2D multi-scale hybrid optimization method for geophysical inversion and its application
Pan Ji-Shun1,2, Wang Xin-Jian1, Zhang Xian-Kang2, Xu Zhao-Fan2, Zhao Ping3, Tian Xiao-Feng2, and Pan Su-Zhen2
1. North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450011 ,China.
4. Geophysical Exploration Center, China Earthquake Administration, Zhengzhou 450002, China.
3. PGS Australia Pty Ltd,1060 Hay St, West Perth, Western Australia, 6005, Australia.
Abstract Local and global optimization methods are widely used in geophysical inversion but each has its own advantages and disadvantages. The combination of the two methods will make it possible to overcome their weaknesses. Based on the simulated annealing genetic algorithm (SAGA) and the simplex algorithm, an efficient and robust 2-D nonlinear method for seismic travel-time inversion is presented in this paper. First we do a global search over a large range by SAGA and then do a rapid local search using the simplex method. A multi-scale tomography method is adopted in order to reduce non-uniqueness. The velocity field is divided into different spatial scales and velocities at the grid nodes are taken as unknown parameters. The model is parameterized by a bi-cubic spline function. The finite-difference method is used to solve the forward problem while the hybrid method combining multi-scale SAGA and simplex algorithms is applied to the inverse problem. The algorithm has been applied to a numerical test and a travel-time perturbation test using an anomalous low-velocity body. For a practical example, it is used in the study of upper crustal velocity structure of the A’nyemaqen suture zone at the north-east edge of the Qinghai-Tibet Plateau. The model test and practical application both prove that the method is effective and robust.
This work is supported by the National Natural Science Foundation of China (Grant Nos. 40334040 and 40974033) and the Promoting Foundation for Advanced Persons of Talent of NCWU.
Cite this article:
PAN Ji-Shun,XU Chao-Fan,ZHANG Xian-Kang et al. 2D multi-scale hybrid optimization method for geophysical inversion and its application[J]. APPLIED GEOPHYSICS, 2009, 6(4): 363-374.
[1]
Bunks, C., Saleck, F. M., Zaleski, S., and Chavent, G., 1995, Multiscale seismic waveform inversion: Geophysics, 60, 1457 - 1473.
[2]
Cary, P. W. and Chapman, C. H., 1988, Automatic 1-D waveform inversion of marine seismic reflection data: Geophys. J. Int., 93, 527 - 546.
[3]
Chunduru, R. K., Sen, M. K., and Stoffa, P. L., 1997, Hybrid optimization methods for geophysical inversion: Geophysics, 62, 1196 - 1207.
[4]
Hole, J. A., Clowes, R. M., and Ellis, R. M., 1992, Interface inversion using broadside seismic refraction data and three-dimensional travel time calculations: J. Geophys. Res., 97, 3417 - 3429.
[5]
Improta, L., Zollo, A., Herrero, M. R., Frattini, J., Virieux, and Dell’Aversana, 2002, Seismic imaging of complex structures by nonlinear travel-time inversion of dense wide-angle data: application to a thrust belt: Geophys. J. Int., 151, 264 - 278.
[6]
Jin, S., and Beydoun, W., 2000, 2-D multi-scale nonlinear velocity inversion: Geophysical Prospecting, 48, 163 - 180.
[7]
Jin, S., and Madariaga, R., 1994, Nonlinear velocity inversion by a two step Monte-Carlo method: Geophysics, 59, 577 - 590.
[8]
Landa, E., Beydoun, W., and Tarantola, A., 1989, Reference velocity model estimation from pre-stack waveforms: coherence optimization by simulated annealing: Geophysics, 54, 984 - 990.
[9]
Lutter, W. J., and Nowack, R. L., 1990, Inversion for crustal structure using reflections from the PASSCAL Ouachita Experiment: J. Geophys. Res., 95, 4633 - 4646.
[10]
Nelder, J. A., and Mead, R., 1965, A simplex method for function minimization: Computer Journal, 7, 308-313.
[11]
Podvin, P., and Lecomte, I., 1991, Finite difference computation of travel time in very contrasted velocity models: a massively parallel approach and its associated tools: Geophys. J. Int., 105(1), 271 - 284.
[12]
Schneider, W. A., Ranzinger, K. A., Balch, A. H., and Kruse, C., 1992, A dynamic programming approach to first travel-time computation in media with arbitrarily distributed velocities: Geophysics, 57(1), 39 - 50.
[13]
Sen, M. K., and Stoffa, P. L., 1991, Nonlinear one-dimensional seismic waveform inversion using simulated annealing: Geophysics, 56, 1624 - 1638.
[14]
Sen, M. K. and Stoffa, P. L., 1995, Global optimization methods in geophysical inversion: Elsvier Science Publishers, Netherlands.
[15]
Stoffa, P. L., and Sen, M. K., 1991, Nonlinear multi-parameter optimization using genetic algorithms: inversion of plane-wave seismogram: Geophysics, 56(11), 1794 - 1810.
[16]
Stork, C., and Kusuma, T., 1992, Hybrid genetic autostatics: New approach for large-amplitude statics with noisy data: 62nd Ann. Int. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1127 - 1131.
[17]
Wang, Y. H., and Houseman, G. A., 1994, Inversion of reflection seismic amplitude data for interface geometry: Geophys. J. Int., 117, 92 - 110.
[18]
Wang, Y. H., and Houseman, G. A., 1995, Tomographic inversion of reflection seismic amplitude data for velocity variations: Geophys. J. Int., 123, 355 - 372.
[19]
Xu, Z. F., Zhang, X. K., Zhang, J. S., and Hu, X. Q., 2006, Ray hit analysis method and its application to complex upper crustal structure survey: Acta Seismologica Sinica (in Chinese), 19(2), 173 - 182.
[20]
Zelt, C. A., and Smith, R. B., 1992, Seismic travel-time inversion for 2-D crustal velocity structure: Geophys. J. Int., 108, 16 - 34.
[21]
Zhao, P., 1996, An efficient computer program for wavefront calculation by the finite difference method: Computers & Geosciences, 22(3), 239 - 251.
[22]
Zhou, H. W., 2003, Multiscale traveltime tomography: Geophysics, 68, 1639 - 1649.
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