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Transcript
LETTER
doi:10.1038/nature12758
Foundering of lower island-arc crust as an
explanation for the origin of the continental Moho
Oliver Jagoutz1 & Mark D. Behn2
crust (VP < 7–7.5 km s21), separated from the underlying mantle
(VP < 8–8.5 km s21) by the sharp Moho4. Globally, with the exception
of active orogenic belts or rifts, the continental Moho occurs at a relatively constant depth of 41 6 6 km (ref. 4). In contrast, the seismic
structure of the lower crust in many active arcs is defined by a transitional increase from lower crustal velocities of VP < 7 km s21 to subMoho velocities of VP < 7.6–7.7 km s21, significantly slower than the
sub-Moho velocities observed in continental regions. The sharply defined
Moho seen in continental crust is generally absent in arcs5–7; instead a
weak discontinuity (increase in VP from about 6.8 to 7.2 km s21) is
observed that has been interpreted to indicate either a contact between
mafic lower crust and unusually hot upper mantle or an intra-crustal
contact between mafic and ultramafic cumulates6. Accordingly, if
continental crust is formed in arcs, significant reworking of arc lower
crust must occur to transform the transitional lower-crust–mantle
interface in arcs into the sharply defined crust–mantle discontinuity
of continental regions.
It is widely accepted that mafic/ultramafic rocks in arc lower crust
can become denser than the underlying upper mantle and could founder
back into the upper mantle8–10. This process can explain the andesitic
chemical composition of continental crust ultimately derived from basaltic
mantle melts10,11. Previous studies have proposed that the maximum
observed thickness of the continental crust (about 70–80 km) is controlled by the depth interval at which a density inversion occurs12; however, the relationship between lower crustal foundering and the location
and nature of the Moho has not been established. Specifically, crustal
A long-standing theory for the genesis of continental crust is that it
is formed in subduction zones1. However, the observed seismic
properties of lower crust and upper mantle in oceanic island arcs2,3
differ significantly from those in the continental crust4. Accordingly,
significant modifications of lower arc crust must occur, if continental crust is indeed formed from island arcs. Here we investigate
how the seismic characteristics of arc crust are transformed into those
of the continental crust by calculating the density and seismic structure of two exposed sections of island arc (Kohistan and Talkeetna).
The Kohistan crustal section is negatively buoyant with respect to
the underlying depleted upper mantle at depths exceeding 40 kilometres and is characterized by a steady increase in seismic velocity
similar to that observed in active arcs. In contrast, the lower Talkeetna
crust is density sorted, preserving only relicts (about ten to a hundred
metres thick) of rock with density exceeding that of the underlying
mantle. Specifically, the foundering of the lower Talkeetna crust
resulted in the replacement of dense mafic and ultramafic cumulates
by residual upper mantle, producing a sharp seismic discontinuity at
depths of around 38 to 42 kilometres, characteristic of the continental Mohorovičić discontinuity (the Moho). Dynamic calculations
indicate that foundering is an episodic process that occurs in most
arcs with a periodicity of half a million to five million years. Moreover, because foundering will continue after arc magmatism ceases, this
process ultimately results in the formation of the continental Moho.
Continental crust is characterized by a lower-velocity upper crust
(seismic P-wave velocity VP < 5–6 km s21) and a higher-velocity lower
b
1.9
c
0
80
m
W
0.4
m –2
artz
0.8 GPa, 900 °C
β-quartz
artz
0.8 GPa, 750 °C
α-quartz
β-qu
1.9
α-qu
a
Talkeetna
60
Pressure (GPa)
–2
VP /VS
–2
VP /VS
m
Wm
0.8
mW
1.7
1.7
40 m
1.8
1.8
Kohistan
1.2
1.6
1.6
6
7
VP (km s–1)
8
1.6
6
7
VP (km s–1)
2.0
8
0
400
800
1,200
Temperature (°C)
50
70
90
SiO2 (wt%)
Figure 1 | Seismic and petrological constraints on the thermal regime in
arcs. a, b, Seismic velocities of representative lower-crustal rocks from
continents and arcs in the a–quartz (a) and b–quartz (b) stability fields
(n 5 428). Boxes indicate the seismic properties observed in the lower crust of
active arcs (see Methods for references). c, Pressure versus temperature
diagram showing the location of the a-quartz to b-quartz transition and
metamorphic pressure and temperature recorded in the Kohistan and
Talkeetna sections18,19,31. Yellow and brown stars indicate the pressure and
temperature conditions used to calculate panels a and b, respectively.
