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Testing fault models with numerical simulation: example from central California
Tectonophysics 343 (2001) 233 – 238 www.elsevier.com/locate/tecto
Testing fault models with numerical simulation: example from central California Yongen Caia,*, Chi-Yuen Wangb a
Department of Geophysics, Geodynamic Research Center of Peking University, Peking University, Beijing 100871, China b Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, USA Received 12 July 2000; accepted 9 July 2001
Abstract Stress distribution in faulted areas is often calculated and used to assess the potential of regional seismic hazard. Yet, the result of the calculation may strongly depend on the modeled fault configuration. Thus, it is important to assess the accuracy of the assumed fault configuration for a specific faulted area. Two distinct tectonic models have been proposed for central California. In one model, a master detachment is assumed to be present below the seismogenic layer, which connects the San Andreas fault and the other faults in the system. In another, no basal detachment is assumed. How significant are the different models in predicting seismic hazards in California? To what extent are geodetic data useful in distinguishing these models? In this paper, we report the results from a 3D finite-element analysis of stress and deformation in a crust containing a straight transform fault bordered by two thrust faults, which is intended to simulate a segment of the San Andreas fault system in central California. Significant results are: (1) the different models predict notably different states of stresses, thus, notably different seismic potentials; and (2) the differences in the predicted surface deformation between the two models are smaller than the current GPS resolution. D 2001 Elsevier Science B.V. All rights reserved. Keywords: Fault model; Central California; Seismic hazard
1. Introduction Geodetic data have long being used by earth scientists to infer the physical processes in the earth’s interior (e.g., Airy, 1855; Pratt, 1855; Heiskanen, 1924; Haskell, 1937; Wang, 1966; Peltier, 1996). The recent rapid accumulation of data from the Global Positioning System (GPS) has allowed a wide application of geodetic measurements. Stress changes in tectonically active areas are important parameters
*
Corresponding author.
for assessing the seismic potential of an area. However, our ability to evaluate stress changes through numerical simulation depends strongly on the assumed fault configuration. Thus, it is important to assess the accuracy of the assumed fault configuration when evaluating the seismic potential in a given area. Here, we examine the questions on how significant the difference between fault models is in predicting seismic hazards, and to what extent would geodetic data be useful in distinguishing the different fault models. A case for study is central California, where a straight segment of the San Andreas fault system
0040-1951/01/$ - see front matter D 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 1 9 5 1 ( 0 1 ) 0 0 1 7 6 - 7
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Y. Cai, C.-Y. Wang / Tectonophysics 343 (2001) 233–238
separates the Pacific plate from the North American plate (Atwater, 1970). Several hundreds of kilometers of right-lateral offset have accumulated across this segment since at least 5 Ma (Thatcher, 1983). Earthquakes of thrust mechanisms frequently occur in the Coast Ranges that run sub-parallel to the San Andreas fault (e.g., Ekstrom et al., 1992). Geologic study of the fold-and-thrust structures (Page, 1982; Aydin, 1982; Namson and Davis, 1987; Jones et al., 1994) suggests a fault-normal shortening that may have continued in the past 4 Ma (Namson and Davis, 1987; Jones et al., 1994). Some authors suggest that the fold-and-thrust mountains are products at the bends or jogs of the San Andreas fault to accommodate the ongoing transform motion (Scholz, 1985; Anderson, 1990; Ten Brink et al., 1996), but between 35° and 36.5°N in central California, the San Andreas fault is mostly straight. Furthermore, tectonic stress shows a regional compression subnormal to fault (Mount and Suppe, 1987; Zoback et al., 1987), and plate-motion models (Minster and Jordon, 1978; DeMets et al., 1990; Argus and Gordon, 1991) show a fault-normal convergence (i.e., the San Andreas discrepancy), which has been interpreted to be due to a clockwise rotation of the Pacific plate with respect to the North American plates since 3.4 – 3.9 Ma (Harbert, 1991). In this paper, we take the San Andreas fault system in central California to include both the San Andreas transform fault and the thrust faults in the Coast Ranges. Several authors have assumed that slip on a lowangle basal detachment beneath central California accommodates the fault-normal convergence (Namson and Davis, 1987; Page and Brocher, 1993; Jones et al., 1994; Braun and Beaumont, 1995). On the other hand, current seismic reflection studies provide no conclusive evidence for this basal detachment (Brocher and Furlong, 1994). In most seismic hazard evaluations, faults are simulated as dislocations in a half-space where no basal detachment was assumed. How significant are the different models in predicting seismic hazards in central California? To what extent are geodetic data useful in distinguishing these models and the different boundary conditions? In the following, we use 3D finite-element simulations to calculate stresses and displacement in a faulted crust in an attempt to answer these questions.
