Robust approaches for inverse problems based on Tsallis and Kaniadakis generalised statistics

Silva, Sérgio Luiz E. F. da; Lima, Gustavo Zampier dos Santos; Volpe, Ernani; Araújo, João M. de; Corso, Gilberto

doi:10.1140/epjp/s13360-021-01521-w

Cited by 14 publications

(6 citation statements)

References 57 publications

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“…This function also appears in studies of complex systems to account for power-law distributions. [106][107][108] Both deformed exponentials reduce to the ordinary exponential in the limits of q → 1 and κ → 0, respectively.…”

Section: Distributions With Deformed Exponentials For Genomesmentioning

confidence: 99%

Approaches to the classification of complex systems: Words, texts, and more

Rovenchak¹

2022

Preprint

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The Chapter starts with introductory information about quantitative linguistics notions, like rank-frequency dependence, Zipf's law, frequency spectra, etc. Similarities in distributions of words in texts with level occupation in quantum ensembles hint at a superficial analogy with statistical physics. This enables one to define various parameters for texts based on this physical analogy, including "temperature", "chemical potential", entropy, and some others. Such parameters provide a set of variables to classify texts serving as an example of complex systems. Moreover, texts are perhaps the easiest complex systems to collect and analyze.Similar approaches can be developed to study, for instance, genomes due to well-known linguistic analogies. We consider a couple of approaches to define nucleotide sequences in mitochondrial DNAs and viral RNAs and demonstrate their possible application as an auxiliary tool for comparative analysis of genomes.Finally, we discuss entropy as one of the parameters, which can be easily computed from rank-frequency dependences. Being a discriminating parameter in some problems of classification of complex systems, entropy can be given a proper interpretation only in a limited class of problems. Its overall role and significance remain an open issue so far.

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Section: Distributions With Deformed Exponentials For Genomesmentioning

confidence: 99%

Approaches to the classification of complex systems: Words, texts, and more

Rovenchak¹

2022

Preprint

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“…In this work, we consider the l 1 ‐norm as a criterion for

\phi (m)

due to its robust ability to deal with various types of seismic noise compared to, for instance, the l 2 ‐norm, preventing adverse impacts from outliers on the FWI solution (Brossier et al., 2010; Crase et al., 1990; da Silva et al., 2021). Furthermore, this criterion proved efficient in analysing the circular shot ocean bottom node (OBN) data set (Duarte et al., 2022; da Silva et al., 2023).…”

Section: Theorymentioning

confidence: 99%

Research note: Application of refraction full‐waveform inversion of ocean bottom node data using a squared‐slowness model parameterization

da Silva,

Costa,

Karsou

et al. 2023

Geophysical Prospecting

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Full‐waveform inversion is a wave equation–based imaging technique for obtaining subsurface model parameters by matching modelled with field data. Full‐waveform inversion is often formulated as a local optimization problem in which the model parameterization influences the gradient preconditioner and the convergence rate associated with the full‐waveform inversion objective function. Model parameterization governs the radiation pattern of the so‐called secondary Born source. In this work, we assess model parameterization effects on the estimation of P‐wave velocities using a three‐dimensional acoustic time‐domain full‐waveform inversion procedure. These include the three commonly used parameterization: velocity, slowness and squared slowness. In this context, we consider a field data set from a deepwater Brazilian pre‐salt field using a recently introduced circular shot ocean bottom node acquisition which favours refracted waves. The results reveal that the squared slowness model parameterization provides a satisfactory trade‐off between the reconstruction of the deep pre‐salt target area and convergence rate, saving 50% of runtime compared to the velocity and slowness cases.

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“…Indeed, if there are a handful of spurious measurements (outliers) in the dataset, the classical approach estimates biased parameters [13,61]. It is possible to see such behavior through the analysis of the adjoint-source (right-hand term in Eq (15)). In fact, if there is an outlier into the observed data (d s,r !…”

Section: Plos Onementioning

confidence: 99%

“…Its success is associated with the long tails of the Laplace distribution [ 12 ]. For this reason, inverse problems based on the Laplace distribution have been extended in the context of generalized statistical mechanics in order to control the weighting performed by the Laplace distribution’s tails [ 15 ]. However, misfit functions based on Laplace distributions suffer from a singularity issue whenever the residual data is very close to zero [ 12 ].…”

Section: Introductionmentioning

confidence: 99%

Full-waveform inversion based on generalized Rényi entropy using patched Green’s function techniques

et al. 2022

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The estimation of physical parameters from data analyses is a crucial process for the description and modeling of many complex systems. Based on Rényi α-Gaussian distribution and patched Green’s function (PGF) techniques, we propose a robust framework for data inversion using a wave-equation based methodology named full-waveform inversion (FWI). From the assumption that the residual seismic data (the difference between the modeled and observed data) obeys the Rényi α-Gaussian probability distribution, we introduce an outlier-resistant criterion to deal with erratic measures in the FWI context, in which the classical FWI based on l2-norm is a particular case. The new misfit function arises from the probabilistic maximum-likelihood method associated with the α-Gaussian distribution. The PGF technique works on the forward modeling process by dividing the computational domain into outside target area and target area, where the wave equation is solved only once on the outside target (before FWI). During the FWI processing, Green’s functions related only to the target area are computed instead of the entire computational domain, saving computational efforts. We show the effectiveness of our proposed approach by considering two distinct realistic P-wave velocity models, in which the first one is inspired in the Kwanza Basin in Angola and the second in a region of great economic interest in the Brazilian pre-salt field. We call our proposal by the abbreviation α-PGF-FWI. The results reveal that the α-PGF-FWI is robust against additive Gaussian noise and non-Gaussian noise with outliers in the limit α → 2/3, being α the Rényi entropic index.

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Robust approaches for inverse problems based on Tsallis and Kaniadakis generalised statistics

Cited by 14 publications

References 57 publications

Approaches to the classification of complex systems: Words, texts, and more

Approaches to the classification of complex systems: Words, texts, and more

Research note: Application of refraction full‐waveform inversion of ocean bottom node data using a squared‐slowness model parameterization

Full-waveform inversion based on generalized Rényi entropy using patched Green’s function techniques

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