Gomberg, Paul Bodin, Nick Beeler, Steve Cohen, and Steve Hickman helped to improve the manuscript. References. Baisch, S., and G. H. R. Bokelmann (2001), ...
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, B05407, doi:10.1029/2003JB002744, 2004
Elevated stresses and creep rates beneath the brittle-ductile transition caused by seismic faulting in the upper crust Susan Ellis Institute of Geological and Nuclear Sciences, Lower Hutt, New Zealand
Bernhard Sto¨ckhert Institute of Geology, Mineralogy, and Geophysics, Ruhr University, Bochum, Germany Received 13 August 2003; revised 30 January 2004; accepted 23 March 2004; published 27 May 2004.
[1] Large faults in the brittle upper continental crust are envisaged to terminate near the
brittle-ductile transition zone, at a depth that is a complex function of material properties, temperature, stress, and strain rate. Here we investigate the effect of coseismic displacement along a fault in the upper crust on the adjacent middle and lower crust using a twodimensional numerical model of faulting within an elastic-frictional-viscous rheology. Results demonstrate that a major displacement event can cause a dramatic increase in differential stress and creep strain rates in the crust near and below the lower termination of the fault, a transient deflection of the brittle-ductile transition zone, and a zone of elevated strain rates down to the base of the crust. The perturbation decays over timescales consistent with postseismic relaxation. The stresses and strain rates predicted in such models are in accord with those inferred from microstructural damage analysis of exhumed metamorphic rocks, indicating short-term deformation at decaying stress and strain INDEX TERMS: 3210 Mathematical Geophysics: Modeling; 8159 Tectonophysics: Rheology—crust rates. and lithosphere; 8164 Tectonophysics: Stresses—crust and lithosphere; 7209 Seismology: Earthquake dynamics and mechanics; KEYWORDS: earthquakes, stress, crust, creep, seismic, faulting Citation: Ellis, S., and B. Sto¨ckhert (2004), Elevated stresses and creep rates beneath the brittle-ductile transition caused by seismic faulting in the upper crust, J. Geophys. Res., 109, B05407, doi:10.1029/2003JB002744.
1. Introduction [2] Seismic events produce an overall reduction in stress within the surrounding crust, but stresses can also increase locally near the terminations of the fault and at local asperities within the fault plane [e.g., Wald and Heaton, 1994; Bouchon, 1997; Bouchon et al., 1998]. Changes in induced elastic stresses scale approximately with the local gradient in slip. Typical stress drops along fault planes may be on the order of a few megapascals [e.g., Scholz, 1990], but changes by up to ±100 MPa along the fault plane have been inferred from seismic observations, derived from slip models averaged over spacings of several kilometers [Bouchon, 1997]. [3] Modeled stress changes from seismic inversions assume that faulting occurs within the part of the crust dominated by brittle (frictional, or pressure-sensitive) deformation, i.e., in the ‘‘schizosphere’’ as defined by Scholz [1990]. However, the microstructural record of exhumed metamorphic rocks of the Sesia Zone in the western Italian Alps suggest that very large stress changes of >200 MPa [Ku¨ster and Sto¨ckhert, 1999; Trepmann and Sto¨ckhert, 2001] may occur in the uppermost ductile region, or ‘‘plastosphere’’ [Scholz, 1990]. From the results of the damage analysis, sudden elastic loading to very Copyright 2004 by the American Geophysical Union. 0148-0227/04/2003JB002744$09.00
high differential stresses, followed by creep at elevated and rapidly decaying rates during stress relaxation [Trepmann and Sto¨ckhert, 2002, 2003], is inferred. This stress history is suspected to be caused by a major seismic event on a fault in the overlying crust, which has subsequently been removed by erosion (Figures 1a and 1b). [4] Motivated by the record of the exhumed rocks, in this paper we examine the consequences of a large instantaneous displacement along a fault in the upper (frictional) crust on the stress field and postseismic deformation of the middle to lower (ductile) crust. We use a two-dimensional numerical model and take local variations in stresses and strain rates into account. We demonstrate that large stress accumulations at the end of faults may cause short-term deformation at high strain rates, with small bulk finite strain and a transient displacement of the brittle-ductile transition.
