Full-waveform Inversion Based on q-Laplace Distribution

Silva, Sérgio Luiz E. F. da; Araújo, João M. de; Corso, Gilberto

doi:10.1007/s00024-021-02839-3

Cited by 4 publications

(1 citation statement)

References 39 publications

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“…In this sense, objective functions based on generalized distributions are interesting because they might be adapted to the specificity of the erratic data by selecting an adequate free-parameter. In fact, several generalized approaches have been proposed to deal with erratic data [ 26 – 30 ]. Thus, generalized distributions based on the Rényi, Tsallis and Kaniadakis statistics have generated objective functions robust to erratic noise [ 31 ].…”

Section: Introductionmentioning

confidence: 99%

Generalized statistics: Applications to data inverse problems with outlier-resistance

Lima

Araújo

et al. 2023

PLoS ONE

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The conventional approach to data-driven inversion framework is based on Gaussian statistics that presents serious difficulties, especially in the presence of outliers in the measurements. In this work, we present maximum likelihood estimators associated with generalized Gaussian distributions in the context of Rényi, Tsallis and Kaniadakis statistics. In this regard, we analytically analyze the outlier-resistance of each proposal through the so-called influence function. In this way, we formulate inverse problems by constructing objective functions linked to the maximum likelihood estimators. To demonstrate the robustness of the generalized methodologies, we consider an important geophysical inverse problem with high noisy data with spikes. The results reveal that the best data inversion performance occurs when the entropic index from each generalized statistic is associated with objective functions proportional to the inverse of the error amplitude. We argue that in such a limit the three approaches are resistant to outliers and are also equivalent, which suggests a lower computational cost for the inversion process due to the reduction of numerical simulations to be performed and the fast convergence of the optimization process.

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Section: Introductionmentioning

confidence: 99%

Generalized statistics: Applications to data inverse problems with outlier-resistance

Lima

Araújo

et al. 2023

PLoS ONE

Self Cite

View full text Add to dashboard Cite

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Data-driven seismic prestack velocity inversion via combining residual network with convolutional autoencoder

Guan-chao

Zhang

Wang

et al. 2022

Journal of Applied Geophysics

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A graph-space optimal transport objective function based on q-statistics to mitigate cycle-skipping issues in FWI

Silva

Karsou

Souza

et al. 2022

Geophysical Journal International

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Summary Full-waveform inversion (FWI) is a powerful seismic imaging methodology to estimate geophysical parameters that honor the recorded waveforms (observed data), and it is conventionally formulated as a least-squares optimization problem. Despite many successful applications, least-squares FWI suffers from cycle skipping issues. Optimal transport (OT) based FWI has been demonstrated to be a useful strategy for mitigating cycle skipping. In this work, we introduce a new Wasserstein metric based on q-statistics in the context of the OT distance. In this sense, instead of the data themselves, we consider the graph of the seismic data, which are positive and normalized quantities similar to probability functions. By assuming that the difference between the graphs of the modeled and observed data obeys the q-statistics, we introduce a robust q-generalized graph-space OT objective function in the FWI context namely q-GSOT-FWI, in which the standard GSOT-FWI based on l2-norm is a particular case. To demonstrate how the q-GSOT-FWI deals with cycle skipping, we present two numerical examples involving 2D acoustic wave-equation modeling. First, we investigate the convexity of q-GSOT objective function regarding different time shifts, and, secondly, we present a Brazilian pre-salt synthetic case study, from a crude initial model which generates significant cycle-skipping seismic data. The results reveal that the q-GSOT-FWI is a powerful strategy to circumvent cycle skipping issues in FWI, in which our objective function proposal presents a smoother topography with a wider attraction valley to the optimal minimum. They also show that q-statistics leads to a significant improvement of FWI objective function convergence, generating higher resolution acoustic models than classical approaches. In addition, our proposal reduces the computational cost of calculating the transport plan as the q-value increases.

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Full-waveform Inversion Based on q-Laplace Distribution

Cited by 4 publications

References 39 publications

Generalized statistics: Applications to data inverse problems with outlier-resistance

Generalized statistics: Applications to data inverse problems with outlier-resistance

Data-driven seismic prestack velocity inversion via combining residual network with convolutional autoencoder

A graph-space optimal transport objective function based on q-statistics to mitigate cycle-skipping issues in FWI

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