001) who
proposed that the Urals did not loose their crustal root
because there was not enough fluid available to overcome
kinetic boundaries and transform the lower crust from
gabbro to eclogite. Both authors assumed that the lower
crust consists of dry basalt and that the transformation from
gabbro to eclogite is the only reaction that causes density
changes. To get the Dq [ 300 kg/m3 that is needed for
both hypotheses to work, Moho temperatures in the
thickened crust initially have to be very high and then
gradually cool to normal continental conditions. Fischer
(2002) had to invoke Moho temperatures of 900–1,000°C
during orogeny and cooling to 400°C in roughly 300 Ma in
order to explain the gradual decrease in density contrast
between lower crust and mantle and associated decrease in
the ratio of mountain surface relief to crustal root thickness
from active mountain belts to ancient orogens. We propose
that our findings on the density variations in buried lower
crust allow for re-evaluation of these hypotheses for the
preservation of ancient crustal roots. We show that mafic
rocks are not the only ones that produce large density
contrasts during metamorphism. Moreover, most possible
crustal compositions (with the exception of entirely dry
rocks) experience the largest densification as a response to
heating, in addition to pressure increase, and not due to
cooling. According to our calculations, dry MORB densities increase by 220 kg/m3 for cooling from 900 to 500°C
at 1.35 GPa, consistent with the assumptions of Fischer
(2002). The same cooling at higher pressures would produce smaller Dq. However, sluggish kinetics will probably
severely inhibit reactions in an entirely dry rock, especially
at the lower temperatures. If the MORB is hydrated, which
may help to speed up reaction kinetics, however, the net
increase in density during the same cooling interval is close
to zero (compare diagrams for wet and dry MORB in
Fig. 10). In contrast, heating of a lower crust consisting of
more felsic rocks, hydrated meta-mafic rocks, or a mixture
of those by 300°C (e.g., from 400 to 900°C) at 1.35 GPa
results in a density increase of 250–300 kg/m3 (Fig. 12).
Considering absolute densities, dry metamorphic MORB
(eclogite) at 1.35 GPa and 500°C has q = 3,400 kg/m3,
increasing to 3,450 kg/m3 at 1.5 GPa. These densities are
indeed higher than those of the mantle under these
123
Int J Earth Sci (Geol Rundsch)
conditions and should be detectable due to higher seismic
velocities (e.g., Mengel and Kern 1992). Moreover, the
density contrast may indeed lead to delamination of the
lower crust if the lithosphere is not rigid enough to hold
this dense body. Fischer (2002) argues that isostatic equilibrium is maintained and isostatic uplift continues during
erosion of the mountain range, which means that the crust
and mantle are weak enough to deform. Meta-pelitic crust
that is buried and heated, in contrast, displays Dq as large
as the gabbro to eclogite transition, but has a density at
1–2 GPa that is lower or equivalent to that of the mantle,
depending on temperature (Fig. 12). The real lower crust
most likely consists of a mixture of mafic and more felsic
components resulting in average crustal root densities
intermediate between those of granulite/eclogite and metapelite under equilibrium conditions. Such a scenario could
explain the observation of Fischer (2002) on the preservation of crustal roots, as well as the gradual decrease in
density contrast with time. It may also be consistent with
the observations of Leech (2001) since metamorphism of a
crust that is not completely mafic will produce similar
features to a dry, mafic lower crust that only partly reacted
to eclogite. Of course, we cannot exclude metastability; the
occurrence of incomplete reactions is well documented
(e.g., Austrheim 1990). We hypothesize, however, that the
metamorphic densification of crustal roots may be caused
by conductive heating of the initially cold thickened lithosphere over more than 100 million years instead of conductive cooling of an initially hot orogen. Our hypothesis
can be tested in future modeling studies, but the general arguments outlined here illustrate the importance
of detailed studies of equilibrium density as a function of
P–T-X.
