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
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 |
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.
|
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. |
| [1] |
TianYu Zheng, YuMei He, Yue Zhu, 2022: A new approach for inversion of receiver function for crustal structure in the depth domain, Earth and Planetary Physics, 6, 83-95. doi: 10.26464/epp2022008 |
| [2] |
Xiao Xiao, Jiang Wang, Jun Huang, Binlong Ye, 2018: A new approach to study terrestrial yardang geomorphology based on high-resolution data acquired by unmanned aerial vehicles (UAVs): A showcase of whaleback yardangs in Qaidam Basin, NW China, Earth and Planetary Physics, 2, 398-405. doi: 10.26464/epp2018037 |
| [3] |
QiZhen Du, WanYu Wang, WenHan Sun, Li-Yun Fu, 2022: Seismic attenuation compensation with spectral-shaping regularization, Earth and Planetary Physics, 6, 259-274. doi: 10.26464/epp2022024 |
| [4] |
Kai Fan, XinLiang Gao, QuanMing Lu, Shui Wang, 2021: Study on electron stochastic motions in the magnetosonic wave field: Test particle simulations, Earth and Planetary Physics, 5, 592-600. doi: 10.26464/epp2021052 |
| [5] |
Rui Yan, YiBing Guan, XuHui Shen, JianPing Huang, XueMin Zhang, Chao Liu, DaPeng Liu, 2018: The Langmuir Probe onboard CSES: data inversion analysis method and first results, Earth and Planetary Physics, 2, 479-488. doi: 10.26464/epp2018046 |
| [6] |
Chun-Feng Li, Jian Wang, 2018: Thermal structures of the Pacific lithosphere from magnetic anomaly inversion, Earth and Planetary Physics, 2, 52-66. doi: 10.26464/epp2018005 |
| [7] |
MingChen Sun, QingLin Zhu, Xiang Dong, JiaJi Wu, 2022: Analysis of inversion error characteristics of stellar occultation simulation data, Earth and Planetary Physics, 6, 61-69. doi: 10.26464/epp2022013 |
| [8] |
XiaoZhong Tong, JianXin Liu, AiYong Li, 2018: Two-dimensional regularized inversion of AMT data based on rotation invariant of Central impedance tensor, Earth and Planetary Physics, 2, 430-437. doi: 10.26464/epp2018040 |
| [9] |
Ya Huang, Lei Dai, Chi Wang, RongLan Xu, Liang Li, 2021: A new inversion method for reconstruction of plasmaspheric He+ density from EUV images, Earth and Planetary Physics, 5, 218-222. doi: 10.26464/epp2021020 |
| [10] |
DeYao Zhang, WenYong Pan, DingHui Yang, LingYun Qiu, XingPeng Dong, WeiJuan Meng, 2021: Three-dimensional frequency-domain full waveform inversion based on the nearly-analytic discrete method, Earth and Planetary Physics, 5, 149-157. doi: 10.26464/epp2021022 |
| [11] |
BaoZhu Zhou, XiangHui Xue, Wen Yi, HaiLun Ye, Jie Zeng, JinSong Chen, JianFei Wu, TingDi Chen, XianKang Dou, 2022: A comparison of MLT wind between meteor radar chain data and SD-WACCM results, Earth and Planetary Physics, 6, 451-464. doi: 10.26464/epp2022040 |
| [12] |
XinYan Zhang, ZhiMing Bai, Tao Xu, Rui Gao, QiuSheng Li, Jue Hou, José Badal, 2018: Joint tomographic inversion of first-arrival and reflection traveltimes for recovering 2-D seismic velocity structure with an irregular free surface, Earth and Planetary Physics, 2, 220-230. doi: 10.26464/epp2018021 |
| [13] |
Ting Lei, HuaJian Yao, Chao Zhang, 2020: Effect of lateral heterogeneity on 2-D Rayleigh wave ZH ratio sensitivity kernels based on the adjoint method: Synthetic and inversion examples, Earth and Planetary Physics, 4, 513-522. doi: 10.26464/epp2020050 |
Article Metrics
- PDF Downloads()
- Abstract views()
- HTML views()
- Cited by(0)