The observed VP/VS and VP values constrain the spatially averaged
temperatures to lie within the a-quartz field17.
1
Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, USA. 2Department of Geology and
Geophysics, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, USA.
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©2013 Macmillan Publishers Limited. All rights reserved
RESEARCH LETTER
b
Average continental crust
(ref. 4)
10
20
IzuBonin
Density stable
a
Density of the upper mantle
0
Depth (km)
30
Moho depth
40
Density
unstable
rocks can become density unstable with respect to the upper mantle
over a significant depth interval from 20 to 60 km or more, depending
on compositions and temperature conditions in the arc lower crust
(see Methods for detailed discussion). Detailed knowledge of the composition and temperature regime in the arc lower crust is therefore
essential to assess how such a foundering process could influence the
seismic properties of the crust–mantle interface.
To constrain the depth at which foundering occurs in arcs we calculate the density and seismic properties of rocks from Kohistan and
Talkeetna, the two best-exposed oceanic arc sections (see Methods for
geological setting). Previous studies have suggested that the Talkeetna
arc crust is generally less dense than the underlying upper mantle peridotites (‘density stable’)13,14, whereas in Kohistan lower-crustal rocks denser
than the upper-mantle peridotites (‘density unstable’) are preserved15.
Here we present thermodynamic modelling of observed crustal compositions at pressures and temperatures appropriate for the formation
of the arc sections (see Methods for details of the modelling). We use
these results to reconstruct the detailed density and seismic structure
of the two arc sections during their formation to (1) determine the depth
at which the density inversion in arcs occurs, and (2) explore the effect
of foundering on the seismic properties of the arc lower crust.
To calculate the seismic/density structure of the Kohistan and Talkeetna
arcs, we first estimated the temperature in the lower crust of active arcs.
Although the thermal structure of an active arc is transient owing to the
interaction between a conductive geothermal gradient and perturbations from frequent melt infiltration events (see ref. 16 for example), we
can use VP/VS (where VS is shear-wave velocity) estimates from the arc
lower crust in combination with geothermometry on metamorphic
mineral assemblages to infer the spatially averaged thermal conditions
during the construction of the arc crust. Estimates show that VP/VS
in the lower crust of active arcs is variable, but is generally 1.70–1.80
with a corresponding VP of 6.5–7.5 km s21 (Fig. 1a, b)17. This low VP/VS
indicates that quartz-bearing lithologies are present in the arc lower
crust and the quartz must be mostly the low-temperature alpha-quartz
pseudomorph (Fig. 1a, b).
These observations constrain the spatially averaged temperature in arc
lower crust to less than 800–850 uC at approximately 25–40 km depth,
consistent with a conductive geothermal gradient of about 60–70 mW m22
(Fig. 1c). Similar metamorphic temperatures are preserved in Kohistan
(700–800 uC at about 40–50 km; ref. 18), whereas higher temperatures
are recorded in Talkeetna (about 900–1,000 uC at depths of around 40 km;
ref. 19) (Fig. 1c). On the basis of these results we calculated density and
seismic properties along appropriate geotherms for Kohistan (60 mW m22)
and Talkeetna (80 mW m22) (Fig. 1c). However, as discussed in the
Methods and shown in Extended Data Fig. 1, the effect of temperature
on key metamorphic reactions controlling density and seismic structure
is modest and does not influence the main conclusions of this study.
In both the Kohistan and Talkeetna sections an abrupt increase in
VP is observed between the dominant felsic/intermediate plutonic rocks
of the upper crust (6.3–6.4 km s21) and underlying mafic arc crust (6.9–
7.1 km s21) (Figs 2 and 3). However, the lower crust in the two arc sections differs significantly. In Kohistan, VP in the lower crust increases
linearly between 35 km depth and 50 km depth with two minor discontinuities (Figs 2 and 3). The first is an increase in VP at about 40 km
depth between gabbroic rock (about 7.0 km s21) and mafic garnet
granulite (about 7.5 km s21). The second is an increase in VP between
the garnet granulite and the underlying ultramafic rocks (about 8.0 km
s21) at approximately 50 km depth. This contact between garnet granulite and ultramafic rocks has traditionally been interpreted to reflect
the seismic Moho of the Kohistan arc20,21. The discontinuity at around
40 km coincides with a density inversion where the lowermost 10 km
of crust is significantly denser (Dr 5 rcrust 2 rmantle 5 40–280 kg m23)
than the underlying mantle (Figs 2 and 3). This density inversion
corresponds to a pressure of about 1.0–1.2 GPa and is related to the
appearance of garnet as a stable phase in mafic lithologies (the ‘garnetin’ reaction; see Methods). Rocks above this discontinuity are generally
50
Kohistan
(running average)
7
8
VP (km s–1)
40
3,000
3,500
Density (kg m–3)
50
60
SiO2 (wt%)
70
80
Figure 2 | Detailed VP and density depth-structure of the exposed Kohistan
arc section compared to the average continental crust and the Izu-Bonin arc
crust. a, The seismic characteristics of the reconstructed Kohistan arc are
similar to those of the Izu-Bonin arc crust (pink line, with pink shading
indicating the variability)32 and differ significantly from the average seismic
characteristics of continental lower crust (purple)4. Specifically, a sharp Moho
that defines the crust–mantle interface in continents is absent in arcs.