Application to large basins
The phase change model for subsidence in intra-cratonic
basins has been extensively studied using numerical and
analytical models (Joyner 1967; O’Connell and Wasserburg 1967, 1972; Haxby et al. 1976; Middleton 1980; Sleep
et al. 1980; Mareschal and Lee 1983; Mareschal 1987;
Hamdani et al. 1991, 1994; Baird et al. 1995; Artyushkov
2005, 2010). Several models have focused on the detailed
temperature evolution of the lithosphere loaded by sediments (Sleep et al. 1980; Mareschal and Lee 1983;
Mareschal 1987) and/or subjected to a change in heat flow
at the base of the lithosphere (Haxby et al. 1976; Hamdani
et al. 1991, 1994), including the effect of latent heat of
reaction (O’Connell and Wasserburg 1967) and sediment
blanketing (O’Connell and Wasserburg 1972). The most
investigated phase transition is the one from gabbro or
granulite to eclogite which occurs close to continental
Moho depths (Lovering 1958; Kennedy 1959; Joyner 1967;
123
Ahrens and Schubert 1975a, b; Mengel and Kern 1992;
Artyushkov 2005, 2010), but the transition from greenschist to amphibolite facies in the mid-lower crust as a
response to heating has also been invoked to explain the
subsidence in the Cooper and Eromanga basins in Australia
(Middleton 1980). Most models explored an increase in
pressure due to loading of the lithosphere by sediments
(O’Connell and Wasserburg 1967, 1972; Sleep et al. 1980;
Mareschal and Lee 1983; Mareschal 1987), but a pressure
increase due to compression or horizontal load has also
previously been suggested as an important mechanism
(Cloetingh and Kooi 1992; Hartz et al. 2007). Some
authors proposed a metastable layer of gabbro at the base
of the crust that converts directly to eclogite triggered by
fluids or heating (Haxby et al. 1976; Datondji 1981;
Artyushkov 2005, 2010). In all those models, the transition
is approximated as one reaction line with a certain Clapeyron slope and fixed Dq.
The East Barents Sea Basin is one of the world’s deepest
basins with up to 20 km of sediments. As already mentioned, the formation mechanisms of intra-cratonic basins
are not well understood. Consequently, previous studies do
not agree on the underlying cause for the formation of the
Barents Sea Basin (O’Leary et al. 2004; Ebbing et al. 2007;
Ritzmann et al. 2007). One of the striking features of the
Barents Sea is a generally flat Moho over large parts of the
region at a depth of 35–37.5 km in the East Barents Sea
area (Ebbing et al. 2007). In addition, the Moho depth does
not reflect observed changes in the depth to the basement,
whereas crustal thickness and Moho geometry should
correlate according to simple crustal extension models for
basin formation (McKenzie 1978). In summary, the depth
of the Moho appears to be largely unaffected by the processes leading to the formation of the deep basin in the
Eastern Barents Sea and the isostatic Moho is 8 km shallower than the seismic Moho (Ebbing et al. 2007). Moreover, there are large differences between the observed and
modeled gravity field in conventional models. Since the
structure of the upper crust is relatively better known, the
additional mass needed to account for the observed gravity
is assumed to reside in the lower crust or the mantle
(Ebbing et al. 2007; Ritzmann et al. 2007). While Ebbing
et al. (2007) argue for this excess mass to be in the mantle,
Neprochnov et al. (2000) concluded that the high-velocity
layers below the basin may represent a crust-mantle rock
mixture in a zone of old rifting. Artyushkov (2005)
excludes oceanic crust below the thick sedimentary cover
and instead suggests a high-grade metamorphic lower
crustal layer below the seismic Moho. He proposed a
model where a mafic body of more than 20 km thickness
with an initial density of 2,900 kg/m3 below the seismic
Moho is transformed to an eclogite with a constant density
of 3,500 kg/m3, in order to account for the observed
Int J Earth Sci (Geol Rundsch)
tectonic subsidence. Based on geophysical observations, he
also argues that the East Barents Sea did not experience
significant stretching and that the main subsidence occurred in a compressional setting in the Permo-Triassic. Even
though this latter statement is controversial, it has been
confirmed recently by Petrov et al. (2008) who interpret the
East Barents basin as the foredeep caused by the Uralian
collision and orogeny. Werner et al. (2010, in press) also
state that the E. Barents region has been under compression
since the Early Mesozoic. If we accept this interpretation,
the E. Barents basin may represent a good test case for
basin formation in a compressional setting due to crustal
phase changes.
