Robust full-waveform inversion using q-statistics

Silva, Sérgio Luiz E. F. da; Costa, Carlos A. N. da; Carvalho, P.; Araújo, João M. de; Lucena, L. S.; Corso, Gilberto

doi:10.1016/j.physa.2020.124473

Cited by 21 publications

(12 citation statements)

References 29 publications

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“…Applying the probabilistic maximum-likelihood method in the q-Gaussian distribution, we have the following objective function [36]…”

Section: Tsallis's Frameworkmentioning

confidence: 99%

“…In particular, we place the objective functions based on α-, qand κ-generalizations in the broad context of the Gauss' law of error [33,34,35], see Refs. [29,36,37]. The three deformed Gaussian distributions mentioned above have already demonstrated robust properties in many applications [29,36,37,38,39,40,41,42].…”

Section: Introductionmentioning

confidence: 99%

“…[29,36,37]. The three deformed Gaussian distributions mentioned above have already demonstrated robust properties in many applications [29,36,37,38,39,40,41,42]. However, the entropic index associated with each of these approaches that make the inversion process more robust requires thorough investigation.…”

Section: Introductionmentioning

confidence: 99%

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

T.¹,

Silva²,

Araújo³

et al. 2022

Preprint

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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 analyse 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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“…Applying the probabilistic maximum-likelihood method in the q-Gaussian distribution, we have the following objective function [36]…”

Section: Tsallis's Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

T.¹,

Silva²,

Araújo³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In order to mitigate the effect of non-Gaussian errors, several robust formulations have been proposed in the literature. Among them, we may mention the criteria based on heavytailed probability functions, such as Student's t and Cauchy-Lorentz distributions [8,9]; hybrid functions [10][11][12]; and generalized probability distributions, such as the deformed Gaussian distributions in the context of Rényi [13][14][15], Tsallis [16][17][18][19], and Kaniadakis statistics [20][21][22]. Very recently, a connection between Jackson, Tsallis, and Hausdorff approaches in the context of generalized statistical mechanics was proposed [23].…”

Section: Introductionmentioning

confidence: 99%

Improving Seismic Inversion Robustness via Deformed Jackson Gaussian

Silva

Souza

et al. 2021

Entropy

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The seismic data inversion from observations contaminated by spurious measures (outliers) remains a significant challenge for the industrial and scientific communities. This difficulty is due to slow processing work to mitigate the influence of the outliers. In this work, we introduce a robust formulation to mitigate the influence of spurious measurements in the seismic inversion process. In this regard, we put forth an outlier-resistant seismic inversion methodology for model estimation based on the deformed Jackson Gaussian distribution. To demonstrate the effectiveness of our proposal, we investigated a classic geophysical data-inverse problem in three different scenarios: (i) in the first one, we analyzed the sensitivity of the seismic inversion to incorrect seismic sources; (ii) in the second one, we considered a dataset polluted by Gaussian errors with different noise intensities; and (iii) in the last one we considered a dataset contaminated by many outliers. The results reveal that the deformed Jackson Gaussian outperforms the classical approach, which is based on the standard Gaussian distribution.

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“…However, from a practical viewpoint, the global minimum is utopian for the FWI problem. Thus, several techniques of preconditioning of the objective function have been proposed to determine a local minimum that is close to the global minimum [ 7 , 16 , 17 ].…”

Section: Introductionmentioning

confidence: 99%

An objective function for full-waveform inversion based on frequency-dependent offset-preconditioning

et al. 2020

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Full-waveform inversion (FWI) is a powerful technique to obtain high-resolution subsurface models, from seismic data. However, FWI is an ill-posed problem, which means that the solution is not unique, and therefore the expert use of the information is required to mitigate the FWI ill-posedness, especially when wide-aperture seismic acquisitions are considered. In this way, we investigate the multiscale frequency-domain FWI by using a weighting operator according to the distances between each source-receiver pair. In this work, we propose a weighting operator that acts on the data misfit as preconditioning of the objective function that depends on the source-receiver distance (offset) and the frequency used during the inversion. The proposed operator emphasizes information from long offsets, especially at low frequencies, and as a consequence improves the update of deep geological structures. To demonstrate the effectiveness of our proposal, we perform numerical simulations on 2D acoustic Marmousi2 case study, which is widely used in seismic imaging tests, considering three different scenarios. In the first two ones, we have used an acquisition geometry with a maximum offset of 4 and 8 km, respectively. In the last one, we have considered all-offsets. The results show that our proposal outperforms similar strategies, for all scenarios, providing more reliable quantitative subsurface models. In fact, our inversion result has the lowest error and the highest similarity to the true model than similar approaches.

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Robust full-waveform inversion using q-statistics

Cited by 21 publications

References 29 publications

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

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

Improving Seismic Inversion Robustness via Deformed Jackson Gaussian

An objective function for full-waveform inversion based on frequency-dependent offset-preconditioning

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