2. A Two-Dimensional Model of Faulting and Postseismic Creep 2.1. Model Description [5] To model the full elastic-viscous-frictional rheology of the crust, we use the two-dimensional engineering finite element package Abaqus [Hibbitt, Karlsson, and Sorensen, 2001]. The modeled domain is shown in Figure 2. A
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uniform elastic strength is coupled with frictional Coulomb behavior and thermally activated power law creep. The initial conditions in the model are represented by a steady state differential stress profile [Sibson, 1982] as shown on the left of Figure 2. The initial stress state is defined for a crust that is everywhere on yield (in the brittle part) and is subject to a shear stress corresponding to the flow strength of quartz at a uniform strain rate of 1014 s1 in the ductile
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part. The maximum Coulomb shear stress ty along any optimally oriented plane is computed for an internal angle of friction f = 30 and a cohesion C = 1 MPa (Table 1). The effective mean stress p0 = p pf, where p is total (mean) stress and pf is the fluid pressure, is used in ty ¼ p0 sinðfÞ þ C cosðfÞ;
ð1Þ
where maximum shear stress ty is half of the maximum differential stress, ty = (1/2)(s1 s3), and the indices 1 and 3 refer to maximum and minimum principal stresses, respectively [e.g., Mandl, 1988]. No strain softening as a result of fault damage is applied in the model rocks surrounding the fault tip. Power law ductile creep follows the constitutive equation: Q tv ¼ B_e1=n exp ; nRT
ð2Þ
where tv and e_ are the second invariants of the deviatoric stress and strain rate tensors, respectively, Q is activation energy, n is the power law exponent, R is the universal gas constant, and T is temperature (K). (Individual deviatoric strain rate tensor components are related to equivalent deviatoric stress tensor components using the effective viscosity derived from equation (2)). B is related to the preexponential constant, A, by B ¼ 3ðnþ1Þ=2n 21n=n A1=n ;
ð3Þ
where the geometric factor in brackets is necessary for conversion from uniaxial creep laboratory data. A is determined (as are Q and n) from laboratory creep experiments on wet synthetic quartzite [Paterson and Luan, 1990] (Table 1). We have assumed that ductile deformation occurs by dislocation creep (i.e., a power law constitutive relation) throughout the stress evolution in the model. No upper limit to strain rate or stress is applied, and the same creep law was used throughout the model experiment. [6] The brittle-ductile transition, shown on Figure 2 as a dashed line in the midcrust, is determined as the depth at which the Coulomb yield shear stress, ty, equals the shear Figure 1. (a) and (b) Cartoon visualizing the inferred situation in the Sesia Zone study area in the western Alps [Ku¨ster and Sto¨ckhert, 1999; Trepmann and Sto¨ckhert, 2001, 2002, 2003], with microstructural record of shortterm ductile deformation at very high stress and strain rate, at a depth of 15– 18 km, and at temperatures of 300– 350C. This short-term deformation occurred in the early Tertiary and is proposed to be related to a seismogenic fault in the overlying upper crust (Figure 1a; fault displacement highly exaggerated; not to scale). As this upper crust is now removed by erosion (Figure 1b), information on the character of the fault and the precise position of the fault tip is not available. (c) Location of the Sesia zone study area in the western European Alps, where the record of the shortterm high-stress deformation referred to in the text is identified. EA, eastern Alps; WA, western Alps, SA, southern Alps. 2 of 10
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Figure 2. Two-dimensional numerical model setup, with parameter values described in Table 1. The model crust has a constant elastic strength. Inelastic material behavior is either frictional or power law creep (choice is determined by minimum predicted yield strength at each location and time) with parameter values corresponding to extrapolations from laboratory tests on wet quartzite [Paterson and Luan, 1990]. Geothermal gradient is constant at 20C km1, crustal density is 2800 kg m3, and fluid pressure is kept at hydrostatic so that high fluid permeability is assumed. The boundary conditions are slip of 8 m over a time interval of 1 s (inertial effects neglected), with slip termination occurring over a distance 1 km down dip at the lower end of the fault. The fault dips at 70. Profile to left shows initial differential stress profile with depth; profiles to right show linear increase in pore pressure and temperature with depth. Insets show slip prescribed along fault in coseismic and interseismic steps. stress tv for ductile creep at ambient temperatures and strain rates. In the model, the transition from brittle to ductile deformation is an abrupt change from a pressure-sensitive rheology to a temperature-controlled rheology. Because strain rate and pressure may vary during the seismic cycle, the depth of brittle-ductile transition will not always coincide with the depth of maximum differential stress, which results from the integrated stress buildup over longer timescales. Material above the brittle-ductile transition, as