Sediment loading amplifies subsidence, in particular in
connection with phase changes, but an initial depression is
needed which must have been caused by other processes.
Hence, we suggest deflection of the lithosphere, so called
buckling, in a compressional tectonic setting. Although
such a lithospheric buckling should not take place if linear
elasticity is assumed for the lithosphere, it has been
reproduced by numerical models using more realistic
lithospheric rheologies (Burg and Podladchikov 1999;
Schmalholz and Podladchikov 2000; Schmalholz et al.
2002, 2005; Kaus and Schmalholz 2006; Burg and Schmalholz 2008; Burov and Cloetingh 2009). Burg and
Podladchikov (1999) showed that a basic response of
stratified lithosphere to compression is buckling independent of the thermal regime and that the folding of the
lithosphere is mechanically preferable to homogeneous
thickening. In addition, cold and therefore stronger lithosphere shows higher amplitude folding with a longer
wavelength than hot lithosphere. Since the main explanation for the collapse of the buckles is the density contrast
between the crust and the mantle at the crust-mantle
boundary (Allen and Allen 2005), the densification of the
lower crust by phase transitions may explain how buckles
are maintained over geological timescales.
A simplified cartoon model for the possible evolution of
a basin formed by buckling and crustal phase changes is
presented in Fig. 16. The initial setup consists of three
major layers: the upper crust, the lower crust, and the
mantle (Fig. 16a). The Moho is shown as the boundary
between a lower density and a higher density rock, which
may be the metamorphosed lower crust or the mantle. In a
compressional setting, a horizontal force is applied to the
initial rock column. This results in the buckling of the
lithosphere (Fig. 16b). As a result of buckling, the crustmantle boundary is deepened, and lower crustal rocks are
exposed to higher pressures. This pressure increase results
in phase changes and a densification of the rocks, which is
illustrated by the P arrow in the density diagram (Fig. 12),
causing a water-loaded isostatic subsidence of up to
1,500 m (Figs. 14, 15). At the same time, sedimentation
starts in the newly formed basin and additional subsidence
is caused due to sediment loading. In addition to the
increase in pressure, the lower crustal rocks are also
Fig. 16 Conceptual model for
subsidence due to compression
and phase transitions, a initial
condition; b stage 1: buckling of
the lithosphere as a result of
compression results in
deepening of the crust-mantle
boundary and therefore pressure
increase. Additional loading due
to sedimentation and
densification of the lower crust
due to pressure-dependent
reactions leads to fast
subsidence (depending on
deformation and sedimentation
rates); c stage 2: thermal
equilibration and further density
increase lead to more and
prolonged subsidence on the
timescale of thermal
conduction. Relaxation of
compressional stresses may lead
to some pressure release and
partial retrogression in the lower
crust; d stage 3: stable state in
isostatic equilibrium. See
Fig. 12 for an approximate P–T
path
123
Int J Earth Sci (Geol Rundsch)
exposed to higher temperatures, but the thermal equilibration is supposed to be slower since it is governed by
thermal diffusion through the lithosphere (Fig. 16c). An
increase in T results in further reactions and density
increase, as shown by the T arrow in Fig. 12. Our simple
subsidence calculations yield 3,500 m of isostatic tectonic
subsidence after pressurization and thermal equilibration
(Fig. 14). Relaxation of compressional stresses may lead to
some pressure release and partial retrogression in the lower
crust (Gac et al. 2008, manuscript in preparation). The last
stage represents complete isostatic re-equilibration with a
lens of eclogite facies (but probably not eclogitic) rocks
sitting between the crust and the mantle (Fig. 16d). This
lens is denser than the former crustal rocks but still lighter
than the mantle and may account for the additional mass
required to explain the gravity signal in the E. Barents
basin (Ebbing et al. 2007; Ritzmann et al. 2007). Due to the
denser and seismically faster material in the crustal lens,
the seismic Moho is also shifted to lower depths. In fact,
crust-mantle transition zones characterized by Vp in the
range of 7.0–7.9 km/s have been identified in many seismic
profiles (Baird et al. 1995; Ziegler and Cloetingh 2004),
and such a lens of intermediate velocities was also detected
in the E. Barents Sea (Ivanova et al. 2006). The crustal
compositions investigated here show major density jumps
around 1.2–2.5 GPa, depending on temperature, and the
more mafic pelite compositions, the Fjørtoft gneiss, and the
dry and hydrous basalts reach densities close to or higher
than those of the mantle at pressures higher than 1.5 GPa in
a warm lithosphere and \2 GPa in a 200-km-thick cold
lithosphere.
