Klein-Gordon Equation and Variable Density Effects on Acoustic Wave Propagation in Brazilian Pre-Salt Fields

Silva, S.L. Da; Karsou, A; Moreira, Roger Matsumoto; Lopez, J.; Cetale, Marco

doi:10.3997/2214-4609.202210385

Cited by 3 publications

(2 citation statements)

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“…In this work, we consider the 𝑙 1 -norm as a criterion for 𝜙(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). In this context, FWI is formulated as the following constrained optimization problem:…”

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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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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show abstract

“…In this section, we explore the potential of the α-PGF-FWI for estimating P-wave velocities in a typical Brazilian pre-salt field. In this regard, we consider the realistic acoustic model depicted in Fig 9(a) [80][81][82] as the true model, which comprises a water layer in which the ocean floor is in average of 2km in-depth, followed by post-salt sediments, a salt body with variable thickness and velocity, the pre-salt reservoir, and the bedrock as the model base. By using the true model, Fig 9(a), we generate a seismic dataset considering an OBN acquisition comprising 21 nodes (receivers) equally spaced every 400m, from 6450m to 14450m, deployed at the ocean floor (see the white squares in Fig 9(b)).…”

Section: Brazilian Pre-salt Case Studymentioning

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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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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Klein-Gordon Equation and Variable Density Effects on Acoustic Wave Propagation in Brazilian Pre-Salt Fields

Cited by 3 publications

References 0 publications

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

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

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

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