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地球与行星物理

ISSN  2096-3955

CN  10-1502/P

Citation: Zhao, Y. Z. and Wang, Y. B. (2019). Comparison of deterministic and stochastic approaches to crosshole seismic travel-time inversions. Earth Planet. Phys., 3(6), 547–559.. http://doi.org/10.26464/epp2019056

2019, 3(6): 547-559. doi: 10.26464/epp2019056

SOLID EARTH: COMPUTATIONAL GEOPHYSICS

Comparison of deterministic and stochastic approaches to crosshole seismic travel-time inversions

Department of Geophysics, School of Earth and Space Sciences, Peking University, Beijing 100871, China

Corresponding author: YanBin Wang, ybwang@pku.edu.cn

Received Date: 2019-09-06
Web Publishing Date: 2019-11-26

The Bayesian inversion method is a stochastic approach based on the Bayesian theory. With the development of sampling algorithms and computer technologies, the Bayesian inversion method has been widely used in geophysical inversion problems. In this study, we conduct inversion experiments using crosshole seismic travel-time data to examine the characteristics and performance of the stochastic Bayesian inversion based on the Markov chain Monte Carlo sampling scheme and the traditional deterministic inversion with Tikhonov regularization. Velocity structures with two different spatial variations are considered, one with a chessboard pattern and the other with an interface mimicking the Mohorovičić discontinuity (Moho). Inversions are carried out with different scenarios of model discretization and source–receiver configurations. Results show that the Bayesian method yields more robust single-model estimations than the deterministic method, with smaller model errors. In addition, the Bayesian method provides the posterior probabilistic distribution function of the model space, which can help us evaluate the quality of the inversion result.

Key words: stochastic approach, deterministic approach, Bayesian inversion, Markov Chain Monte Carlo, Tikhonov regularization

Aki, K., and Richards, P. G. (2002). Quantitative Seismology (2nd ed). Herndon: University Science Books.

Aster, R. C., Borchers, B., and Thurber, C. H. (2019). Parameter Estimation and Inverse Problems (3rd ed). Amsterdam: Elsevier.

Dettmer, J., and Dosso, S. E. (2012). Trans-dimensional matched-field geoacoustic inversion with hierarchical error models and interacting Markov chains. J. Acoust. Soc. Am., 132(4), 2239–2250. https://doi.org/10.1121/1.4746016

Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82(4), 711–732. https://doi.org/10.1093/biomet/82.4.711

Green, P. J. (2003). Trans-dimensional Markov chain Monte Carlo. In P. J. Green, et al. (Eds.), Highly Structured Stochastic Systems. (pp. 179-206). London: Oxford University Press.

Hansen, P. C., and O’Leary, D. P. (1993). The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput., 14(6), 1487–1503. https://doi.org/10.1137/0914086

Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97–109. https://doi.org/10.1093/biomet/57.1.97

Jackson, D. D., and Matsu’ura, M. (1985). A Bayesian approach to nonlinear inversion. J. Geophys. Res. Solid Earth, 90(B1), 581–591. https://doi.org/10.1029/JB090iB01p00581

Matsu’ura, M. (1984). Bayesian estimation of hypocenter with origin time eliminated. J. Phys. Earth, 32(6), 469–483. https://doi.org/10.4294/jpe1952.32.469

Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). Equation of state calculations by fast computing machines. J. Chem. Phys., 21(6), 1087–1092. https://doi.org/10.1063/1.1699114

Mosegaard, K., and Tarantola, A. (1995). Monte Carlo sampling of solutions to inverse problems. J. Geophys. Res. Solid Earth, 100(B7), 12431–12447. https://doi.org/10.1029/94JB03097

Pachhai, S., Tkalčić, H., and Dettmer, J. (2014). Bayesian inference for ultralow velocity zones in the earth’s lowermost mantle: Complex ULVZ beneath the east of the Philippines. J. Geophys. Res. Solid Earth, 119(11), 8346–8365. https://doi.org/10.1002/2014JB011067

Rothman, D. H. (1985). Nonlinear inversion, statistical mechanics, and residual statics estimation. Geophysics, 50(12), 2784–2796. https://doi.org/10.1190/1.1441899

Schwarz, G. (1978). Estimating the dimension of a model. Ann. Stat., 6(2), 461–464. https://doi.org/10.1214/aos/1176344136

Tarantola, A. (2005). Inverse Problem Theory and Methods for Model Parameter Estimation. Philadelphia: SIAM.

Tarits, P., Jouanne, V., Menvielle, M., and Roussignol, M. (1994). Bayesian statistics of non-linear inverse problems: Example of the magnetotelluric 1-D inverse problem. Geophys. J. Int., 119(2), 353–368. https://doi.org/10.1111/j.1365-246X.1994.tb00128.x

Tikhonov, A. N., and Arsenin, V. Y. (1977). Solutions of Ill-Posed Problems. Washington: V.H. Winston.

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Comparison of deterministic and stochastic approaches to crosshole seismic travel-time inversions

YanZhe Zhao, YanBin Wang