GEOPHYSICAL RESEARCH LETTERS, VOL. 38, L24308, doi:10.1029/2011GL049719, 2011
Deep structure of lithospheric fault zones
J. P. Platt1 and W. M. Behr2
Received 20 September 2011; revised 15 November 2011; accepted 16 November 2011; published 21 December 2011.
[1] We calculate the cumulative width w of ductile shear
zones accommodating plate motion in continental lithosphere,
based on the assumptions that (1) the flow stress is controlled
by the yield strength of intact rock at any given depth; (2) the
yield strength profile through the crust can be constrained
from observations in exhumed shear zones; and (3) strain
localization is primarily caused by grainsize reduction leading
to a switch to grainsize-sensitive creep. We use a mid-crustal
stress-temperature profile measured in the Whipple Mountains,
California, and calculate stress profiles at depth from published
flow laws for feldspar and olivine. We conclude that w for a
plate boundary shear zone accommodating 50 mm/yr displacement (comparable to the San Andreas Transform) may reach
180 km in the quartz-rich mid-crust, depending on water
fugacity and thermal gradient. It narrows to a few meters in
feldspathic lower crust and in the uppermost mantle, and then
widens rapidly with depth in the lower lithosphere. We explore
the effects of differences in crustal thickness and composition,
thermal gradient, and water activity. Citation: Platt, J. P., and
W. M. Behr (2011), Deep structure of lithospheric fault zones,
Geophys. Res. Lett., 38, L24308, doi:10.1029/2011GL049719.
1. Introduction
[2] There is no consensus at present on the width and
structure of plate-boundary fault zones below the seismogenic
layer. Estimates for fault-zone widths in the lower crust range
from <10 km [e.g., Henstock et al., 1997], to several tens of
km [e.g., Vauchez and Tomassi, 2003; Wilson et al., 2004],
and in the lithospheric mantle estimates vary from <100 km
[e.g., Herquel et al., 1999; Titus et al., 2007] to several
hundreds of km [Baldock and Stern, 2005]. Fault-zone width
at any depth should be a function of the constitutive relationship between stress and strain-rate in the shear zone, and
therefore should be calculable [Platt and Behr, 2011b]. The
difficulties with doing this stem from uncertainties both in
shear-zone rheology and the level of deviatoric stress in the
lithosphere. We propose three concepts that can help resolve
these problems, and allow calculation of fault zone width as a
function of depth and temperature. These concepts, discussed
in more detail below, are as follows.
[3] 1. The deviatoric stress in a plate-boundary shear zone
at any given depth approximates the yield stress of the surrounding rock at that depth [Platt and Behr, 2011b].
[4] 2. Following from (1), stress-temperature data from
exhumed ductile shear zones provide proxies for strength
profiles through the lithosphere [Behr and Platt, 2011].
1
Department of Earth Sciences, University of Southern California,
Los Angeles, California, USA.
2
Department of Geological Sciences, Brown University, Providence,
Rhode Island, USA.
Copyright 2011 by the American Geophysical Union.
0094-8276/11/2011GL049719
[5] 3. Strain localization to form ductile shear zones is
primarily a result of grainsize reduction causing a switch to
grainsize-sensitive creep. This allows the assignment of a
rheology to the shear zone material [Platt and Behr, 2011a].
[6] Using these concepts, we calculate the minimum
cumulative width of a plate-boundary ductile shear zone as a
function of relative plate velocity, rock rheology, temperature, and water fugacity, and we explore the effects of these
variables.
2. Ductile Shear Zones Are Constant
Stress Experiments
[7] Ductile shear zones reflect strain localization, which
result from microstructural changes produced by deformation. These changes require the surrounding rock to deform,
so the ambient stress must reach and remain at the yield
stress sy of intact rock [Platt and Behr, 2011b]. For an
imposed plate velocity V, the cumulative width w of the
shear zones accommodating that motion will stabilize at a
value given by w = V/ės. The strain rate ė in the shear zones
is controlled by the rheology of the shear zone material, so
that ė = Assyn, where As and n are material parameters. The
shear zones act as a self-organizing system: w cannot exceed
the value given above, or the strain-rate will drop, and hence
the stress will too, preventing any further widening at the
expense of the surrounding rock. If w is less than this value,
the stress will exceed sy, and the surrounding rock will
deform, widening the shear zone. The velocity-boundary
condition imposed by plate motion is therefore converted to
a stress boundary condition within the shear zone, buffered
by the yield stress of the surrounding rock. This concept
leads to the conclusion that shear zone width is related to the
material properties of the shear zone by:
w ¼ V =As sny
ð1Þ
Shear zones that are reactivated, or that experience a drop in
the imposed relative plate velocity, may not obey this constraint. In contractional and extensional shear zones rocks
change depth and hence temperature, so that their rheology
changes, but the stress in the shear zone should still
approximate the strength of the surrounding rock at any
given depth [Platt and Behr, 2011b].