2. Models We consider a section of the lithosphere 350-km wide, 1000-km long and 100-km thick (Fig. 1). The upper 15 km of the crust is seismogenic and is simulated as an elastic layer with embedded faults. The lower crust and the uppermost mantle are assumed to be viscoelastic with thicknesses of 15 and 70 km, respectively. This is similar to the wellstudied ‘‘viscoelastic coupling model’’ (Nur and Mavko, 1974; Savage, 1990; Savage and Prescott, 1978; Thatcher, 1983); the difference lies in that, here, we included in the system thrust faults and a basal detachment, in addition to a strike-slip fault. As noted above, we consider a system including a strike-slip fault flanked by thrust faults. In Model A (Fig. 1a), all faults terminate at the base of the seismogenic layer. In Model B (Fig. 1b), the faults terminate at a detachment at the base of the seismogenic layer. The boundary conditions of the models are taken as follows. On the west boundary, a normal displace-
Fig. 1. Schematic drawings of two different fault configurations in this study. (a) all faults terminate at the base of the seismogenic layer. (b) all faults connect to a detachment at the base of the seismogenic layer. ( ) Shear in to page; ( ) shear out of page.
Y. Cai, C.-Y. Wang / Tectonophysics 343 (2001) 233–238
ment is specified to simulate the fault-normal convergence and the principal stress field in the region (Zoback et al., 1987; Mount and Suppe, 1987). Elastic springs are numerically applied on the northern, southern, eastern and the basal boundaries of the model. These springs are meant to simulate the mechanical reaction of the lithosphere outside the modeled region in response to the forces transmitted across the boundaries. Superimposed on this initial compression, a basal shear is applied to drive the shear displacement across the San Andreas fault. Different driving forces (not reported here), such as forces applied on the lateral boundaries, do not change the conclusions of this study. In the numerical experiment, we use a finite element program (ABAQUS, by Hibbitt, Karlsson and Soren-
235
sen) with contact elements to simulate the faults. At shear stresses below the shear strength of the fault, controlled by the Amonton – Columb frictional law, the relative displacement is elastic. At shear stresses equal to the shear strength of the faults, on the other hand, discontinuous displacement occurs across the faults. Fault frictional coefficient is assumed to be 0.2 for the strike-slip fault and 0.3 for the thrust faults and detachment. Other material parameters are taken as follows. The upper crust is simulated as an elastic layer with a Young’s modulus of 3.0 109 Pa and a Poisson’s ratio of 0.35. The lower crust and the lithospheric mantle are simulated as visco-elastic layers, with the lower crust characterized by a Young’s modulus of 4.0 1010 Pa, a Poisson’s ratio of 0.35 and a viscosity of 3 1020 Pa s, and the lithospheric mantle
Fig. 2. Calculated strike-parallel shear stresses (unit: Pa) on the faults based on the two models: (a) Model A without a basal detachment; (b) Model B with a basal detachment.
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characterized by a Young’s modulus of 4.0 1010 Pa, a Poisson’s ratio of 0.35, and a viscosity of 5.0 1020 Pa s.
3. Results and discussion Earthquake cycles and faulting are complex processes and are likely to change from one cycle to another. Geodetic measurements give the change between two surveys; thus, what is detected is (part of) an earthquake cycle plus the background plate motion. In the present analysis, instead of simulating a particular earthquake cycle, we induce a total shear displacement of 500 m between the North American plate and the Pacific plate, which is equivalent to a time interval of 10 kyear if an average shearing rate of 50 mm/year is assumed. Thus, the result may represent a quasi-steady-state average of the deformation due to many earthquake cycles superimposed on a background of continuous deformation.
