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Seismic Tomography by Monte Carlo Sampling

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Abstract

The paper discusses the performance and robustness of the Bayesian (probabilistic) approach to seismic tomography enhanced by the numerical Monte Carlo sampling technique. The approach is compared with two other popular techniques, namely the damped least-squares (LSQR) method and the general optimization approach. The theoretical considerations are illustrated by an analysis of seismic data from the Rudna (Poland) copper mine. Contrary to the LSQR and optimization techniques the Bayesian approach allows for construction of not only the “best-fitting” model of the sought velocity distribution but also other estimators, for example the average model which is often expected to be a more robust estimator than the maximum likelihood solution. We demonstrate that using the Markov Chain Monte Carlo sampling technique within the Bayesian approach opens up the possibility of analyzing tomography imaging uncertainties with minimal additional computational effort compared to the robust optimization approach. On the basis of the considered example it is concluded that the Monte Carlo based Bayesian approach offers new possibilities of robust and reliable tomography imaging.

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Acknowledgments

I would like to thank Prof. S. J. Gibowicz for years of very fruitful collaboration, many interesting discussions and all the assistance he has given me. C. Trifu, the editor of this special issue, and the anonymous reviewers are acknowledged for their efforts in significantly enhancing the paper. This work was partially supported by the Polish Committee for Scientific Research under Grant No. 2P04D 033 30.

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  1. Institute of Geophysics, Polish Academy of Sciences, ul. Ksiecia Janusza 64, 01-452, Warsaw, Poland

    Wojciech Dȩbski

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Dȩbski, W. Seismic Tomography by Monte Carlo Sampling. Pure Appl. Geophys. 167, 131–152 (2010). https://doi.org/10.1007/s00024-009-0006-3

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