b, The depth of the continental Moho coincides with the depth at which crustal
rocks from Kohistan become density-unstable with respect to the depleted
upper mantle (green line). Black lines indicate the running average.
density-stable compared to a depleted upper mantle, whereas the rocks
below are generally density-unstable and could founder back into the
upper mantle.
In Talkeetna, the Moho is a sharp contact between the basal gabbronorite and the underlying depleted mantle22 occurring at pressures
(about 1 6 0.14 GPa; ref. 19) comparable to those of the observed density
inversion in Kohistan, and corresponding to a maximum crustal thickness of around 40 km depth (Fig. 3). Petrological considerations indicate that significant volumes of mafic/ultramafic cumulates are missing
from the base of the Talkeetna arc22. Density-unstable garnet granulites
(VP < 7.5–7.7 km s21), similar to those preserved in Kohistan, are only
present as relicts in a thin layer (less than about 100 m thick) situated
between the basal gabbronorite and the upper mantle (Fig. 2)22. With
the exception of these garnet granulites, the Talkeetna arc crust is generally density-stable (Dr 5 < 2160 kg m23) and a single large increase
in VP is calculated at around 40 km depth, between gabbroic rocks
(about 7.0 km s21) and the underlying depleted harzburgite (about
7.9–8.0 km s21).
The calculated seismic properties of the density-stable Talkeetna lower
crust match those of the continental lower crust, whereas the densityunstable Kohistan lower crust has seismic characteristics comparable
to the sub-Moho structure in active arcs (Fig. 3 and Extended Data Fig. 2).
An important difference between the two sections is that the Talkeetna
crust is density sorted, whereas the lower Kohistan arc is not (Fig. 3).
Density sorting of the Kohistan arc lower crust, in which unstable cumulates are replaced by harzburgitic sub-arc mantle, would result in a lower
crust with seismic properties comparable to those of Talkeetna and the
continental lower crust (Figs 2 and 3). From these observations we
propose that density sorting of arc lower crust is a crucial mechanism
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LETTER RESEARCH
Kohistan
0
Talkeetna
Volcanic
rocks
Volcanic
rocks
Felsic plutonics
6
12
Felsic
plutonics
???
Gap
)
Depth (km)
18
Model A
of ref. 14
(gap filled
by felsic
plutonics)
24
Quartz diorite
and tonalite
Gabbro
norite
30
Diorite/
gabbro
36
Diorite/
gabbro
42
Granite-granulite/
granite-gabbro
Hornblendite/
garnetite
Pyroxenite
48
54
Granite-granulite/
pyroxenite
Harzburgite/
dunite
6
7
8
VP (km s–1)
2,600
3,200
3,800
2,600 3,200
3,800
Density (kg m–3) Density Density (kg m–3)
unstable
6
7
8
VP (km s–1)
Figure 3 | Schematic illustrations of the lithological, seismic and density
properties of the Kohistan and Talkeetna arc sections. Shown are simplified,
schematic crustal columns (after refs 19, 22 and 33) and the calculated average
seismic VP velocities and densities (black lines) of the main crustal building
blocks of the two arcs. The thickness of the different units was approximated
using the calculated densities and existing barometric pressure estimates19,22,33.
The pink and purple lines indicate the seismic velocities of the Izu-Bonin and
continental arc crust, respectively (as in Fig. 2). The VP and VS estimates of
Kohistan are after Fig. 2, and those of Talkeetna are recalculated after ref. 14.
for the transformation of an arc-type Moho to a continental-type
Moho.