2a and b, we see strong difference between the calculated stress pattern for Model A and that for Model B. In the model without a basal detachment (Fig. 2a), the strike-parallel shear stress is greatest along the strike-slip fault, whereas it is significantly smaller on the thrust fault. In the model with a basal detachment (Fig. 2b), on the other hand, the strikeparallel shear stress is greatest both on the strike-slip fault and near the base of the thrust faults where they intersect the basal detachment. On an actual fault surface, the geometry and physical condition are likely to be complex and the stress pattern may never be as uniform as indicated in the figures. Nevertheless, the above results indicate that, if Model A is used, one would predict the highest seismic potential to occur on the strike-slip fault. On the other hand, if Model B is used, one would predict the highest seismic potential to occur both on the strike-slip fault and at the base of the thrust faults. 3.2. Fault slip
3.1. Stress pattern The calculated shear stresses are plotted in Fig. 2. Although the stress values may change with different material properties and/or boundary conditions, the stress patterns will remain the same. Comparing Fig.
The calculated surface deformation and fault slip, along a profile normal to the fault system, is plotted in Fig. 3. On the strike-slip fault, the shear displacements for Models A and B are 25.6 and 33.7 m, respectively, corresponding to a slip rate of 2.56 and 3.37 mm/year.
Fig. 3. Calculated strike-parallel surface displacement along a profile normal to the fault system.
Y. Cai, C.-Y. Wang / Tectonophysics 343 (2001) 233–238
On the thrust faults, the displacement rates along the strike of the faults are 0.74 and 0.68 mm/year, respectively. The fact that the slip rate on the strike-slip fault is significantly greater in Model B than in Model A, implies that the presence of a basal detachment may facilitate the transfer of shear deformation from the base of the lithosphere. The maximum difference of the displacement rates occurred on the strike-slip fault between Models A and B, however, is less than 0.81 mm/year, which is within the noise level of the current GPS data, suggesting that it may be difficult to use geodetic data in discriminating models with or without a basal detachment.
4. Conclusion The results of this study allow the following conclusions: (1) The stresses predicted by different models are notably different, leading to potentially different assessment of the seismic potential in a given region. (2) The calculated surface deformation for the different models is so similar that the current GPS results may not be effective in resolving their differences.
Acknowledgements We acknowledge the assistance of the Seismological Laboratory, University of California, Berkeley, for providing computational facilities for this work. We also would like to acknowledge James Savage and Shawn Larsen for their peer reviews and comments. Support for Yongen Cai was provided by the Major State Basic Research Development Program of China (G1999075511). References Airy, G.B., 1855. On the computation of the effect of the attraction of mountain masses as disturbing the apparent astronomical latitude of stations in geodetic surveys. Philos. Trans. R. Soc. London 145, 101 – 104. Anderson, R.S., 1990. Evolution of the Santa Cruz Mountains by advection of crust past a restraining bend on the San Andreas Fault. Science 249, 397 – 401. Argus, D.F., Gordon, R.G., 1991. Current Sierra Nevada-North
237