3. Measuring Stress Profiles Through the Crust
[8] Exhuming shear zones preserve a record of the stress
and temperature profile through the deforming crust. We
constructed such a profile for an exhumed normal-sense
ductile shear zone underlying the Whipple detachment fault
in SE California, using the dynamically recrystallized grainsize piezometer for quartz [Stipp and Tullis, 2003], and the
Ti-in-quartz thermobarometer [Thomas et al., 2010]. By
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Figure 1. (left) Differential stress profile and (right) cumulative shear zone width w through continental lithosphere with a
composition and thermal gradient comparable to southern California, cut by a plate boundary shear zone with a displacement
rate of 50 mm/yr. Curves shown are calculated for wet (blue) and dry (red) rheologies. The stress profile was calculated
using Byerlee’s Law for strike-slip faulting in the seismogenic layer, stress-temperature data from paleopiezometry in the
Whipple Mountains for the mid-crust after Behr and Platt [2011], and dislocation creep laws for feldspar [Rybacki et al.,
2006] and olivine [Hirth and Kohlstedt, 2003]. w is calculated for quartz-dominated middle crust using the DRX creep
law (P&B DRX creep) and climb-assisted dislocation creep laws (P&B climb creep) from Platt and Behr [2011a], and
the creep law from Hirth et al. [2001] (green). For feldspar dominated lower crust we used the diffusion creep laws for feldspar [Rybacki et al., 2006] and olivine [Hirth and Kohlstedt, 2003] (see text for further explanation). Data are presented in
tabular form in Table S2 in the auxiliary material.
modelling the cooling history during exhumation, we converted this to a stress-depth profile [Behr and Platt, 2011].
The Whipple Mountains accommodated Basin and Range
extension during early Miocene time at a rate of 5 mm/yr
[Stockli, 2005]. The stress profile from the Whipple Mountains therefore provides a proxy for a strength profile
through the ductile crust of the Cordillera to a depth of
25 km. Because the yield strength of intact rock is independent of the strain-rate in the shear zone, this profile
can be applied to shear zones such as the San Andreas
Transform system that move at different rates from the
Whipple Mountains shear zone.
4. Controls on the Rheology of Ductile
Shear Zones
[9] The most potent cause of weakening in shear zones is
likely to be dynamic recrystallization, resulting in grain-size
reduction and a switch to grainsize-sensitive creep [Platt and
Behr, 2011a]. The change in deformation mechanism occurs
because at small grain-sizes the grain-size sensitive creep
mechanism can accommodate a higher strain-rate at any
given stress. At low temperature and high stress, dynamic
recrystallization occurs primarily by grain-boundary migration driven by lattice strain energy (rGBM). rGBM may be
the dominant mechanism of recovery during dislocation
creep under these conditions [Tullis and Yund, 1985;
Fliervoet and White, 1995]. This leads to a form of grainsize-sensitive dislocation creep (DRX creep) with a flow law
of the form:
ė¼
Ad Dgb s3
;
dr
ð2Þ
where Ad incorporates lattice-dependent material parameters,
Dgb is the diffusion coefficient for grain-boundary migration, and dr is grainsize [Platt and Behr, 2011a]. The grain
size in materials undergoing dynamic recrystallization
depends on the flow stress raised to the power -p, where p
has a value in the range 1.26 for quartz [Stipp and Tullis,
2003] to 1.33 for olivine [Van der Wal et al., 1993]. The
effective stress exponent in this flow law is therefore a little
over 4, which corresponds well to experimental and observational constraints [Hirth et al., 2001; Hirth and Kohlstedt,
2003]. We constrained the material parameters in this flow
law for quartz using published experimental data and our
measurements of differential stress, strain-rate, and shearzone width in the Whipple Mountains shear zone [Platt and
Behr, 2011b] (see also Table S1 in the auxiliary material).1
[10] Grainsize reduction in olivine and feldspar may result
in a switch to diffusion creep, with a grain-size exponent of -3
[Hirth and Kohlstedt, 2003; Rybacki et al., 2006; Warren and
Hirth, 2006], resulting in substantial weakening. In a constant
stress shear zone, the flow stress remains high, and under these
conditions grain growth is suppressed, and hence does not
limit the weakening process [Platt and Behr, 2011a].