determined here, is not always on frictional yield but may have lower differential stress, in which case elastic stress can accumulate, although, the maximum differential stress in the brittle region is limited by frictional strength. On Figure 2, at the start of the model experiment the crust is everywhere on yield (frictional or ductile) and the brittleductile transition depth does coincide with depth of maximum differential stress, but as we will see, this changes during a subsequent faulting event. [7] During the faulting step in the model, we impose a uniform reverse fault slip, s = 8 m from the surface down to 15 km depth along a fault plane dipping at 70. Between 15 and 16 km depth, slip decreases gradually to s = 0 m (Figure 2, inset). Fault slip dying out over 1 km or more is supported by seismic observations [e.g., Bouchon, 1997] and by predictions from rate-state models [e.g., Tse and Rice, 1986]. The finite distance over which slip terminates, d, prevents infinite stresses from building up at the fault tip. Maximum elastic stress is instead proportional to (Es/d),
where E is Young’s modulus [Starr, 1928]. We have verified that the numerical model has sufficient grid resolution to correctly predict elastic stress buildup in the fault tip region. Model calculations were performed on a variable-resolution structured mesh with a minimum mesh dimension of 100 m near to the fault tip. [8] Fault slip is imposed in order to investigate the effect of a sudden elastic stress increase on midcrustal deformation [e.g., Barr and Houseman, 1996]. We prescribe the fault slip to end in the midcrust (15 – 16 km) because the observations from the Sesia Zone study area indicate rapid loading to very high stresses at such depths, and because predictions from rate-state models also suggest slip down to midcrustal levels along a fault that is weaker than the
Table 1. Parameters Used in Numerical Model Experiments Parameter
Nominal Value
Young’s modulus E, Pa Poisson’s ratio Cohesion C, MPa Angle of internal friction f, deg Power law exponent n Activation energy Q, kJ mol1 Preexponential constant A, MPan s1 Dip of fault, deg Fault slip s, m Termination depth d, km Fault mechanism
5 1010 0.25 1 30 3.1 135 6.5 108 70 8 15 – 16 reverse
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surrounding medium [e.g., Tse and Rice, 1986]. The chosen fault geometry is a steeply dipping reverse fault. This geometry is arbitrarily chosen by analogy to the present Insubric Line (a steeply dipping transpressive fault) adjacent to the Sesia Zone of the western Alps [Schmid et al., 1989], but the geometry of the ancient fault responsible for the short-term deformation in the Sesia Zone study area is actually unknown, as the former upper crust is not preserved (Figure 1). Taking into account this uncertainty, we have also investigated cases with shallow dipping faults. Results are qualitatively similar to those shown here and are available in the auxiliary material Figure ER11. [9] In the model experiment shown here, we determine fault behavior for drained conditions where it is assumed that at least subsequent to an earthquake, permeability is high enough near the fault to cause immediate fluid pressure equilibration [e.g., Miller and Nur, 2000] and that hydrostatic fluid pressure occurs throughout the crust for the time span of interest. This simplification is supported by the observations in the Sesia Zone study area that pore fluid pressure must have been well below lithostatic (and possibly hydrostatic) in the early stages of ductile deformation at high stresses [Ku¨ster and Sto¨ckhert, 1999] and that a nearlithostatic pore fluid pressure is only attained at a very late stage of the postseismic creep [Trepmann and Sto¨ckhert, 2002, 2003]. Deformation of the middle and lower crust by thermally activated, pressure insensitive ductile creep, on the length scale of interest in the present study, is not notably affected by this simplification. [10] Cocco and Rice [2002] consider effects of pore pressure changes for undrained conditions during the very short postseismic response and drained conditions for longer postseismic timescales. We have calculated that our hydrostatic approximation is valid for hydraulic conductivities greater than 107 m s1 when investigating effects over timescales greater than a few days. Such conductivities are certainly too high for ductile crust prior to faulting, but may be a valid assumption for the middle crust adjacent to a fault immediately after the fault has broken. In section 2.3 we discuss an additional experiment in which we assume undrained conditions. Such experiments are preliminary and we caution that, without better knowledge about variations in permeability in space and time around a fault tip, model experiments are unlikely to adequately capture fluid pressure evolution. [11] Shear heating is neglected in the present study and a constant temperature field is assumed. Ductile shear heat flux is proportional to the product of shear stress and strain rate [e.g., Yuen et al., 1978; Thatcher and England, 1998], which are both high in our case (temporarily well above 100 MPa and 1012 s1, respectively). However, in our simulation we are dealing with a single short-term event and small bulk strain (