Density sorting of the lower crust can occur during collision, tectonic
underplating and/or normal arc buildup23. To constrain the maximum
thickness that an unstable layer can achieve before foundering occurs,
we calculated the timescale for the initiation of a Rayleigh–Taylor-type
instability at the base of the arc crust as a function of the density and
temperature of the underlying mantle and the density and thickness of
the unstable layer13,24–26 and compared it to the timescale for crustal
growth for different magma supply rates10 (see Methods for details). For
a given temperature, we assume that the unstable layer will grow until
the timescale for instability initiation is less than the time required to
form the layer. For temperatures below about 700–800 uC, instability
times exceed reasonable geological timescales, because the high viscosity of the ‘cold’ crust and underlying mantle inhibits instability growth
(Fig. 4). In contrast, for temperatures over 800 uC, instability growth
becomes more efficient and the unstable layer grows to a thickness of
only a few kilometres before foundering into the underlying mantle (on
a timescale of 0.5–5 million years). The difference in the observed thermal regime between Kohistan and Talkeetna (Fig. 1c) is consistent with
the preservation of a thick layer of density-unstable material at the base
of the Kohistan arc section, whereas in the warmer Talkeetna arc foundering is predicted to be more efficient, resulting in the preservation of
a significantly thinner unstable layer (Fig. 4).
Our results show that foundering can explain both the location and
primary seismic characteristics of the continental Moho. In active arcs,
an unstable layer removed by foundering will be rebuilt within a few
million years and so the chance of seismically imaging a newly densitysorted lower crust with a sharp Moho at about 40 km is low. After magmatism ceases at an arc, Moho temperatures will remain high until the
geotherms conductively relax16. As long as the Moho temperature remains
above about 700 uC, foundering will continue, but the foundering layer
will not be rebuilt. Instead, it will be replaced by upper-mantle rocks,
resulting in the formation of a density-sorted continental lower-crust/
upper-mantle interface with a sharp Moho discontinuity. We speculate that unusually thick Archaean continental crust with a preserved
5–10-km-thick transitional zone between crust and mantle represents
lower crust that has not been density sorted27. More detailed seismic
studies of stable continental regions are needed to test the abundance
of such preserved relicts.
25
215 km3 km–1 Myr –1
290 km3 km–1 Myr –1
20
0k
=5
–3
kg m
gm
200
10
Kohistan
Δρ
15
Talkeetna
5
Δρ =
–1
3
Cumulate layer thickness (km)
5
5
1
1
0.5
0.5
0
500
600
700
800
900
1,000
1,100
Mantle temperature (°C)
Figure 4 | Modelled thickness of the density-unstable layer at the base of arc
crust. The thickness was calculated by equating the timescale required for
an instability to form14 with the timescale required to grow a cumulate layer
based on estimated magma fluxes10 (blue and red curves, respectively). The
boxed numbers are times required to grow the layer in millions of years. Layer
growth assumes that 70% of the original melt mass is partitioned into the
cumulate layer10. Solid and dashed curves are based on different density
contrasts between the layer and underlying mantle. The vertical bands indicate
the approximate Moho temperatures for the Talkeetna (orange) and Kohistan
(green) arcs, and horizontal fields indicate the preserved thickness of the
density-unstable layer in the two arcs.
METHODS SUMMARY
Calculation of density and seismic velocity. We used Perple_X (ref. 28) to calculate
subsolidus thermodynamic phase equilibria for a range of whole-rock compositions from the Kohistan11 and Talkeetna22,29 arcs assuming 1 wt% H2O. Seismic
velocities and densities of the stable mineral assemblage and mode were calculated
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©2013 Macmillan Publishers Limited. All rights reserved
RESEARCH LETTER
using a compilation of geophysical mineral properties30. We implemented an
updated version of the compilation (B. Hacker and G. Abers, personal communication, 2010) into Perple_X. The variable intrusion pressures of the rocks studied
are from refs 11, 19 and 31 for Kohistan and Talkeetna, respectively; corresponding
depths were calculated by integrating the calculated density profiles for pressure.
Temperatures were calculated along a 60 mW m22 geotherm for the Kohistan arc31
and a 80 mW m22 geotherm for Talkeetna19. We used the following solid solution
models: Atg, Chl (HP), Ctd (HP), Cpx (HP), Ep (HP), GlTrPg, Gt (HP), Pheng
(HP), O (HP), Opx (HP), Pl (h), San, Sp, and T. To investigate the influence of
variable oxygen fugacity (fO2 ) on the seismic velocity structure of an arc, we calculated seismic properties and densities at Fe31/Fetotal values of 0.15, 0.25 and 0.35.