5. Width of Plate-Boundary Shear Zones
[11] We apply the relationship between shear zone width
and rock mechanics expressed in equation (1) to calculate
the cumulative width w of a transform plate boundary with a
slip rate of 50 mm/year (comparable to the San Andreas
Transform) through the lithosphere below the brittle-ductile
1
Auxiliary materials are available in the HTML. doi:10.1029/
2011GL049719.
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Figure 2. (left) Differential stress profile and (right) cumulative shear zone width w through continental lithosphere with a
cratonic composition and thermal gradient (red), and hot wet orogenic crust (blue), cut in each case by a plate boundary shear
zone with a displacement rate of 50 mm/yr. Calculations were carried out as described in the caption to Figure 1. Note difference in scale to Figure 1. Data are presented in tabular form in Table S2 in the auxiliary material.
transition, and we explore a variety of possible shear zone
rheologies, lithospheric structures and geotherms. To do
this, we need to estimate the yield stress of the lithosphere as
a function of temperature, depth, composition, and water
content. For quartz-rich middle crust with a composition and
thermal gradient comparable to that in southern California,
we use the stress-temperature profile from the Whipple
Mountains determined by Behr and Platt [2011]. Naturally
constrained stress profiles do not exist for the lower crust or
upper mantle, however, and yield strengths for rocks under
geological conditions are not well known. To estimate stress
profiles through these parts of the lithosphere we assume
that in the absence of strain localization, rocks at these
depths deform by dislocation creep at 1015 sec1. This
rate corresponds to non-localized deformation (equivalent to
distributing Pacific / North America plate motion over the
entire width of the North American Cordillera). We then use
published flow laws for feldspar and olivine to calculate
stress profiles for various crustal thicknesses, compositions,
thermal gradients and water contents (shown on the left side
of the plots in Figures 1 and 2). We assume that strain localization takes place at constant stress for any given depth,
following the stress profile, as a result of a switch to grainsize-sensitive creep caused by dynamic recrystallization. For
feldspar and olivine, the deformation switches from dislocation to diffusion creep, and for quartz the deformation
switches to the DRX creep law discussed above.
[12] In all models we arbitrarily assume the brittle part of
the transform zone in the upper crust has a cumulative width
of 1 km – this does not affect the calculations. We do not
allow for stress transfer between different levels in the lithosphere [e.g., Roy and Royden, 2000], transient effects
associated with the seismic cycle [e.g., Freed et al., 2010], or
the effects of stress concentrations as modeled by RegenauerLieb et al. [2006], for example. These effects are real and
important, but they are likely to be small relative to the
effects of uncertainties in the rheology, which is the primary
focus of this paper. We also accept that real rock materials,
such as peridotite, gabbro, and granite, are polyphase systems, and that these are likely to differ significantly in
their rheology from pure quartz, feldspar, and olivine
[Dell’Angelo and Tullis, 1996; Dimanov and Dresen, 2005].
[13] To outline the effect of variations in the parameters,
we show in Figures 1 and 2 the following combinations. In
Figure 1 we take a lithospheric column and geotherm that is
appropriate to southern California, where the San Andreas
Transform cuts through continental crust similar in age,
composition, and thickness to that exposed in the Whipple
Mountains. Rather than assume the water content, we
assume our stress profile is correct, and explore the consequences of using wet (blue in Figure 1) and dry (red)
rheologies for quartz, feldspar and olivine. Wet rheologies
assume water activity equal to unity, and the water weakening effect is linearly dependent on the water fugacity
[Gleason and Tullis, 1995]. Dry rheologies assume a constant and low water fugacity. The effective water fugacity
during deformation is difficult to constrain, as water present
in the system may not in fact be able to enter the crystal
lattice [Post and Tullis, 1998]. Neither of the two alternatives described above is likely to be correct in general:
while water fugacity is likely to increase with depth due to
the effects of temperature and pressure [Paterson, 1986], this
will be counteracted by hydration reactions in crystalline
rocks, which consume water [Yardley and Valley, 1997].