American motion from Very Long Baseline Interferometry: implications for the kinematics of the western United States Geology 19, 1085 – 1088. Atwater, T., 1970. Implications of plate tectonics for the Cenozoic tectonic evolution of western North America. Geol. Soc. Am. Bull. 81 (12), 3513 – 3535. Aydin, A., 1982. The East Bay hills, a compressional domain resulting from interaction between the Calaveras and Hayward – Rodgers creek faults. In: Hart, E.W., Hirschfeld, S.E., Schulz, S.S. (Eds.), Proc. Conf. Earthquake Hazards in the Eastern San Francisco Bay Region. California Division of Mines and Geology, pp. 11 – 21. Braun, J., Beaumont, C., 1995. Three-dimensional numerical experiments of strain partitioning at oblique plate boundaries: implications for contrasting tectonic styles in the southern Coast Ranges, California, and central South Island, New Zealand. J. Geophys. Res. 100, 18059 – 18074. Brocher, T.M., Furlong, K.P., 1994. Resolving the tectonic framework of the San Francisco Bay area, California. U.S.G.S. Open File Rpt., 94-259. DeMets, C., Gordon, R.G., Argus, D.F., Stein, S., 1990. Current plate motions Geophys. J. Int. 101, 425 – 478. Ekstrom, G., Stein, R.S., Eaton, J.P., Eberhart-Phillips, D., 1992. J. Geophys. Res. 97, 4843 – 4864. Harbert, W., 1991. Late Neogene relative motions of the Pacific and North America plates. Tectonics 10 (1), 1 – 15. Haskell, N.A., 1937. The viscosity of the asthenosphere. Am. J. Sci. 33, 22 – 28. Heiskanen, W., 1924. Untersuchungen uber Schwerkraft and Isostasie. Finn. Geod. Inst., pp. 1 – 96, No. 4. Jones, D.L., Graymer, R., Wang, C.-Y., McEvilly, T.V., Lomax, A., Brabb, E., 1994. Neogene transpressive tectonics of the California Coast Ranges. Tectonophysics 13, 561 – 574. Minster, J.B., Jordon, T.H., 1978. Present-day plate motions. J. Geophys. Res. 83, 5331 – 5353. Mount, V.S., Suppe, J., 1987. State of stress near the San Andreas fault: implications for wrench tectonics. Geology. 15, 1143 – 1146. Namson, J.S., Davis, T.L., 1987. Seismically active fold and thrust belt in the San Joaquin Valley, Central California. Geol. Soc. Am. Bull. 100 (2), 257 – 273. Nur, A., Mavko, G., 1974. Postseismic viscoelastic rebound Science 183, 204 – 206. Page, B.M., 1982. Modes of Quaternary tectonic movement in the San Francisco Bay region, California. In: Hart, E.W., Hirschfeld, S.E., Schulz, S.S. (Eds.), Proc. Conf. Earthquake Hazards in the Eastern San Francisco Bay Region. California Division of Mines and Geology, pp. 1 – 10. Page, B.M., Brocher, T.M., 1993. Thrusting of the central California margin over the edge of the Pacific plate during the transform regime. Geology 21, 635 – 638. Peltier, W.R., 1996. Mantle viscosity and ice-age ice sheet topography Science 273, 1359 – 1364. Pratt, J.H., 1855. On the attraction of Himalaya mountains and of the elevated regions beyond them upon the plumb line in India. Philos. Trans. R. Soc. London 145, 53 – 100. Savage, J.C., 1990. Equivalent strike-slip cycles in half-space and
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lithosphere – asthenosphere Earth models. J. Geophys. Res. 95, 4873 – 4879. Savage, J.C., Prescott, W.H., 1978. Asthenosphere readjustment and the earthquake cycle. J. Geophys. Res. 83, 3369 – 3376. Scholz, C.H., 1985. The black mountain asperity: seismic hazard of the southern San Francisco Peninsula, California. Geophys. Res. Lett. 12, 717 – 719. Ten Brink, U.S., Katzman, R., Lin, J., 1996. Three-dimensional models of deformation near strike-slip faults. J. Geophys. Res. 101 (b7), 16205 – 16220.
Thatcher, W., 1983. Nonlinear strain buildup and the earthquake cycle on the San Andreas fault. J. Geophys. Res. 88, 5893 – 5902. Wang, C.-Y., 1966. Earth’s zonal deformation. J. Geophys. Res. 71 (6), 1713 – 1720. Zoback, M.D., Zoback, M.L., Mount, V.S., Suppe, J., Eaton, J.P., Healy, J.H., Oppenheimer, D.H., Reasonberg, P.A., Jones, L.M., Raleigh, C.B., Wong, I.G., Wentworth, C.M., 1987. New evidence on the state of stress of the San Andreas fault system. Science 238, 1105 – 1111.
