Extensive and nonextensive statistics in seismic inversion

Sérgio Luiz Eduardo Ferreira da Silva, Gustavo Zampier dos Santos Lima, João Medeiros de Araújo and Gilberto Corso

Physica A: Statistical Mechanics and its Applications, 2021, vol. 563, issue C

Abstract: Seismic inversion is a central procedure for estimating subsurface physical parameters from observed data. In geophysical applications, the seismic inversion is usually formulated as an optimisation problem that aims to minimise the difference between modelled and observed data through the Gauss’ error law, which is linked to the extensive Boltzmann–Gibbs (BG) statistics. However, this approach is known to be sensitive to non-Gaussian errors, especially to outliers in the data set. Therefore, error laws determined by non-Gaussian statistics are essential for robust seismic inversion. In this way, we present a comparative study of seismic inversions using the extensive statistics of Rényi and also on the nonextensive statistics of Tsallis and Kaniadakis. In particular, we consider a classical seismic inversion problem so-called Post-Stack Inversion (PSI), which analyses the interaction between seismic waves and subsurface reflectivity to infer geological structures. Considering a realistic subsurface reflectivity model taking into account spike-noisy data, the numerical results show that the PSI based on generalised statistics outperforms the PSI based on standard BG statistics. We note that, the best results are for the Tsallis case in which the Lévy–Gnedenko central-limit theorem is valid (q>53).

Keywords: Gauss’ error law; Maximum entropy; Likelihood; Inverse problems; Seismic imaging (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:563:y:2021:i:c:s0378437120307949

DOI: 10.1016/j.physa.2020.125496

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