时间域内有限地震断层的反演问题
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摘要
为了解决有限地震断层破裂过程研究中的正演和反演问题，本文提出：（1）用广义反射、透射系数矩阵和广义射线理论计算上地幔及远场范围体波理论地震图的混合方法．同时采用格林函数的一种新的组合方式，可节约1／3计算机内存．（2）采用基于模拟退火的热浴算法进行全局搜索反演，不仅提高了在计算过程中新模型被接收的可能性，而且使得在时间域内目标函数的计算速度提高了近二个数量级．对1994年台湾海峡地震震源破裂过程的研究结果表明，这次地震的破裂过程相对比较简单．在前4．0s内地震断层的破裂相当剧烈，错动距离的平均值随着破裂时间增加而迅速减少．开始时破裂速度较高，前4．0s的平均值为3．1km／s，之后逐渐降至2．2km／s．错动方向随破裂的变化不大．
For the forward and inverse problems in the study of earthquake rupture process by finite fault method, tWo algorithms are suggested. First, a new hybrid method,which combined of reflective and transmission coefficient matrix method and Generalized ray theory, is presented to calculate upper mantle and teleseismic body-wave synthetic seismogram. Besides so, A new combination of Green function is also suggested that can save one-third computer memory. Second, the heat-bath algorithm is used to solve this inverse problem. It can not only increase the acceptance probability in lower annealing temperature, but also great enhance the computer speed of the bine-domain objective function for nearly 100 bines. The rupture process of 1994 Taiwan strait earthquake was studied. The results show that the rupture process of this event is relative simple. During the first 4.0s, the fault rupture is qinte acute and then the average slip amplitude is fast decreased as the increasing of rupture bine. There is an initial fast rupture with average velocity of 3.1km / s during the first 4.0s, then it gradually reduces to 2.2 km/s. Relatively, the variation of rupture direction is small.
For the forward and inverse problems in the study of earthquake rupture process by finite fault method, tWo algorithms are suggested. First, a new hybrid method,which combined of reflective and transmission coefficient matrix method and Generalized ray theory, is presented to calculate upper mantle and teleseismic body-wave synthetic seismogram. Besides so, A new combination of Green function is also suggested that can save one-third computer memory. Second, the heat-bath algorithm is used to solve this inverse problem. It can not only increase the acceptance probability in lower annealing temperature, but also great enhance the computer speed of the bine-domain objective function for nearly 100 bines. The rupture process of 1994 Taiwan strait earthquake was studied. The results show that the rupture process of this event is relative simple. During the first 4.0s, the fault rupture is qinte acute and then the average slip amplitude is fast decreased as the increasing of rupture bine. There is an initial fast rupture with average velocity of 3.1km / s during the first 4.0s, then it gradually reduces to 2.2 km/s. Relatively, the variation of rupture direction is small.
引文
[1] 张德存,郭燕平,全球地震台网拥有的台站及分布,国际地震动态,6,17-20,1996.
[2] Hartzell, S., Heaton,T., Inversion of strong ground motion and teleseismic wave form data for the fault rupture history of the 1979 Imperial Valley, California, earthquake, Bull. Seis. Soc. Am., 73,1553-1583, 1983.
[3] Mendoza,C., Hartzell,S., Slip distribution of the 19 September 1985 ichoacan. Mexico, earthquake: near-source and telseismic contraints, Bull. eis. Soc. Am., 79,655-669, 1989.
[4] Hartzell, S., P. Liu, Mendoza, C., The 1994 Northridge, California, carthquake: Investigation of rupture velocity, risetime, and high-frequency radiation, J. Geophys, Res., 101,91-20,108,1996.
[5] Hartzell, S., Stewart, G., Menodza, C., Comparison of L1 and L2 norms in a teleseismic eaveform inversion for the slip history of the Loma Prieta, earthquake, Bull. Seis. Soc. Am., 81,1518-1539, 1991.
[6] Hartzell, S., P. Liu, Caculation of earthquake rupture histories using a hybrid global search algorithm: application to the 1992 Landers, Californa, earthquake, Phys. Earth Planet., 95, 79-99, 1996.
[7] Helmberger,D., Theory and application of synthetic seismograms, In: Earthquake: Obervation, Tehory and Interpretation, LXXXV Coros Soc. Italiana di Fisica-Bologna-Italy, 1983
[8] Yao Zhen-xing., Harkrider, D. G., A generalized reflection transmission coefficient matric and discrete wavenumber method for synthetic seismograms, Bull., Seis., Soc., Am., 73, 1685-1699, 1983.
[9] 姚振兴、郑天愉,计算综合地震图的广义反射、透射系数矩阵和离散波数方法(二)─—对不同深度点源情况的算法,地球物理学报,27,338-347,1984.
[10] 姚振兴,郑天愉,曹相如,王凯,用P波波形资料研究中强地震震源过程的方法,地球物理学进展, 6(4),6-36,1991.
[11] Tarantola, a., Valette,B., Generalized nonlinear inverse problem solved using the least squares criterion, Rev, Geophys., 20, 219-232, 1982.