Testing fault models with numerical simulation: example from central California Yongen Caia,*, Chi-Yuen Wangb a
Department of Geophysics, Geodynamic Research Center of Peking University, Peking University, Beijing 100871, China b Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, USA Received 12 July 2000; accepted 9 July 2001
Abstract Stress distribution in faulted areas is often calculated and used to assess the potential of regional seismic hazard. Yet, the result of the calculation may strongly depend on the modeled fault configuration. Thus, it is important to assess the accuracy of the assumed fault configuration for a specific faulted area. Two distinct tectonic models have been proposed for central California. In one model, a master detachment is assumed to be present below the seismogenic layer, which connects the San Andreas fault and the other faults in the system. In another, no basal detachment is assumed. How significant are the different models in predicting seismic hazards in California? To what extent are geodetic data useful in distinguishing these models? In this paper, we report the results from a 3D finite-element analysis of stress and deformation in a crust containing a straight transform fault bordered by two thrust faults, which is intended to simulate a segment of the San Andreas fault system in central California. Significant results are: (1) the different models predict notably different states of stresses, thus, notably different seismic potentials; and (2) the differences in the predicted surface deformation between the two models are smaller than the current GPS resolution. D 2001 Elsevier Science B.V. All rights reserved. Keywords: Fault model; Central California; Seismic hazard
1. Introduction Geodetic data have long being used by earth scientists to infer the physical processes in the earth’s interior (e.g., Airy, 1855; Pratt, 1855; Heiskanen, 1924; Haskell, 1937; Wang, 1966; Peltier, 1996). The recent rapid accumulation of data from the Global Positioning System (GPS) has allowed a wide application of geodetic measurements. Stress changes in tectonically active areas are important parameters
*
Corresponding author.
for assessing the seismic potential of an area. However, our ability to evaluate stress changes through numerical simulation depends strongly on the assumed fault configuration. Thus, it is important to assess the accuracy of the assumed fault configuration when evaluating the seismic potential in a given area. Here, we examine the questions on how significant the difference between fault models is in predicting seismic hazards, and to what extent would geodetic data be useful in distinguishing the different fault models. A case for study is central California, where a straight segment of the San Andreas fault system
0040-1951/01/$ - see front matter D 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 1 9 5 1 ( 0 1 ) 0 0 1 7 6 - 7
234
Y. Cai, C.-Y. Wang / Tectonophysics 343 (2001) 233–238
separates the Pacific plate from the North American plate (Atwater, 1970). Several hundreds of kilometers of right-lateral offset have accumulated across this segment since at least 5 Ma (Thatcher, 1983). Earthquakes of thrust mechanisms frequently occur in the Coast Ranges that run sub-parallel to the San Andreas fault (e.g., Ekstrom et al., 1992). Geologic study of the fold-and-thrust structures (Page, 1982; Aydin, 1982; Namson and Davis, 1987; Jones et al., 1994) suggests a fault-normal shortening that may have continued in the past 4 Ma (Namson and Davis, 1987; Jones et al., 1994). Some authors suggest that the fold-and-thrust mountains are products at the bends or jogs of the San Andreas fault to accommodate the ongoing transform motion (Scholz, 1985; Anderson, 1990; Ten Brink et al., 1996), but between 35° and 36.5°N in central California, the San Andreas fault is mostly straight. Furthermore, tectonic stress shows a regional compression subnormal to fault (Mount and Suppe, 1987; Zoback et al., 1987), and plate-motion models (Minster and Jordon, 1978; DeMets et al., 1990; Argus and Gordon, 1991) show a fault-normal convergence (i.e., the San Andreas discrepancy), which has been interpreted to be due to a clockwise rotation of the Pacific plate with respect to the North American plates since 3.4 – 3.9 Ma (Harbert, 1991). In this paper, we take the San Andreas fault system in central California to include both the San Andreas transform fault and the thrust faults in the Coast Ranges. Several authors have assumed that slip on a lowangle basal detachment beneath central California accommodates the fault-normal convergence (Namson and Davis, 1987; Page and Brocher, 1993; Jones et al., 1994; Braun and Beaumont, 1995). On the other hand, current seismic reflection studies provide no conclusive evidence for this basal detachment (Brocher and Furlong, 1994). In most seismic hazard evaluations, faults are simulated as dislocations in a half-space where no basal detachment was assumed. How significant are the different models in predicting seismic hazards in central California? To what extent are geodetic data useful in distinguishing these models and the different boundary conditions? In the following, we use 3D finite-element simulations to calculate stresses and displacement in a faulted crust in an attempt to answer these questions.
