Split-step complex Padé-Fourier depth migration

Zhang, Linbin; Rector, James W.; Hoversten, G. Michael; Fomel, Sergey

doi:10.1111/j.1365-246x.2007.03610.x

Cited by 12 publications

(12 citation statements)

References 21 publications

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“…A complex treatment of the exponential term is applied to mitigate inaccuracy and instabilities due to the evanescent waves (Milinazzo et al, 1997;Zhang et al, 2004). This can be done using a complex Padé approximation of the square root.…”

Section: Theory and The Methodsmentioning

confidence: 99%

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Wave equation depth migration using complex Padé approximation

Pestana¹,

Freitas²,

Costa³

2009

Rev. Bras. Geof.

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ABSTRACT. We propose a new method of depth migration based on a constant density variable velocity wave equation in the space-frequency domain. A complex Padé approximation of the wave equation evolution operator is used for wavefield extrapolation. This method mitigates the inaccuracies and instabilities due to evanescent waves and produces images with fewer numerical artifacts than those obtained with a real Padé approximation of the exponential operator, mainly in media with strong velocity variations. Tests on zero-offset data from the SEG/EAGE salt model and the 2D Marmousi prestack dataset show that the proposed migration method can handle strong lateral variations and also has a good steep dip response. We compare the results of the proposed method with those obtained using split-step Fourier (SSF), phase shift plus interpolation (PSPI) and Fourier finite-difference (FFD) methods.Keywords: depth migration, one-wave equation, complex Padé approximation, prestack migration. RESUMO.Propomos um novo método de migração em profundidade baseado na solução da equação da onda com densidade constante no domínio da freqüência.Uma aproximação de Padé complexaé usada para aproximar o operador de evolução aplicado na extrapolação do campo de ondas. Esse método reduz as imprecisões e instabilidades devidoàs ondas evanescentes e produz imagens com menos ruídos numéricos que aquelas obtidas usando-se a aproximação de Padé real para o operador exponencial, principalmente em meios com fortes variações de velocidades. Testes em dados de afastamento nulo do modelo de sal SEG/EAGE e nos dados de tiro comum 2-D Marmousi foram realizados. Os resultados obtidos mostram que o método de migração proposto consegue lidar com fortes variações laterais e também tem uma boa resposta para refletores com mergulhosíngremes. Os resultados foram comparadosàqueles resultados obtidos com os métodos split-step Fourier (SSF), phase shift plus interpolarion (PSPI) e Fourier diferenças-finitas (FFD).Palavras-chave: migração em profundidade, equação unidirecional da onda, aproximação de Padé complexa, migração pré-empilhamento.

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Section: Theory and The Methodsmentioning

confidence: 99%

“…Zhang et al (2003) used the method in finitedifference migration however its implementation was not efficient for wide-angle migration. We use the exact acoustic wave equation to derive the downward continuation operator, instead of starting from an one-way wave equation.…”

Section: Introductionmentioning

confidence: 99%

Wave equation depth migration using complex Padé approximation

Pestana¹,

Freitas²,

Costa³

2009

Rev. Bras. Geof.

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“…However, their implementation were not suited for wide angles. Later, Zhang et al (2004) proposed a split-step migration based on complex Padé.…”

Section: Introductionmentioning

confidence: 99%

Wide-angle FD and FFD migration using complex Padé approximations

et al. 2007

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Seismic Migration by downward continuation using the one-way wave equation approximations has two shortcomings: imaging steep dip reflectors and handling evanescent waves. Complex Padé approximations allow a better treatment of evanescent modes, stabilizing finite-difference migration without requiring special treatment for the migration domain boundaries. Imaging steep dip reflectors can be improved using several terms in the Padé expansion. We discuss the implementation and evaluation of wide-angle complex Padé approximations for finite-difference and Fourier finite-difference migration methods. The dispersion relation and the impulsive response of the migration operator provide criteria to select the number of terms and coefficients in the Padé expansion. This assures stability for a prescribed maximum propagation direction. The implementations are validated on the Marmousi model dataset and SEG/EAGE salt model data.

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“…The complex Padé expansion was previously used in applied geophysics. Zhang et al (2003) used the method in finitedifference migration however its implementation was not efficient for wide-angle migration. Zhang et al (2004) (2007) used the complex Padé approximation for wide-angle FD and FFD prestack depth migration.…”

Section: Introductionmentioning

confidence: 99%

“…Zhang et al (2003) used the method in finitedifference migration however its implementation was not efficient for wide-angle migration. Zhang et al (2004) (2007) used the complex Padé approximation for wide-angle FD and FFD prestack depth migration. These works show that complex Padé approximation mitigates the inaccuracy and instability due to evanescent waves.…”

Section: Introductionmentioning

confidence: 99%

Wave equation depth migration using complex Padéapproximation

Pestana

Freitas

2007

10th International Congress of the Brazilian Geophysical Society &Amp; EXPOGEF 2007, Rio De Janeiro, Brazil, 19-23 November 200

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We propose a new method of depth migration based on a constant density variable velocity wave equation in the space-frequency domain. A complex Padé approximation of the wave equation evolution operator is used for wavefield extrapolation. This method mitigates the inaccuracies and instabilities due to evanescent waves and produces images with fewer numerical artifacts than those obtained with a real Padé approximation of the exponential operator, mainly in media with strong velocity variations. Tests on zero-offset data from the SEG/EAGE salt model and the 2D Marmousi prestack dataset show that the proposed migration method can handle strong lateral variations and also has a good steep dip response. We compare the results of the proposed method with those obtained using split-step Fourier (SSF), phase shift plus interpolation (PSPI) and Fourier finite-difference (FFD) methods. RESUMO.Propomos um novo método de migração em profundidade baseado na solução da equação da onda com densidade constante no domínio da freqüência.Uma aproximação de Padé complexaé usada para aproximar o operador de evolução aplicado na extrapolação do campo de ondas. Esse método reduz as imprecisões e instabilidades devidoàs ondas evanescentes e produz imagens com menos ruídos numéricos que aquelas obtidas usando-se a aproximação de Padé real para o operador exponencial, principalmente em meios com fortes variações de velocidades. Testes em dados de afastamento nulo do modelo de sal SEG/EAGE e nos dados de tiro comum 2-D Marmousi foram realizados. Os resultados obtidos mostram que o método de migração proposto consegue lidar com fortes variações laterais e também tem uma boa resposta para refletores com mergulhosíngremes. Os resultados foram comparadosàqueles resultados obtidos com os métodos split-step Fourier (SSF), phase shift plus interpolarion (PSPI) e Fourier diferenças-finitas (FFD).Palavras-chave: migração em profundidade, equação unidirecional da onda, aproximação de Padé complexa, migração pré-empilhamento.

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Split-step complex Padé-Fourier depth migration

Cited by 12 publications

References 21 publications

Wave equation depth migration using complex Padé approximation

Wave equation depth migration using complex Padé approximation

Wide-angle FD and FFD migration using complex Padé approximations

Wave equation depth migration using complex Padéapproximation

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