The wet and dry rheologies we assume therefore bracket the
likely range of natural water fugacities.
[14] To explore the effects of thermal gradient and tectonic
setting, we take a lithospheric column and geotherm characteristic of a dry craton, and contrast that with a column
characteristic of a hot wet orogen or orogenic plateau, such
as the Tibetan plateau (Figure 2).
[15] The “California wet” model (blue curve in Figure 1)
shows w increasing gradually with depth in the middle crust,
reaching 11 km at 23 km depth (550°C). This reflects the
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competition between the effects of increasing temperature
(which increases strain-rate at any level of stress) and
decreasing stress following our stress profile. The results are
extremely sensitive to the precise level of stress, and to the
flow law used to calculate strain-rates. For comparison we
show w calculated on the same assumptions, but using the
quartz flow-law estimated from experimental and natural
data by Hirth et al. [2001]: this predicts w increasing with
depth to nearly 200 km. The strain rates predicted by this
flow law appear to be more than an order of magnitude less
than those we observe at corresponding stresses and temperatures in the Whipple Mountains. Our predictions for
w are therefore likely to be minima. In the feldspathic lower
crust we predict an extremely narrow shear zone, with w ≤
200 m. This reflects the effect of the switch to diffusion
creep in fine-grained feldspar [Rybacki et al., 2006], combined with the high stresses needed to develop the shear
zone. Note that the strain-rates in such narrow ductile shear
zones will be very high, and at high stress, shear heating will
be significant, and may lead to melting and seismogenic
faulting [John et al., 2009]. In the mantle, w is 850 m at the
Moho, due to the activity of grainsize sensitive creep [Hirth
and Kohlstedt, 2003], but it widens downwards, reaching
over 300 km at 42 km depth (850°C). Below 45 km depth
(900°C) the dominant flow law changes to dislocation creep,
and our model predicts non-localized strain. In practice,
processes that we have not taken into account, such in
ingress of water, development of crystallographic preferred
orientation, or the effect of lateral contrasts in temperature or
composition, may cause some degree of localization.
[16] In the “California dry” model (red curve in Figure 1)
w increases to 156 km at the base of the quartz-rich layer.
This results from the much greater strength of dry quartzite,
so that using our measured stress values from the Whipple
Mtns, strain-rates are lower, and hence the shear zone has to
be wider to accommodate the imposed plate velocity. Calculated stresses in the felspathic lower crust are so high that
we predict brittle failure in this region. In the upper mantle
the shear zone is 50 m wide at the Moho, widening to over
1100 km at 54 km depth (1000°C), below which we predict
no strain localization.
[17] For our “dry craton” model we calculated a stresstemperature profile through the upper crust using the quartz
flow law determined by Rutter and Brodie [2004], which
may be a good approximation to the behavior of unweakened quartz, and in the feldspathic lower crust and upper
mantle we used published flow laws for dry rheologies, as
described above (red curve in Figure 2). Stresses are very
high, and we predict ductile shear in the upper crust only at
depths greater than 20 km (375°C), forming a shear zone
less than 1 km wide. Brittle behavior is predicted in the
feldspathic lower crust and uppermost mantle to a depth of
60 km (700°C). This reflects the high stress required for
dislocation creep under dry conditions in these rocks, which
exceeds the brittle failure strength. Below 60 km w increases, reaching 174 km at 180 km depth (1200°C).
[18] For a hot wet orogen we use the Whipple Mountains
stress profile to 550°C (blue curve in Figure 2), but we
recognize that this may overpredict the stress (and hence
underpredict w). Above 550°C we use a stress profile calculated from the quartz flow law determined by Rutter and
Brodie [2004]. Our calculations predict a mid-crustal shear
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zone widening downwards to 177 km wide at 46 km depth
(800°C). At temperatures above 550°C we lack an observational stress profile, so that values for w at depths > 29 km,
where the shear zone is 7 km wide, are highly uncertain. We
predict a shear zone 1.8 km wide in feldspathic lower crust at
46 km depth (800°C), which widens rapidly downwards to
46 km at the Moho (60 km depth, 1000°C). Below the Moho
at these temperatures the dominant flow law in olivine is
dislocation creep, and hence we predict no strain localization.