2. Models We consider a section of the lithosphere 350-km wide, 1000-km long and 100-km thick (Fig. 1). The upper 15 km of the crust is seismogenic and is simulated as an elastic layer with embedded faults. The lower crust and the uppermost mantle are assumed to be viscoelastic with thicknesses of 15 and 70 km, respectively. This is similar to the wellstudied ‘‘viscoelastic coupling model’’ (Nur and Mavko, 1974; Savage, 1990; Savage and Prescott, 1978; Thatcher, 1983); the difference lies in that, here, we included in the system thrust faults and a basal detachment, in addition to a strike-slip fault. As noted above, we consider a system including a strike-slip fault flanked by thrust faults. In Model A (Fig. 1a), all faults terminate at the base of the seismogenic layer. In Model B (Fig. 1b), the faults terminate at a detachment at the base of the seismogenic layer. The boundary conditions of the models are taken as follows. On the west boundary, a normal displace-
Fig. 1. Schematic drawings of two different fault configurations in this study. (a) all faults terminate at the base of the seismogenic layer. (b) all faults connect to a detachment at the base of the seismogenic layer. ( ) Shear in to page; ( ) shear out of page.
Y. Cai, C.-Y. Wang / Tectonophysics 343 (2001) 233–238
ment is specified to simulate the fault-normal convergence and the principal stress field in the region (Zoback et al., 1987; Mount and Suppe, 1987). Elastic springs are numerically applied on the northern, southern, eastern and the basal boundaries of the model. These springs are meant to simulate the mechanical reaction of the lithosphere outside the modeled region in response to the forces transmitted across the boundaries. Superimposed on this initial compression, a basal shear is applied to drive the shear displacement across the San Andreas fault. Different driving forces (not reported here), such as forces applied on the lateral boundaries, do not change the conclusions of this study. In the numerical experiment, we use a finite element program (ABAQUS, by Hibbitt, Karlsson and Soren-
235
sen) with contact elements to simulate the faults. At shear stresses below the shear strength of the fault, controlled by the Amonton – Columb frictional law, the relative displacement is elastic. At shear stresses equal to the shear strength of the faults, on the other hand, discontinuous displacement occurs across the faults. Fault frictional coefficient is assumed to be 0.2 for the strike-slip fault and 0.3 for the thrust faults and detachment. Other material parameters are taken as follows. The upper crust is simulated as an elastic layer with a Young’s modulus of 3.0 109 Pa and a Poisson’s ratio of 0.35. The lower crust and the lithospheric mantle are simulated as visco-elastic layers, with the lower crust characterized by a Young’s modulus of 4.0 1010 Pa, a Poisson’s ratio of 0.35 and a viscosity of 3 1020 Pa s, and the lithospheric mantle
Fig. 2. Calculated strike-parallel shear stresses (unit: Pa) on the faults based on the two models: (a) Model A without a basal detachment; (b) Model B with a basal detachment.
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Y. Cai, C.-Y. Wang / Tectonophysics 343 (2001) 233–238
characterized by a Young’s modulus of 4.0 1010 Pa, a Poisson’s ratio of 0.35, and a viscosity of 5.0 1020 Pa s.
3. Results and discussion Earthquake cycles and faulting are complex processes and are likely to change from one cycle to another. Geodetic measurements give the change between two surveys; thus, what is detected is (part of) an earthquake cycle plus the background plate motion. In the present analysis, instead of simulating a particular earthquake cycle, we induce a total shear displacement of 500 m between the North American plate and the Pacific plate, which is equivalent to a time interval of 10 kyear if an average shearing rate of 50 mm/year is assumed. Thus, the result may represent a quasi-steady-state average of the deformation due to many earthquake cycles superimposed on a background of continuous deformation.