[12] 刘鹏程,纪晨,Hartzell, S., 改进的模拟退火─—单纯形综合反演方法,地球物理学报,38,199-205,1995.
[13] 郑天愉,刘鹏程,1994年9月16日台湾海峡地震及其构造背景研究,地球物理学报,39,68-79,1996.
[14] 陈祥熊,袁定强,吴长江,台湾海峡Ms7.3地震震源破裂特征及东南沿海地震形势分析地震学报,18,145-155,1996.
[15] Xirkpatrick,S., Delatt, C., Vcchi,M., Optimization by simulated annealing, Sciece, 220, 671-680,1983.
[16] 纪晨,地震波传播及波形反演(硕士论文),北京:中国科学院地球物理研究所,1994.
[17] Rebbi. C., Monte Carlo,calculations in lattice gauge theories. in Binder. K., Ed., Applications of the Monte Carlo method, Springer-Verlag. 277-298. 1984.
[18] Rothman, D. H., Automatic estimation fo large residual statics corection. Geophysics, 51, 332-346, 1986.
[19] Sen, M. K., Stoffa, P.L., Clobal Optimization Methods in Geophysical Inversion. Netherlands Elsevier. Science Publications, 1995.
[20] Day,S. M., Three-dimensional finite difference simulation of fault dynamics: rectangular faults with fixed rupture veocity, Bull. Seism. Soc. Am., 72, 705-727, 1982.
[2] Hartzell, S., Heaton,T., Inversion of strong ground motion and teleseismic wave form data for the fault rupture history of the 1979 Imperial Valley, California, earthquake, Bull. Seis. Soc. Am., 73,1553-1583, 1983.
[3] Mendoza,C., Hartzell,S., Slip distribution of the 19 September 1985 ichoacan. Mexico, earthquake: near-source and telseismic contraints, Bull. eis. Soc. Am., 79,655-669, 1989.
[4] Hartzell, S., P. Liu, Mendoza, C., The 1994 Northridge, California, carthquake: Investigation of rupture velocity, risetime, and high-frequency radiation, J. Geophys, Res., 101,91-20,108,1996.
[5] Hartzell, S., Stewart, G., Menodza, C., Comparison of L1 and L2 norms in a teleseismic eaveform inversion for the slip history of the Loma Prieta, earthquake, Bull. Seis. Soc. Am., 81,1518-1539, 1991.
[6] Hartzell, S., P. Liu, Caculation of earthquake rupture histories using a hybrid global search algorithm: application to the 1992 Landers, Californa, earthquake, Phys. Earth Planet., 95, 79-99, 1996.
[7] Helmberger,D., Theory and application of synthetic seismograms, In: Earthquake: Obervation, Tehory and Interpretation, LXXXV Coros Soc. Italiana di Fisica-Bologna-Italy, 1983
[8] Yao Zhen-xing., Harkrider, D. G., A generalized reflection transmission coefficient matric and discrete wavenumber method for synthetic seismograms, Bull., Seis., Soc., Am., 73, 1685-1699, 1983.
[9] 姚振兴、郑天愉,计算综合地震图的广义反射、透射系数矩阵和离散波数方法(二)─—对不同深度点源情况的算法,地球物理学报,27,338-347,1984.
[10] 姚振兴,郑天愉,曹相如,王凯,用P波波形资料研究中强地震震源过程的方法,地球物理学进展, 6(4),6-36,1991.
[11] Tarantola, a., Valette,B., Generalized nonlinear inverse problem solved using the least squares criterion, Rev, Geophys., 20, 219-232, 1982.
[12] 刘鹏程,纪晨,Hartzell, S., 改进的模拟退火─—单纯形综合反演方法,地球物理学报,38,199-205,1995.
[13] 郑天愉,刘鹏程,1994年9月16日台湾海峡地震及其构造背景研究,地球物理学报,39,68-79,1996.
[14] 陈祥熊,袁定强,吴长江,台湾海峡Ms7.3地震震源破裂特征及东南沿海地震形势分析地震学报,18,145-155,1996.
[15] Xirkpatrick,S., Delatt, C., Vcchi,M., Optimization by simulated annealing, Sciece, 220, 671-680,1983.
[16] 纪晨,地震波传播及波形反演(硕士论文),北京:中国科学院地球物理研究所,1994.
[17] Rebbi. C., Monte Carlo,calculations in lattice gauge theories. in Binder. K., Ed., Applications of the Monte Carlo method, Springer-Verlag. 277-298. 1984.
[18] Rothman, D. H., Automatic estimation fo large residual statics corection. Geophysics, 51, 332-346, 1986.
[19] Sen, M. K., Stoffa, P.L., Clobal Optimization Methods in Geophysical Inversion. Netherlands Elsevier. Science Publications, 1995.
[20] Day,S. M., Three-dimensional finite difference simulation of fault dynamics: rectangular faults with fixed rupture veocity, Bull. Seism. Soc. Am., 72, 705-727, 1982.
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