All results were plotted with Fe31/Fetot 5 0.25 but the results discussed here are not
dependent on fO2 .
Calculation of instability timescales. Our calculation of the thickness of the unstable
layer follows the approach of ref. 13. The timescale required to form an instability
scales inversely with the thickness of the dense layer and the density contrast
between the layer and underlying mantle (that is, thicker layers and greater density
contrasts lead to shorter instability times)24,25. For temperature-dependent viscosity
the instability time decreases exponentially with increasing mantle temperature.
For a given temperature, we assume that the unstable layer will grow until the timescale for instability initiation is less than the time required to form the layer.
Online Content Any additional Methods, Extended Data display items and Source
Data are available in the online version of the paper; references unique to these
sections appear only in the online paper.
Received 19 April; accepted 3 October 2013.
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Acknowledgements The work was supported by NSF grant numbers EAR 0910644 (to
O.J.) and EAR 1316333 (to M.D.B.). We thank N. Arndt for comments that helped to
improve the manuscript. J. Connolly’s help in recalibrating the elastic property
calculation of Perple_X is appreciated, as are discussions with P. Kelemen and
B. Hacker.
Author Contributions O.J. designed the project. Both authors conducted the
calculations, contributed to the interpretation of the results and wrote the manuscript.
Author Information Reprints and permissions information is available at
www.nature.com/reprints. The authors declare no competing financial interests.
Readers are welcome to comment on the online version of the paper. Correspondence
and requests for materials should be addressed to O.J. ([email protected]).
1 3 4 | N AT U R E | VO L 5 0 4 | 0 5 D E C E M B E R 2 0 1 3
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LETTER RESEARCH
METHODS
The density of arc lower crust rocks. Crustal rocks that are denser than the underlying upper mantle peridotite are considered density unstable. Density-unstable rocks
can either form as relatively Fe-rich ultramafic cumulates derived from mantlederived melts, which are as dense or slightly denser than the underlying mantle
at magmatic temperature but can become significantly denser upon cooling9,41.
Additionally, dense garnet-bearing cumulates can form from hydrous basaltic–
andesitic liquids at high pressures (above about 1 GPa)42. Three important pressuredependent metamorphic reactions result in the formation of dense minerals (such
as spinel and garnet), which strongly control the density of Fe-rich and Al-rich
(such as gabbroic) compositions in the arc lower crust.
The three main densification reactions likely to be important in the lower arc
crust are: (1) The breakdown of plagioclase next to olivine, which occurs at pressures of about 0.6–0.7 GPa (ref. 43): olivine 1 plagioclase R pyroxene 1 spinel (I)
(2) The formation of metamorphic garnet due to the breakdown of plagioclase at
0.8–1 GPa (ref. 43): plagioclase 1 orthopyroxene R garnet 1 quartz (II) (3) The
breakdown of plagioclase at about 1.2–1.6 GPa: albite R jadeite 1 quartz (III).
The importance of each reaction for densification depends on the bulk composition of the system. Reaction (I) is important for olivine and plagioclase-rich
rocks (troctolite and olivine-gabbro)15, which probably form in thin arcs where
magma fractionation occurs at shallower crustal levels and the olivine 1 plagioclase
stability field is increased42. Reaction (II) is important for rocks with high Fe/Mg
ratios and high Al-content and low Si-content, such as cumulates formed from
hydrous arc magmas at increased pressures15. Reaction (III) will only be relevant
for strongly over-thickened arc crust.
Additionally, the depth range corresponding to pressures of about 0.8–1 GPa at
which reaction (II) occurs varies significantly depending on the density structure
of the arc crust. In juvenile arcs, where most of the arc crust is composed of rocks
with approximately basaltic compositions with densities of around 2,900–3,100 kg
m23, pressures of 0.8–1 GPa correspond to depths of about 26–34 km. In contrast,
in mature arcs that have a significant thickness of granitic upper crust (such as the
Izu-Bonin arc) with densities as low as 2,600–2,800 kg m23, pressures of 0.8–1 GPa
can correspond to depths of up to 32–40 km. Accordingly, the depth range in which
delamination—owing to the formation of magmatic/metamorphic garnet and/or
pyroxene and spinel—occurs is 20–70 km, depending in detail on the composition
of the rocks in the arc crust.