2a and b, we see strong difference between the calculated stress pattern for Model A and that for Model B. In the model without a basal detachment (Fig. 2a), the strike-parallel shear stress is greatest along the strike-slip fault, whereas it is significantly smaller on the thrust fault. In the model with a basal detachment (Fig. 2b), on the other hand, the strikeparallel shear stress is greatest both on the strike-slip fault and near the base of the thrust faults where they intersect the basal detachment. On an actual fault surface, the geometry and physical condition are likely to be complex and the stress pattern may never be as uniform as indicated in the figures. Nevertheless, the above results indicate that, if Model A is used, one would predict the highest seismic potential to occur on the strike-slip fault. On the other hand, if Model B is used, one would predict the highest seismic potential to occur both on the strike-slip fault and at the base of the thrust faults. 3.2. Fault slip
3.1. Stress pattern The calculated shear stresses are plotted in Fig. 2. Although the stress values may change with different material properties and/or boundary conditions, the stress patterns will remain the same. Comparing Fig.
The calculated surface deformation and fault slip, along a profile normal to the fault system, is plotted in Fig. 3. On the strike-slip fault, the shear displacements for Models A and B are 25.6 and 33.7 m, respectively, corresponding to a slip rate of 2.56 and 3.37 mm/year.
Fig. 3. Calculated strike-parallel surface displacement along a profile normal to the fault system.
Y. Cai, C.-Y. Wang / Tectonophysics 343 (2001) 233–238
On the thrust faults, the displacement rates along the strike of the faults are 0.74 and 0.68 mm/year, respectively. The fact that the slip rate on the strike-slip fault is significantly greater in Model B than in Model A, implies that the presence of a basal detachment may facilitate the transfer of shear deformation from the base of the lithosphere. The maximum difference of the displacement rates occurred on the strike-slip fault between Models A and B, however, is less than 0.81 mm/year, which is within the noise level of the current GPS data, suggesting that it may be difficult to use geodetic data in discriminating models with or without a basal detachment.
4. Conclusion The results of this study allow the following conclusions: (1) The stresses predicted by different models are notably different, leading to potentially different assessment of the seismic potential in a given region. (2) The calculated surface deformation for the different models is so similar that the current GPS results may not be effective in resolving their differences.
Acknowledgements We acknowledge the assistance of the Seismological Laboratory, University of California, Berkeley, for providing computational facilities for this work. We also would like to acknowledge James Savage and Shawn Larsen for their peer reviews and comments. Support for Yongen Cai was provided by the Major State Basic Research Development Program of China (G1999075511). References Airy, G.B., 1855. On the computation of the effect of the attraction of mountain masses as disturbing the apparent astronomical latitude of stations in geodetic surveys. Philos. Trans. R. Soc. London 145, 101 – 104. Anderson, R.S., 1990. Evolution of the Santa Cruz Mountains by advection of crust past a restraining bend on the San Andreas Fault. Science 249, 397 – 401. Argus, D.F., Gordon, R.G., 1991. Current Sierra Nevada-North
237
