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6 Supplement A. Effective Coulomb Stress Analysis We assessed changes in Coulomb stress beneath reservoirs by the general theory of decoupled linear poroelasticity [Biot, 1956; Roeloffs, 1988; Wang 2000; Cocco and Rice, 2002]. We define an effective Coulomb stress change S e in terms of the mechanical effect and hydrologic effect: S x, z, t x, z x, z P x, z, t P x, z t (A1) e n u d, The first two terms represent the Coulomb stress change due to the static weight of the reservoir. The third term is the undrained pressure contribution that depends on change in the mean stress due to the static load of the reservoir. The last term reflects the contribution due to pressure diffusion or fluid flows into the rock from the bottom of the reservoir. The first three terms can be regrouped under the principle of effective stress and called the undrained part of the Coulomb stress change S u. The last term is referred to as the hydraulic diffusion part of the Coulomb stress change S d. Then (A1) becomes: S S S (A2) e u d The effective Coulomb stress change due to hydraulic diffusion S d is governed by the following diffusion equation: D 2 P d P t d (A3) where D is the hydraulic diffusivity. For given initial and boundary conditions, equation (A3) is solved using a numerical model [McDonald and Harbaugh, 1988; WHI, 2005] for P d, which is then multiplied by the friction coefficient,, to obtain the time-and-space-dependent S d. 8/1/2009 1

7 The effective Coulomb stress change due to the undrained part S u can be obtained from (A1) and (A2): S x, z, t x, z x, z P x, z t (A4) u n u, The initial spatial distribution of change in pore pressure P u upon a reservoir loading depends on the change in the mean stress. Through time, P u diffuses governed by the diffusion equation (A3) and hydraulic diffusivity D. If we assume P u = B n with B being the Skempton constant, varying between zero and unity depending on rock type, equation (A4) becomes: S x, z, t x, z 1 B x, z x, z ' x z (A5) u n n, where = (1-B) is the effective or apparent friction coefficient [Cocco and Rice 2002]. It should be recognized that is a convenient parameter but not a material property. Its use obscures the time-dependent nature of P u. The more rigorous solution of (A4) used in this study is obtained by setting P u (x, z, 0) = B [Rice and Cleary, 1976] upon loading, at which time P u is at its maximum and so is S u. Over time, P u diminishes through diffusion and S u approaches its minimum. In computing the effective Coulomb stress change defined in (A1), the first two terms are the stress changes from a static loading due to reservoir impoundment, computed by a numerical model [Li et al., 2005]. The third term has the initial value of P u (x,z,0) = B (x, z) that is obtained from the mean stress change. The fourth term is simulated using the numerical model with zero pressure boundary conditions everywhere except the time dependent pressure condition at the bottom of the reservoir. 8/1/2009 2

8 B. Hydraulic Diffusivity Estimation The hydraulic diffusivity beneath reservoirs has been extensively studied by using reservoir-induced seismicity data [Roeloffs, 1988; Kessels and Kuck, 1995; Talwani, 1997; Guha, 2000]. Based on 36 cases studies of reservoir-induced earthquakes, hydraulic diffusivity has been shown to vary between 0.1 and 10 m 2 /s [Talwani et al., 2007], as shown in Supplementary Fig. 1. Based on approximately 300 seismic events within 50 km from the Zipingpu reservoir between November 1, 2006 to May 15, 2007 [Lei et al., 2008], we estimated the hydraulic diffusivity under the reservoir to be around 0.5 and 1.2 m 2 /s, using the equation of D = L 2 /(4t) with L being either the vertical or dipping distances below the reservoir and t being the average lag time since September 2005 when the impoundment occurred. It should be noted that this approach tends to overestimate the diffusivity. Distance (km) sites around the world where reservoir-induced earthquakes of 5.0 < M < 6.4 from 1932 to 1993 Zipingpu reservoir site, ~300 events of 2 < M < 5 from 11/1/2006 to 5/15/2007) D = 10.0 m 2 /s D = 1.0 m 2 /s D = 0.1 m 2 /s Time lag (day) Supplement Figure 1. Inferred hydraulic diffusivity values from reservoir-induced earthquakes. Data shown in black dots are from Talwani et al. [2007] and pink bar the estimated range using the seismic events reported in Lei et al. [2008]. 8/1/2009 3

9 Reference Biot. M.A. 1956, General Solutions of the Equations of Elasticity and Consolidation for a Porous Material. J. Appl. Mech. 23, Cocco, M. and Rice, J. R. 2000, Pore Pressure and Poroelasticity Effects in Coulomb Stress Analysis of Earthquake Interactions, J. Geophys. Res. 107(B2), /2000JB Guha, S.K. 2000, Induced Earthquakes, Kluwer Academic Publishers, 314pp. Kessels, K. and Kuck, J. 1995, Hydraulic Communication in Crystalline Rocks between the Two Boreholes of the Continental Deep Drilling Programme in Germany, Int. J. Rock. Mech. Sci. Geomech. Abstr. 32, Lei, X.L., Ma, S., Wen, X., Su, J., and Du F. 2008, Integrated Analysis of Stress and Regional Seismicity by Surface Loading A Case Study of Zipingpu Reservoir. Geol. Seismol. 30(4), , (in Chinese with English abstract). Li, Q., Liu, M. and Sandvol, E.A. 2005, Stress Evolution Following the Large Earthquakes in the New Madrid Seismic Zone. Geophys. Res. Lett. 32, doi: /2004gl McDonald, M.G. and Harbaugh, A.W. 1988, A modular three-dimensional finite-difference ground-water flow model. US Geological SurveyTechniques of Water-Resources Investigations, 06-Al. Rice, J.R. and Cleary, M.P. 1976, Some Basic Stress Diffusion Solutions for Fluid Saturated Elastic Porous Media with Compressible Constituents. Rev. Geophys. 14, Roeloffs, E.A. 1988, Fault Stability Changes Induced beneath a Reservoir with Cyclic Variation in Water Level. J. Geophys. Res. 93(B3), Talwani, P. 1997, On the Nature of Reservoir-induced Seismicity. Pure Appl. Geophys. 150, /1/2009 4

10 Talwani, P., Chen, L. and Gahalaut, K. 2007, Seismogenic Permeability, k s, J. Geophys. Res. 112, B07309, doi: /2006jb Wang, H.F. 2000, Theory of Linear Poroelasticity. Princeton University Press, Princeton, N.J. 287p. WHI, 2005, Waterloo Hydrogeologic, Inc. Visual MODFLOW. Waterloo, Ontario, Canada. 8/1/2009 5