Geological setting. The Kohistan arc, exposed in northeast Pakistan, was a longlived Jurassic/Cretaceous to Tertiary island arc that formed in the equatorial part
of the Neotethyan ocean separating India and Eurasia before the India–Asia collision. The Kohistan arc exposes a complete arc section ranging from unmetamorphosed sediments in the north to upper-mantle rocks in the south. Pressure
and temperature estimates for the lowermost mafic arc crust indicate pressures in
excess of about 1.5 GPa for the crust–mantle transition.
The Talkeetna arc, exposed in south central Alaska, is a Triassic island arc that
was active from about 200–175 million years ago. It exposes rocks ranging from
unmetamorphosed sediments and associated volcanics in the north of the arc to
upper-mantle rock in the south of the arc. Owing to large-offset strike–slip faulting, the middle crust is partly missing19. The lowermost mafic arc crust records
maximum pressures of 1.0–1.1 GPa, indicating a slightly shallower crust–mantle
transition in the Talkeetna compared to the Kohistan.
Calculation of density and seismic velocity. We used Perple_X (ref. 28) to calculate subsolidus thermodynamic phase equilibria for a wide range of whole-rock
compositions from the Kohistan11 and Talkeetna22,29 arcs assuming 1 wt% H2O.
Seismic velocities (VP, VS) and densities of the stable mineral assemblage and
mode were calculated using a compilation of geophysical mineral properties30.
We implemented an updated version of the compilation (B. Hacker and G. Abers,
personal communication, 2010) into Perple_X. The variable intrusion depths of
the rocks studied are from refs 11, 19, 31 and 44 for Kohistan and Talkeetna,
respectively. Temperatures were constrained along a 60 mW m22 geotherm constrained for the Kohistan arc31,44 and a 80 mW m22 geotherm for the Talkeetna
arc19. We used the following solid solution models in our calculation: Atg, Chl
(HP), Ctd (HP), Cpx (HP), Ep (HP), GlTrPg, Gt (HP), Pheng (HP), O (HP), Opx
(HP), Pl (h), San, Sp and T.
To investigate the influence of variable fO2 on the seismic velocity structure of an
arc, we calculated seismic properties and densities at Fe31/Fetotal values of 0.15,
0.25 and 0.35. All results were plotted with Fe31/Ftotal 5 0.25 (ref. 45) but the
results discussed here are not dependent on fO2 .
The effect of temperature on the density structure. The thermal regime in the
lower crust is poorly constrained and probably highly variable through time owing
to the intrusion of hot basaltic liquids. To evaluate the effect of variable temperature we calculated the density and seismic structure of the Kohistan and Talkeetna
crust at 40, 60 and 80 mW m22 geotherms (Extended Data Fig. 1). Because magmatic and metamorphic phase boundaries involving significant volume changes
(and corresponding density changes) are dominantly pressure-dependent, and only
to a limited extent temperature-dependent, the density structure is only marginally
influenced by the thermal structure. The most important reaction at higher temperature is the breakdown of hydrous phases (for example, amphibole), which generally
break down to a denser phase (for example, pyroxene). However, this transformation has only a limited effect on density and seismic properties (Extended Data Fig. 1).
Calculation of instability timescales. Our calculation of the thickness of the unstable
layer follows the approach of ref. 13. The timescale required for an instability to
form scales inversely with the thickness of the dense layer, and the density contrast
between the layer and underlying mantle (that is, thicker layers and greater density
contrasts lead to shorter instability times)24,25. In addition, for temperature-dependent viscosity the instability time decreases exponentially with increasing mantle
temperature. For a given temperature, we assume that the unstable layer will grow
until the time required for instability initiation is less than the time required to form
the layer.
References for Fig. 1. The VP/VS and VP estimates for different arcs in Fig. 1 are
taken from refs 46–49.
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RESEARCH LETTER
Extended Data Figure 1 | Seismic velocity and density along different
geotherms for the Kohistan arc. Plotted are the mean and range in VP and
density as calculated along the 40, 60 and 80 mW m22 geotherms.
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LETTER RESEARCH
Extended Data Figure 2 | Seismic velocities of the lower arc and continental
crust. Histogram showing distribution of average seismic velocities directly
above and below the Moho in continents (red, after ref. 4) and from active arcs
(refs 6, 8, 32, 34–40). Also shown are the range of VP for density-stable and
density-unstable rocks from the Kohistan and Talkeetna arcs, as dashed fields
calculated from this study. In the arcs, sub-Moho rocks have on average a
VP that is 0.5 km s21 slower than do sub-Moho rocks in continents. The
observed low velocities in the arcs agree with the velocities calculated for
density-unstable crustal rocks from Kohistan.
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