American motion from Very Long Baseline Interferometry: implications for the kinematics of the western United States Geology 19, 1085 – 1088. Atwater, T., 1970. Implications of plate tectonics for the Cenozoic tectonic evolution of western North America. Geol. Soc. Am. Bull. 81 (12), 3513 – 3535. Aydin, A., 1982. The East Bay hills, a compressional domain resulting from interaction between the Calaveras and Hayward – Rodgers creek faults. In: Hart, E.W., Hirschfeld, S.E., Schulz, S.S. (Eds.), Proc. Conf. Earthquake Hazards in the Eastern San Francisco Bay Region. California Division of Mines and Geology, pp. 11 – 21. Braun, J., Beaumont, C., 1995. Three-dimensional numerical experiments of strain partitioning at oblique plate boundaries: implications for contrasting tectonic styles in the southern Coast Ranges, California, and central South Island, New Zealand. J. Geophys. Res. 100, 18059 – 18074. Brocher, T.M., Furlong, K.P., 1994. Resolving the tectonic framework of the San Francisco Bay area, California. U.S.G.S. Open File Rpt., 94-259. DeMets, C., Gordon, R.G., Argus, D.F., Stein, S., 1990. Current plate motions Geophys. J. Int. 101, 425 – 478. Ekstrom, G., Stein, R.S., Eaton, J.P., Eberhart-Phillips, D., 1992. J. Geophys. Res. 97, 4843 – 4864. Harbert, W., 1991. Late Neogene relative motions of the Pacific and North America plates. Tectonics 10 (1), 1 – 15. Haskell, N.A., 1937. The viscosity of the asthenosphere. Am. J. Sci. 33, 22 – 28. Heiskanen, W., 1924. Untersuchungen uber Schwerkraft and Isostasie. Finn. Geod. Inst., pp. 1 – 96, No. 4. Jones, D.L., Graymer, R., Wang, C.-Y., McEvilly, T.V., Lomax, A., Brabb, E., 1994. Neogene transpressive tectonics of the California Coast Ranges. Tectonophysics 13, 561 – 574. Minster, J.B., Jordon, T.H., 1978. Present-day plate motions. J. Geophys. Res. 83, 5331 – 5353. Mount, V.S., Suppe, J., 1987. State of stress near the San Andreas fault: implications for wrench tectonics. Geology. 15, 1143 – 1146. Namson, J.S., Davis, T.L., 1987. Seismically active fold and thrust belt in the San Joaquin Valley, Central California. Geol. Soc. Am. Bull. 100 (2), 257 – 273. Nur, A., Mavko, G., 1974. Postseismic viscoelastic rebound Science 183, 204 – 206. Page, B.M., 1982. Modes of Quaternary tectonic movement in the San Francisco Bay region, California. In: Hart, E.W., Hirschfeld, S.E., Schulz, S.S. (Eds.), Proc. Conf. Earthquake Hazards in the Eastern San Francisco Bay Region. California Division of Mines and Geology, pp. 1 – 10. Page, B.M., Brocher, T.M., 1993. Thrusting of the central California margin over the edge of the Pacific plate during the transform regime. Geology 21, 635 – 638. Peltier, W.R., 1996. Mantle viscosity and ice-age ice sheet topography Science 273, 1359 – 1364. Pratt, J.H., 1855. On the attraction of Himalaya mountains and of the elevated regions beyond them upon the plumb line in India. Philos. Trans. R. Soc. London 145, 53 – 100. Savage, J.C., 1990. Equivalent strike-slip cycles in half-space and
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lithosphere – asthenosphere Earth models. J. Geophys. Res. 95, 4873 – 4879. Savage, J.C., Prescott, W.H., 1978. Asthenosphere readjustment and the earthquake cycle. J. Geophys. Res. 83, 3369 – 3376. Scholz, C.H., 1985. The black mountain asperity: seismic hazard of the southern San Francisco Peninsula, California. Geophys. Res. Lett. 12, 717 – 719. Ten Brink, U.S., Katzman, R., Lin, J., 1996. Three-dimensional models of deformation near strike-slip faults. J. Geophys. Res. 101 (b7), 16205 – 16220.
Thatcher, W., 1983. Nonlinear strain buildup and the earthquake cycle on the San Andreas fault. J. Geophys. Res. 88, 5893 – 5902. Wang, C.-Y., 1966. Earth’s zonal deformation. J. Geophys. Res. 71 (6), 1713 – 1720. Zoback, M.D., Zoback, M.L., Mount, V.S., Suppe, J., Eaton, J.P., Healy, J.H., Oppenheimer, D.H., Reasonberg, P.A., Jones, L.M., Raleigh, C.B., Wong, I.G., Wentworth, C.M., 1987. New evidence on the state of stress of the San Andreas fault system. Science 238, 1105 – 1111.