Wide-angle FD and FFD migration using complex Padé approximations

Amazonas, Daniela; Costa, Jessé C.; Schleicher, Jörg; Pestana, Reynam C.

doi:10.1190/1.2785813

Cited by 41 publications

(31 citation statements)

References 12 publications

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“…For stabilizing the real Padé approximation there are a few approaches [17,18,19] that allow suppressing unstable components of a wave field. On the other hand, setting the coefficients γ s , β s to be complex [20,21,22,23], a better consistency of the right-hand and the left-hand sides of equation (2) can be attained. From the physical viewpoint this means the introduction of artificial dissipation that restricts an increase in instability for evanescent waves.…”

Section: Introductionmentioning

confidence: 99%

The stabilization of high-order multistep schemes for the Laguerre one-way wave equation solver

Terekhov

2018

Journal of Computational Physics

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This paper considers spectral-difference methods of a high-order of accuracy for solving the one-way wave equation using the Laguerre integral transform with respect to time as the base. In order to provide a high spatial accuracy and calculation stability, the Richardson method can be employed. However such an approach requires high computer costs, therefore we consider alternative algorithms based on the Adams multistep schemes. To reach the stability first for the 1D one-way equation and then for the 2D case, the stabilizing procedures using the spline interpolation were developed. This made possible to efficiently implement a predictor-corrector type method in terms of which a boundary value problem for highorder elliptic equations is substituted for a sequence of inversions of second order elliptic operators thus decreasing computer costs. To assess the accuracy and stability of difference approximations for the 1D one-way wave equation, the analytical solution based on the double Laguerre transform was obtained. This solution can be efficiently calculated if for summation one makes use of fast algorithms of computing a discrete linear convolution. For the 2D one-way wave equation the stability and accuracy of the procedures proposed have been studied on implementing the migration algorithm within a problem of seismic prospecting.

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Section: Introductionmentioning

confidence: 99%

The stabilization of high-order multistep schemes for the Laguerre one-way wave equation solver

Terekhov

2018

Journal of Computational Physics

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“…Thus, an important means to evaluate the quality of the constructed depth velocity models is to use them for depth migration. In this work, we employed a two-dimensional Fourier finitedifference (FFD) migration with the complex Padé approximation as discussed in Amazonas et al (2007). One of the reasons that led us to choose this method is that it was proven to be fast and robust.…”

Section: Migration Resultsmentioning

confidence: 99%

“…The quality of the results are evaluated by depth migrated images from the Marmousi data set with the extracted velocity models. We use a two-dimensional Fourier finite-difference (FFD) migration with the complex Padé approximation as discussed in Amazonas et al (2007).…”

Section: Outline Of This Thesismentioning

confidence: 99%

“…In all cases, we compare the determined depth velocity model to those estimated by image-ray tracing according to Cameron et al (2008). Finally, we complement our numerical evaluation with a comparison of the depth-migrated sections obtained using the complex Padé Fourier finite-difference technique of Amazonas et al (2007).…”

Section: Numerical Examplesmentioning

confidence: 99%

“…We test the approach on a synthetic Gaussian example and on the Marmousi data set. For the latter, we use Fourier Finite-difference (FFD) migration based on complex Padé approximations (Amazonas et al, 2007) to evaluate the quality of the depth-migrated images. Finally, we apply our method to the same field data example of the North Sea used by Cameron et al (2008).…”

Section: Introductionmentioning

confidence: 99%

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Initial depth model building using robust time-migration velocity analysis methods

Santos¹

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ResumoA necessidade de investigar regiões formadas por estruturas geológicas complexas tem motivado o desenvolvimento de métodos de imageamento que atuem no domínio da profundidade. Exemplos notáveis são as técnicas de migração pré-empilhamento em profundidade (PSDM, do inglês "prestack depth migration") e a tomografia de onda completa (FWT, do inglês "full-waveform tomography"). No entanto, a aplicação desses métodos enfrenta ao menos dois desafios: eles requerem (1) um modelo de velocidade (inicial) preciso, e (2) elevado poder computacional. Por outro lado, a migração em tempo provou ser um processo robusto e muito rápido, tornando-se rotineiramente empregado para o imageamento sísmico. Além disso, a construção de modelos de velocidade em tempo é um processo bem compreendido. Portanto, é altamente desejável usar as técnicas de conversão tempo-profundidade para construir, a partir desses modelos de velocidade no domínio do tempo, modelos de velocidade iniciais para técnicas que operam em profundidade. Neste trabalho, investigamos a aplicabilidade de um fluxo de trabalho formado por alguns recémdesenvolvidos métodos (semi-) automáticos de análise de velocidade de migração em tempo (MVA, do inglês "migration velocity analysis"), capazes de gerar modelos de velocidade e imagens migradas no tempo sem precisar de informações a priori, seguido por uma técnica robusta de conversão tempo-profundidade. Discutimos as vantagens e limitações desse fluxo de trabalho e suas perspectivas para se tornar uma ferramenta plenamente automática, capaz de gerar modelos de velocidade sísmica para o uso subsequente em métodos de FWT. Nos nossos testes em diferentes versões dos dados Marmousi, o procedimento proposto produziu modelos de velocidade iniciais suficientemente precisos para uma FWT sob condições quase ideais. Começando no modelo de velocidade do domínio do tempo convertido para profundidade, a FWT convergiu para um modelo final com qualidade comparável a quando feito a partir de uma versão suavizada do modelo de velocidade verdadeiro. Isso indica que a correta informação sobre a velocidade de fundo pode ser extraída com sucesso pela MVA automática no domínio do tempo mesmo em meios onde a migração em tempo não pode fornecer imagens sísmicas satisfatórias. Como resultado, esta tese não só contribui para o desenvolvimento de um fluxo de trabalho para a construção de modelos de velocidade iniciais para a FWT, mas também apresenta várias aplicações inovadoras.

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Sparsity-promoting wide-angle least-squares one-way migration

Zhu,

Wang,

et al. 2023

Acta Geophys.

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Wide-angle FD and FFD migration using complex Padé approximations

Cited by 41 publications

References 12 publications

The stabilization of high-order multistep schemes for the Laguerre one-way wave equation solver

The stabilization of high-order multistep schemes for the Laguerre one-way wave equation solver

Initial depth model building using robust time-migration velocity analysis methods

Sparsity-promoting wide-angle least-squares one-way migration

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