While we propose that the E. Barents basin today is in a
situation similar to that shown in Fig. 16d, Fig. 16b, c
might be representative for other basins, where phase
transitions did not go to completion; bending of the plate
due to loading is not compensated by densification of the
lower crust. An example of such a basin that did not reach
isostatic equilibrium and displays a gravity anomaly is the
Congo basin (Downey and Gurnis 2009). In contrast, a
typical basin originally caused by plate bending, the PreUralian Foredeep, does not show a pronounced gravity
anomaly, and the light sedimentary infill appears to be
compensated by dense lower crustal material (Döring and
Götze 1999). This may indicate that densification of lower
crust as a response to burial is responsible for the preservation of both, the Uralian foreland basin and the thick
crustal root of the Uralian Mountains. The situation in the
Pre-Uralian Foredeep may be analogue to that of the E.
Barents Sea and indeed Petrov et al. (2008) interpret the E.
Barents basin as (another) foredeep related to the Uralian
collision and orogeny.
Our isostasy calculations show that a reacting layer with
a minimum thickness of 30 km and a density contrasts
123
similar to that of our Fe–Mg-rich pelite model composition
is needed to produce the isostatically balanced tectonic
subsidence observed in the E. Barents basin during the
Permo-Triassic, if the total load is around 1 GPa (Fig. 14).
To test and validate our conceptual model, however, it has
to be investigated how high the amplitude of the buckling
needs to be to generate sufficient lower crustal burial and
how much additional pressure is generated due to horizontal loading. The timescale of these processes depends
on the speed of deformation, sedimentation, and thermal
equilibration. The coupling of phase transitions with a fully
coupled thermo-mechanical dynamic finite element model
and application to the East Barents Sea basin is in progress
(Gac et al. 2008, manuscript in preparation).
However, because substantial extension and crustal
thinning can be ruled out in a compressional setting, the
lower crust is in any case buried to larger depth in such a
sedimentary basin. Therefore, our general approach for the
analyses of subsidence due to phase changes remains valid
independent of the mechanism that leads to the deepening
of the crust-mantle boundary.
Most intra-cratonic basins, however, are much shallower
than the E. Barents Sea and are characterized by a stepwise
pattern of fast subsidence followed by long-term slow
subsidence or uplift (e.g., Haddad et al. 2001; Armitage
and Allen 2010). Our model predicts abrupt subsidence due
to pressurization, followed by a period of extended slow
subsidence or even uplift (Fig. 15). The phase transition
model we propose may therefore explain the observed
stepwise subsidence in intra-cratonic basins if compressional events occur repeatedly or periodically, similar to
the model proposed by DeRito et al. (1983). The quantitative validation of our model, however, requires more
advanced thermo-mechanical modeling and comparison
with actual data.
Conclusions
We present systematic calculations of densities as a function of pressure and temperature for a large range of dry
and hydrated compositions from pelitic to mafic using an
internally consistent thermodynamic data set. Our calculations show that large density changes can occur due to
pressure- and temperature-dependent reactions and hence
that jumps in densities (and therefore also seismic velocities) do not necessarily imply a different rock composition.
