一种新的地震射线层析成像计算方法
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摘要
地震射线层折成像方法是一个非线性的反演过程。从方法原理上讲，它主要由两部分组成，即任意速度分布的射线追踪和求解线性化反演问题。本文中，作者在这两个方面均采用了新的方法。在正演中，（1）应用Moser[1]提出的“最短路径”原理模拟地震射线，用较为简单的方法实现任意复杂介质结构的射线追踪，计算出每一对地点一接收点的最小走时及其对应的射线路径；（2）用线性平面函数去近似矩形单元内的速度分布，从而求出走时相对于每个节点上的速度变化的雅可比矩阵元素的解析式。在反演中，给出两种求解加权最小范数、最小二乘和对偶空间约束反演问题[2]的迭代算法。通过我们的计算机模拟实验表明，这种方法比常规的地震层析成像方法（如ART，LSQR，CGLS）不仅在精度上大大提高，而且有较强的抗噪声能力。在计算方面采用了Scales[3]提出的大型稀疏矩阵的算法，既加快了运算速度，又不需要很大的内存空间。
Seismic ray tomography is referrcd to a nonlincar inversion problem which can be in principle solved in two phases: raytracing in an arbitrarily distributed velocity field and then solving a linearized inversion problem. In this paper, new techniqucs are adopted in the above two phases.In the forward problcm: (1) the shortest path method advocated by Moser (1991 ) is applied to construct ray paths, A relatively simple algorithm is then used to implement the raytracing and Calculate the minimum traveltime and the homologous trajectory for each pair of shot-receiver points; (2) the velocity distribution within each rectangular cell is approximated with a linear planar function, so that the analytic exprcssion of the elements in a Jacobian matrix or the derivatives of velocity with respect to traveltime at each node can be determined. In the inversion problem, two iterative algorithms used for least-square method and constrained dual space inversion problem and the derivation for damped minimum norm are presented. Computer simulation shows that the new method has advantage over conventional seismic tomographic methods such as ART, LSQR and CGLS, in precision and noise resistance. Moreover, due to applying the algorithm for large sparse matrix proposed by Scales, the computational speed is improved and there necds no large memory space.
Seismic ray tomography is referrcd to a nonlincar inversion problem which can be in principle solved in two phases: raytracing in an arbitrarily distributed velocity field and then solving a linearized inversion problem. In this paper, new techniqucs are adopted in the above two phases.In the forward problcm: (1) the shortest path method advocated by Moser (1991 ) is applied to construct ray paths, A relatively simple algorithm is then used to implement the raytracing and Calculate the minimum traveltime and the homologous trajectory for each pair of shot-receiver points; (2) the velocity distribution within each rectangular cell is approximated with a linear planar function, so that the analytic exprcssion of the elements in a Jacobian matrix or the derivatives of velocity with respect to traveltime at each node can be determined. In the inversion problem, two iterative algorithms used for least-square method and constrained dual space inversion problem and the derivation for damped minimum norm are presented. Computer simulation shows that the new method has advantage over conventional seismic tomographic methods such as ART, LSQR and CGLS, in precision and noise resistance. Moreover, due to applying the algorithm for large sparse matrix proposed by Scales, the computational speed is improved and there necds no large memory space.
引文
[1]J Moser,T. J., Shortest path calculation of seismic ray, Geophysics, 56, 59- 67. 1991-
[2]Carrion,P., Dual tomography for imaging complex structure, Geophysics, 56, 1395 - 1404,1991.
[3]Scales, J. A., Tomographic inversion via the conjugate gradient method, Geophysics, 52, 179-185, 1987.
[4]Nolet, Seismic wave propagation and seismic tomography, D, Reidel Publ Co, 1987.
[5]Singh, R. P. and Singh, Y. P., RAYPT: a new inversion technique for geotomographic data, Geophysics, 56, 1215-1227. 1991.
[6]Bregman, N. D., Chapman, C. H. and Bailey, R- C., Crosshole seismic tomography,Geophpeics, 54,200 - 215, 1989.
[7]Devaney, A. J-, Geophysical diffeaction tomography, Trans., Inst. Electr. Electron. Eng.GE - 22, 3- 13, 1984.
[8]Wu,R., and Toksoz, M. N., Diffraction tomography and multjsource holography applied toseismic imaging, Geophysics, 52, 11-25'.1987.
[9]Lo, T. W., Toksoz, M. N., Xu, S. and Wu, R., Ultrasonic laboratory tests of geophysicaltomographic reconstruction, Geophpoics, 53,947-956. 1988.
[10]Tura, M- A. C., Application of diffraction tomography to ftacture detection, SEG 1991Annual meeting, Houston, Expanded Abstract, 836-839. 1991.