6. Conclusions
[19] Our exploration of shear zone width for wet and dry
rheologies in active tectonic and cratonic crustal environments covers a reasonable range of parameter space, and
allows us to draw some general conclusions.
[20] 1. Cumulative widths for plate boundary ductile shear
zones below the seismogenic layer may reach 180 km in
quartz-rich crystalline continental crust, but depend on both
water content and the yield strength of undeformed crust,
which controls the ambient stress. Shear zone width results
from the interplay between the effects of deformation
mechanism switches, increasing temperature, and decreasing
stress with depth. In strong, dry, cratonic crust shear zones
may be <1 km width. Our predicted widths are within the
range reported in geological studies of greenschist facies,
quartz-rich shear zones exhumed from the middle crust [e.g.,
West and Hubbard, 1997; Whitmeyer and Simpson, 2003;
Faleiros et al., 2010], and are consistent with the general
observation that strain becomes increasingly distributed at
depth within the crust [Vauchez and Tomassi, 2003]. Our
prediction that w may reach 180 km beneath a San Andreas
type transform zone suggests that the upper crust may be
largely decoupled from the underlying lower crust and
mantle lithosphere. Upper crustal faults may be kinematically linked at depth, as suggested by Platt & Becker [2010],
and the narrow shear zones we predict in the lower crust and
upper lithospheric mantle may not have a direct spatial
connection to upper crustal faults, as suggested by Roy and
Royden [2000]. Note that the wide shear zones we predict
in the mid-crust do not directly relate to the concept of
channel flow at these levels [e.g., Beaumont et al., 2004].
We predict wide shear zones where there is a relatively low
level of strain-related weakening compared to undeformed
rock. By contrast, channel flow and related phenomena
result from the presence of inherently weak zones within the
lithosphere, such as zones of partial melt, and their thickness
reflects the thickness of the thermal perturbation or weak
compositional layer that controls the process.
[21] 2. In feldspar-dominated lower crust and in the
uppermost mantle, stresses are high, resulting in very narrow
shear zones, and in dry crust they may exceed the brittle
fracture strength of rock. Even where the stresses are low
enough for ductile shear zones to develop, the effect of shear
heating may result in thermal runaway, melting, and seismogenic faulting [John et al., 2009]. These predictions are
consistent with the occurrence of earthquakes in the lower
crust, particularly of cratonic regions [Maggi et al., 2000].
[22] 3. Below the Moho, shear zones widen dramatically
with depth. This results from the progressively decreased
effectiveness of grainsize-sensitive creep as a weakening and
strain localization mechanism with increasing temperature.
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Strain ceases to be localized at depths ranging from 46 km
(in wet warm lithosphere) to >180 km (in cool dry lithosphere): this transition generally occurs within the thermal
boundary layer, rather than at the base of the lithosphere.
Several recent geophysical and geodetic studies are consistent with large-scale upper mantle flow [Baldock and Stern,
2005; Freed et al., 2007; Sol et al., 2007] beneath transform
plate boundaries, supporting our prediction that deformation
in the lower part of the lithosphere may be very broadly
distributed in actively deforming regions. The abruptness of
shear zone widening and its proximity to the Moho may
affect the likelihood of large-scale decoupling between the
crust and lithospheric mantle, including, for example, the
development of seismically active mega-detachments at
Moho depths [e.g., Davis et al., 2006; Wernicke et al.,
2008], or the foundering and delamination of lithospheric
mantle.
[23] Acknowledgments. We thank Thorsten Becker for helpful comments, and Brian Wernicke and an anonymous referee for their helpful
reviews. This research was supported by NSF grant EAR-0809443 awarded
to John Platt.
[24] The Editor thanks Brian Wernicke and an anonymous reviewer for
their assistance in evaluating this paper.
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W. M. Behr, Department of Geological Sciences, Brown University,
324 Brook St., Providence, RI 02912, USA. ([email protected])
J. P. Platt, Department of Earth Sciences, University of Southern
California, Los Angeles, CA 90089-0742, USA. ([email protected])
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