We show, however, that density also strongly depends on
rock composition. Density increases linearly with increasing Al2O3 as well as MgO and FeO contents in the rocks.
Moreover, Al- and Fe-rich rocks yield the highest absolute
densities. Compositional variations can easily cause more
than 6% density variation at fixed P–T conditions; at
Int J Earth Sci (Geol Rundsch)
certain conditions, meta-pelitic rocks can become denser
than meta-mafic rocks. Our new density quantification is
useful not only for the specific application to geodynamic
settings where the crust is thickened, but in general also for
e.g., improved gravity modeling, kinetic and dynamic basin
models, and models involving gravitational instability.
Densities extracted along a continental shield geotherm
show that all hydrated rocks yield a larger Dq along the P–T
path than the dry compositions and that a wet Fe- and Mgrich meta-pelite has the largest Dq. While dry MORB yields
the highest absolute densities, the increase in equilibrium
density (Dq) is small compared to many other compositions.
In fact, all rocks that contain some hydrous minerals show
densification as a response to heating, opposite to the
behavior of dry meta-mafic rocks, which most studies
investigating the geodynamic implications of lower crustal
density changes used as representative compositions.
By investigating the effect of lower crustal burial on
densities and evaluating the resulting subsidence, we found
that a wet meta-pelite rich in Fe and Mg consequently also
yields much larger subsidence than a dry MORB. The
density change due to thermal expansion, an extensively
used concept in geodynamic models, is one order of
magnitude smaller than Dq calculated from our diagrams
for burial of lower crust. Moreover, the density predicted
using q = q0(1 - aT) decreases, whereas in real crustal
rocks, densities may increase due to pressurization and
heating. For the Fe–Mg-rich pelite and wet average mafic
lower crust compositions, water-loaded subsidence is substantial and increases with the thickness and depth of the
reacting layer, while dry MORB shows much less subsidence. These results are remarkable given that most previous phase change models are based on reactions in dry
basalt. Moreover, our Fe–Mg-rich pelite composition is
close to estimates for average middle and lower crust and
may constitute a large part of normal continental crust.
Phase transitions and compositional variations in the
mantle have a significant effect on geodynamics (Simon
and Podladchikov 2008). Due to the wide compositional
range and large P–T-X-dependent density variations in
crustal rocks, the influence of the crustal density on geodynamic processes should be even bigger, provided the
crust makes up a significant part of the lithospheric column. This is the case in stable continental shields and if
continental crust is thickened, e.g., due to compression.
Acknowledgments This research was funded through a Norwegian
Research Council grant to J. S. and N. S. within the Petrobar Project. We thank our partners in the Petrobar project, in particular
R. Huismans, S. Gac, and J. I. Falleide, and our colleagues at PGP, in
particular J. C. Vrijmoed, for discussions and two anonymous
reviewers for helpful criticism on a previous version of the manuscript.
Two more reviews helped to condense and finalize the paper.
Appendix
For simplicity, reactions are formulated in the most relevant system, either MASH, FASH, or NASH.