[11]Phillips, W. S- and Fehler, M. C., Traveltime tomography: A Comparison of popularmet hods, Geophysics, 56, 1639 - 1649.1991.
[12]Paige, C. C. and M. A. Saunders, LSQR: An algorithm for sparse linear equations andsparse least squares, ACM Trans. Math. Softwave,8,43-71, 1982.
[13] McMechan, G. A., Harris, J. M., and Anderson. L. M., Cross-hole tomography forstrongly vartable media with application to scale model data, Bull., Seis. Soc. Am, 77,1945- 1960, 1987.
[14] Tarantola, A., Inverse problem theory, Elsevier Publishing Company, Inc., NY, 1987.
[15]cerveny, V., Molotkov, I. A., and Psencik, I., Ray methods in seismology, Univ.Karlova. Prapue, 1977.
[16]Schneider, W. A., Ranzinger, K. A., Balch, A- H. and Kruse,C., A dynamic programmingapproach to first arrival traveltime computation in media with arbitrary distributed velocities,Geophysics,,57, 39- 50, 1992.
[17]Matsuoka, T. and Ezaka, T., Ray tracing using reciprocity, Geophpeics, 57, 326 - 333,1992.
[18] Zhou, B., Greenhalgh, S. A. and Sinadinovski, Non-linear traveltime tomography: Anaginghigh contrast inhomogeneities, ASEG, 1992 Annual Meeting, Queensland, ExpandedAbstract, 1992.
[19]Zhou, B., Gteenhalgh, S. A. and C. Sinadinovski, Iterative algorithms for the dampedminimun norm, least-squared and constrained problem in seismic tomograpby, The 2ndSEGJ/SEG international symposium Geotomography, Tokyo, 1992.
[2]Carrion,P., Dual tomography for imaging complex structure, Geophysics, 56, 1395 - 1404,1991.
[3]Scales, J. A., Tomographic inversion via the conjugate gradient method, Geophysics, 52, 179-185, 1987.
[4]Nolet, Seismic wave propagation and seismic tomography, D, Reidel Publ Co, 1987.
[5]Singh, R. P. and Singh, Y. P., RAYPT: a new inversion technique for geotomographic data, Geophysics, 56, 1215-1227. 1991.
[6]Bregman, N. D., Chapman, C. H. and Bailey, R- C., Crosshole seismic tomography,Geophpeics, 54,200 - 215, 1989.
[7]Devaney, A. J-, Geophysical diffeaction tomography, Trans., Inst. Electr. Electron. Eng.GE - 22, 3- 13, 1984.
[8]Wu,R., and Toksoz, M. N., Diffraction tomography and multjsource holography applied toseismic imaging, Geophysics, 52, 11-25'.1987.
[9]Lo, T. W., Toksoz, M. N., Xu, S. and Wu, R., Ultrasonic laboratory tests of geophysicaltomographic reconstruction, Geophpoics, 53,947-956. 1988.
[10]Tura, M- A. C., Application of diffraction tomography to ftacture detection, SEG 1991Annual meeting, Houston, Expanded Abstract, 836-839. 1991.
[11]Phillips, W. S- and Fehler, M. C., Traveltime tomography: A Comparison of popularmet hods, Geophysics, 56, 1639 - 1649.1991.
[12]Paige, C. C. and M. A. Saunders, LSQR: An algorithm for sparse linear equations andsparse least squares, ACM Trans. Math. Softwave,8,43-71, 1982.
[13] McMechan, G. A., Harris, J. M., and Anderson. L. M., Cross-hole tomography forstrongly vartable media with application to scale model data, Bull., Seis. Soc. Am, 77,1945- 1960, 1987.
[14] Tarantola, A., Inverse problem theory, Elsevier Publishing Company, Inc., NY, 1987.
[15]cerveny, V., Molotkov, I. A., and Psencik, I., Ray methods in seismology, Univ.Karlova. Prapue, 1977.
[16]Schneider, W. A., Ranzinger, K. A., Balch, A- H. and Kruse,C., A dynamic programmingapproach to first arrival traveltime computation in media with arbitrary distributed velocities,Geophysics,,57, 39- 50, 1992.
[17]Matsuoka, T. and Ezaka, T., Ray tracing using reciprocity, Geophpeics, 57, 326 - 333,1992.
[18] Zhou, B., Greenhalgh, S. A. and Sinadinovski, Non-linear traveltime tomography: Anaginghigh contrast inhomogeneities, ASEG, 1992 Annual Meeting, Queensland, ExpandedAbstract, 1992.
[19]Zhou, B., Gteenhalgh, S. A. and C. Sinadinovski, Iterative algorithms for the dampedminimun norm, least-squared and constrained problem in seismic tomograpby, The 2ndSEGJ/SEG international symposium Geotomography, Tokyo, 1992.
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