弹性半空间位错内源的数值解
NUMERICAL SOLUTION OF WAVE FIELD NEAR A DIS- LOCATION SOURCE IN AN ELASTIC HALF-SPACE
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摘要: 本文首先将一般剪切位错点源表示成四种基本点位错的组合,断层面倾角和滑动系数仅与组合系数有关.利用将三维动力学问题化为两维的处理方法,将每一基本点源问题化成求解位移函数的轴对称问题,最后将人工透射边界的处理方法同有限差分结合起来,提出一种简便、节省的计算理论地震图的方法.利用这种方法获得了四种基本点位错源的典型近场理论地震图,并初步讨论了近场地面运动的若干特征,表明浅源地震近场地面位移中震相不能分离,且点位错源在近场产生大小相当的水平与垂直位移.本文的方法可用于研究复杂的近场地震波传播问题.Abstract: A less-costly numerical method is developed to obtain the theoretical seismograms at locations near a seismic source in an elastic half-space. An arbitrary shear dislocation point source is first considered as a linear combination of four basic ones, their combination coefficients are determined by the fault dip angle and slip direction. Each basic point source problem is then reduced to an axis-symmetric problem which is solved by the numerical method combining finite difference method and a new scheme dealing with the artificial boundary. By comparing the method of this paper with the present available analytical method, it can be concluded that the method of this paper consumes much less computer time for complicated near field problems.A set of near field theoretical seismograms for the basic dislocation point sources is presented and some features of near field ground motion, such as the horizontal displacements may be of about the same magsitude as the vertical ones and etc., are discussed.The numerical method of this paper can easily generalized to resolve problems of a finite shear dislocation source in a layered medium. Puthermore, it can be applied to study more complex near field wave propagation problems.
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[3] Achenbach, J. D., Wave Propagation in Elastic Solids, North——Holland Pub. Co., 1973.
[4] Alterman, Z., and Loewanthal, D., Computer Generated Seismograms, Methods in Computational oh ysics, 12, 35, Acad, press, 1972.
[5] Boore, D. M., Finite Difference Methods for Seismic Wave Propagation in Heterogeneous Materials,Methods动Computational Physics, 11, 1, Acad. Press, 1972.
[6] Lysmer, J,and Drake, L. A., A Finite Element Method for Seismology, Methods in Computational physics, 11, 181, Acad. Press, 1972.
[7] Ben——Menahem A., and Singh, S. J., Multipolar Elastic Fields in a Layered Half——Space, BSSA, 58, 5,519,1968.
[8] 陈运泰,多层弹性半空间中的地震波,地球物理学报,17, 1, 20, 1974.
[9] 廖振鹏,空腔爆炸产生的地震波,地球物理学报,19, 1, 50, 1976,
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[17] Cohen, M., Silent Boundary Methods for Transient Wave Analysis, Ph. D. Disertation, California Institute of Technology, 1981.
[18] 陈运泰等,巧家、石棉小震震源参数的测定及其地震危险性沽计,地球物理学报,19, 3, 206, 1976.
[19] Kawasaki, L, Suzuki Y,and Sato, R., SeismicWave Due to a Shear Fault in a Semi——Infinite Medium,Part 1: Point Source, J. Phys. Earth,21, 3, 251, 1973.
[20] Yang, B. P., Liao, Z. P,and Liu S. Q., Analysis of Soil——Structure Interaction During an Earthquake, The Third International Earthquake Microxonation Conference Proceeding, 3, 1041, 1982.
[21] Luoo, J. E., and Apsel, R. J., On The Green's Function for a Layered Half——Space, Part II, BSSA,73, 4, 909, 1983.
[22] Apsel, R. J., and Luco, J. E., On The Green's Function for a Layered Half——Space, Part I, BSSA,73, 4, 931, 1983.
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[24] 徐植信,洪锦如,层状弹性半空间内剪切位错产生的近场地面运动计算,全国地F}工程会议论文集,B——4,1984.[1] 寥振鹏、袁一凡,近场地震学简介,国外地震工程,4, 1981,
[2] Aki, K., and Richerds, P. G., Quantitative Seismology Theory and Methods, 1 and 2, W. H. Freeman and Company, 1980.
[3] Achenbach, J. D., Wave Propagation in Elastic Solids, North——Holland Pub. Co., 1973.
[4] Alterman, Z., and Loewanthal, D., Computer Generated Seismograms, Methods in Computational oh ysics, 12, 35, Acad, press, 1972.
[5] Boore, D. M., Finite Difference Methods for Seismic Wave Propagation in Heterogeneous Materials,Methods动Computational Physics, 11, 1, Acad. Press, 1972.
[6] Lysmer, J,and Drake, L. A., A Finite Element Method for Seismology, Methods in Computational physics, 11, 181, Acad. Press, 1972.
[7] Ben——Menahem A., and Singh, S. J., Multipolar Elastic Fields in a Layered Half——Space, BSSA, 58, 5,519,1968.
[8] 陈运泰,多层弹性半空间中的地震波,地球物理学报,17, 1, 20, 1974.
[9] 廖振鹏,空腔爆炸产生的地震波,地球物理学报,19, 1, 50, 1976,
[10] Helmberger D. V., and Harkrider, D. G., Mcdeling Earthquakes with Generalized Ray Theory, Moderv Problems in Elastic Wave Propagation, Edited by J. Miklowitz and J. D. Achenbach, 499,1978.
[11] 廖振鹏,杨柏坡,袁一凡,暂态弹性波分析中人工边界的研究,地震工程与工程振动,2, 1, 1, 1982.
[12] 廖振鹏,无限弹性介质中暂态标量波间题的有限模型,地震工程与工程振动,2, 4, 38, 1982,
[13] 廖振鹏、黄孔亮、杨柏坡和袁一凡,暂态波透射边界,中国科学(待发表).
[14] 廖振鹏、黄孔亮,透射边界的一个推广,科学通报,29, 5, 312, 1984.
[15] 廖振鹏,杨柏坡,袁一凡,三维地形对地震地面运动的影响,地震工程与工程振动,1, 1, 56, 1981,
[16] Kausel E., and Tassonlas, J. L., Transmitting Boundaries: A Closed——form Comparison, BSSA,71,143, 1981.
[17] Cohen, M., Silent Boundary Methods for Transient Wave Analysis, Ph. D. Disertation, California Institute of Technology, 1981.
[18] 陈运泰等,巧家、石棉小震震源参数的测定及其地震危险性沽计,地球物理学报,19, 3, 206, 1976.
[19] Kawasaki, L, Suzuki Y,and Sato, R., SeismicWave Due to a Shear Fault in a Semi——Infinite Medium,Part 1: Point Source, J. Phys. Earth,21, 3, 251, 1973.
[20] Yang, B. P., Liao, Z. P,and Liu S. Q., Analysis of Soil——Structure Interaction During an Earthquake, The Third International Earthquake Microxonation Conference Proceeding, 3, 1041, 1982.
[21] Luoo, J. E., and Apsel, R. J., On The Green's Function for a Layered Half——Space, Part II, BSSA,73, 4, 909, 1983.
[22] Apsel, R. J., and Luco, J. E., On The Green's Function for a Layered Half——Space, Part I, BSSA,73, 4, 931, 1983.
[23] Yao, Z. X., and Zheng, T. Y,A generalized reflection——transmission coefficient matrix and discrete wavenumber method for synthetic seismograms ( II )—for multiple sources with different de——pths, Acta Geophysica sinica (in press), 1984.
[24] 徐植信,洪锦如,层状弹性半空间内剪切位错产生的近场地面运动计算,全国地F}工程会议论文集,B——4,1984. -
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