Cpx, Ky, and Grt-forming reactions at high-P, high-T
conditions:
ðaÞ 3MgCp þ Qtz ¼ 3Ky þ Tlc þ 5H2 O
ðbÞ 3MgAl2 Si2 O6 ðOHÞ4 þSiO2
ð3Þ
¼ 3Al2 SiO5 þ Mg3 Si4 O10 ðOHÞ2 þ5H2 O
ðaÞ 3FeCld þ 2Qtz ¼ Alm þ 2Ky þ 3H2 O
ðbÞ 3FeAl2 SiO5 ðOHÞ2 þ 2SiO2 ¼ Fe3 Al2 Si3 O12
ð4Þ
þ 2Al2 SiO5 þ 3H2 O
ðaÞ Pg ¼ Ky þ Jd þ H2 O
ðbÞ NaAl3 Si3 O10 ðOHÞ2 ¼ Al2 SiO5 þ NaAlSi2 O6 þ H2 O
ð5Þ
ðaÞ Ab ¼ Jd þ Qtz
ð6Þ
ðbÞ NaAlSi3 O8 ¼ NaAlSi2 O6 þ SiO2
Grt, Tlc, Cp, and Cld-forming reactions at lower P,
intermediate-T:
ðaÞ 3Clin þ 13Qtz ¼ 4Tlc þ 3MgCp þ 2H2 O
ðbÞ 3Mg5 Al2 Si3 O10 ðOHÞ8 þ 13SiO2
¼ 4Mg3 Si4 O10 ðOHÞ2 þ3MgAl2 Si2 O6 ðOHÞ4 þ 2H2 O
ð7Þ
ðaÞ 3Clin þ 10Qtz ¼ 3MgCld þ 4Tlc þ 5 H2 O
ðbÞ 3Mg5 Al2 Si3 O10 ðOHÞ8 þ10SiO2 ¼ 3MgAl2 SiO5 ðOHÞ2
þ 4Mg3 Si4 O10 ðOHÞ2 þ 5H2 O
ð8Þ
ðaÞ 3Clin þ 8Qtz ¼ 3Prp þ 2Tlc þ 10H2 O
ðbÞ 3Mg5 Al2 Si3 O10 ðOHÞ8 þ 8SiO2 ¼ 3Mg3 Al2 Si3 O12
þ 2Mg3 Si4 O10 ðOHÞ2 þ10H2 O
ð9Þ
ðaÞ 3Daph þ 3Ames þ 12Qtz ¼ 4Prp þ 5Alm þ 24H2 O
ðbÞ 3Fe5 Al2 Si3 O10 ðOHÞ8 þ 3Mg4 Al4 Si2 O10 ðOHÞ8
þ 12SiO2 ¼ 4Mg3 Al2 Si3 O12 þ 5Fe3 Al2 Si3 O12 þ 24H2 O
ð10Þ
ðaÞ 31Daph þ 41Ms ¼ 41Ann þ 8FeSt þ 33Qtz
þ 108 H2 O
ðbÞ 31Fe5 Al2 Si3 O10 ðOHÞ8 þ 41KAl3 Si3 O10 ðOHÞ2
¼ 41KFe3 AlSi3 O10 ðOHÞ2 þ 8Fe4 Al18 Si7:5 O44 ðOHÞ4
þ 33SiO2 þ 108 H2 O
ð11Þ
ðaÞ Ann þ Sil þ 2Qtz ¼ Alm þ San þ H2 O
ðbÞ KFe3 AlSi3 O10 ðOHÞ2 þ Al2 SiO5 þ 2SiO2
¼ Fe3 Al2 Si3 O12 þ KAlSi3 O8 þ H2 O
ð12Þ
123
Int J Earth Sci (Geol Rundsch)
ðaÞ 4Ann þ 3FeCrd þ 3Qtz ¼ 6Alm þ 4San þ 4H2 O
ðbÞ 4KFe3 AlSi3 O10 ðOHÞ2 þ 3Fe2 Al4 Si5 O18 þ 3SiO2
¼ 6Fe3 Al2 Si3 O12 þ 4KAlSi3 O8 þ 4H2 O
ð13Þ
ðaÞ 3FeCrd ¼ 2Alm þ 4Si þ 5Qtz
ðbÞ 3Fe2 Al4 Si5 O18 ¼ 2Fe3 Al2 Si3 O12
þ 4Al2 SiO5 þ 5SiO2
ð14Þ
ðaÞ FeCrd þ Fs ¼ 2Alm þ 3Qtz
ðbÞ Fe2 Al4 Si5 O18 þ Fe2 Si2 O6
¼ 2Fe3 Al2 Si3 O12 þ 3SiO2
ð15Þ
ðaÞ Phl þ East þ 6Qtz ¼ Prp þ 2Cel
ðbÞ KMg3 AlSi3 O10 ðOHÞ2 þ KMg2 Al3 Si2 O10 ðOHÞ2
þ 6SiO2 ¼ Mg3 Al2 Si3 O12 þ 2KAlMgSi4 O10 ðOHÞ2
ð16Þ
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