Data parallel implementation of 3‐D PSPI

Bagaini, Claudio; Bonomi, Ernesto; Pieroni, E.

doi:10.1190/1.1887502

Cited by 21 publications

(20 citation statements)

References 5 publications

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“…An important issue in implementing PSPI and extended‐split‐step‐Fourier is the selection of reference velocities. There are two approaches available: geometric progression method (Gazdag and Sguazzero 1984) and the statistical method (Bagaini et al 1995; Han 1998). We will present these two methods and give some theoretical analysis.…”

Section: Selection Of Reference Velocitiesmentioning

confidence: 99%

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Kinematic characteristics and the influence of reference velocities of phase‐shift‐plus‐interpolation and extended‐split‐step‐Fourier migration methods

2010

Geophysical Prospecting

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A B S T R A C TThe phase-shift-plus-interpolation and extended-split-step-Fourier methods are wavefield-continuation algorithms for seismic migration imaging. These two methods can be applied to regions with complex geological structures. Based on their unified separable formulas, we show that these two methods have the same kinematic characteristics by using the theory of pseudodifferential operators. Numerical tests on a Marmousi model demonstrate this conclusion. Another important aspect of these two methods is the selection of reference velocities and we explore the influence of the selection of reference velocities by comparing the geometric progression method and the statistical method. We show that the geometric progression method is simple but does not take into account the velocity distribution while the statistical approach is relatively complex but reflects the velocity distribution.

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Section: Selection Of Reference Velocitiesmentioning

confidence: 99%

“…Statistical method (Bagaini et al 1995; Han 1998). Let v min and v max denote the minimum and maximum velocities in the velocity model, respectively.…”

Section: Selection Of Reference Velocitiesmentioning

confidence: 99%

Kinematic characteristics and the influence of reference velocities of phase‐shift‐plus‐interpolation and extended‐split‐step‐Fourier migration methods

2010

Geophysical Prospecting

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“…Neste trabalho utiliza-se o critério de entropia como medida da dispersão das velocidades (Bagaini et al, 1995), para determinar o número e as velocidades de referênciaótimas em cada nível de extrapolação.…”

Section: Migração Pspi E Pspi-ss Com Amplitude Verdadeiraunclassified

Migração PSPI baseada nas equações da onda unidirecionais com amplitude verdadeira

Vivas

Pestana

2007

Rev. Bras. Geof.

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ABSTRACT. The true-amplitude one-way wave equation suggested recently is both dynamically and kinematically correct. This one-way wave equations produces accurate traveltime in accordance to the eikonal equation and accurate amplitudes in accordance to the transport equation for the two-way wave equation. In laterally inhomogeneous media the implementation of this true-amplitude one-way wave equation involves the numeric calculation of a differential-integral operator that can be approximated by summation and solved by finite-difference methods. In only depth-dependent media, the new term in the one-way wave equation can be eliminated and the new one-way wave equations can be solved using the conventional phase-shift method with the appropriated boundary and imaging condition, reduced to products in the Fourier domain. Here, we present an extension of phase shift plus interpolation (PSPI) migration for true-amplitude migration based in the phase-shift true-amplitude migration developed in depth-dependent media. Numerical tests in the common shot domain with the new PSPI true-amplitude method and the Extended split-step PSPI-SS proposed were compared with the output of the conventional PSPI and PSPI-SS. The imaging quality in relation to amplitude is better with the proposed methods and the kinematic part is preserved.Keywords: common-shot migration, true-amplitude migration, one-way wave equations, depth migration, PSPI migration, PSPI-SS migration. RESUMO.As equações da onda unidirecionais com amplitude verdadeira, propostas nos trabalhos mais recentes, levam em conta de forma correta a parte cinemática e dinâmica da equação completa da onda equivalentementeàs obtidas a partir da aproximação de altas freqüências. Istoé, as equações iconal e de transporte obtidas para estes operadores se correspondem com as obtidas com a equação completa da onda. Num meio com variação lateral de velocidade, a implementação das equações unidirecionais com amplitude verdadeira envolve o cálculo numérico de operadores integro-diferenciais que podem ser aproximados por somatórios e resolvidos por técnicas de diferenças finitas. Para um meio que varia somente com a profundidade, as novas equações unidirecionais com amplitude verdadeira podem ser solucionadas através do tradicional método phase-shift , e as novas condições de fronteira e de imagem se reduzem a multiplicações no domínio de Fourier. Neste trabalho estamos propondo estender a migração phase-shift com amplitude verdadeira para meios com variação lateral v(x, z), através da metodologia Phase shift plus interpolation (PSPI). Experimentos numéricos no domínio de tiro comum com o novo método PSPI com amplitude verdadeira e sua extensão split-step (PSPI-SS), produzem imagens com amplitudes mais corretas em relação aos operadores unidirecionais convencionais, enquanto as características cinemáticas da migração PSPI e PSPI-SS são preservadas.

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“…The Fourier methods, such as Split‐Step Fourier method (SSF) (Stoffa et al 1990) and Phase Shift Plus Interpolation (PSPI) (Gazdag & Sguazzero 1984; Bagani et al 1995) can handle both wide‐angle propagation and lateral velocity variations, but the imaging becomes less accurate when the lateral velocity variations are strong. The FD methods can easily handle strong lateral velocity variations.…”

Section: Introductionmentioning

confidence: 99%

Split-step complex Padé-Fourier depth migration

Zhang

Rector

Hoversten

et al. 2007

Geophysical Journal International

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S U M M A R YWe present a split-step complex Padé-Fourier migration method based on the one-way wave equation. The downward-continuation operator is split into two downward-continuation operators: one operator is a phase-shift operator and the other operator is a finite-difference operator. A complex treatment of the propagation operator is applied to mitigate inaccuracies and instabilities due to evanescent waves. It produces high-quality images of complex structures with fewer numerical artefacts than those obtained using a real approximation of a square-root operator in the one-way wave equation. Tests on zero-offset data from the SEG/EAGE salt data show that the method improves the image quality at the cost of an additional 10 per cent computational time compared to the conventional Fourier finite-difference method.Key words: depth migration, Fourier finite-difference method, Padé approximation. I N T RO D U C T I O NWave equation migration is a rapidly growing tool for complex structure imaging (Claerbout 1985;Stoffa et al. 1990;Lee et al. 1991;Ristow & Ruhl 1994;Wu & Jin 1997; Bonomi & Cazzola 1999). Wave equation migration methods can produce accurate images provided that the background velocity field is well defined. Most widely used wave equation methods are based on solving the one-way acoustic wave equation. There are many different methods to numerically solve the one-way equation. They can be classified into three main approaches: Fourier methods (Gazdag & Sguazzero 1984;Stoffa et al. 1990) solved in the wavenumber domain and space domain; finite-difference methods (FD) (Claerbout 1985;Hale 1991) and mixed methods that are a linear combination of spectral and FD methods (Ristow & Rulh 1994; Biondi 2002).The Fourier methods, such as Split-Step Fourier method (SSF) (Stoffa et al. 1990) and Phase Shift Plus Interpolation (PSPI) (Gazdag & Sguazzero 1984; Bagani et al. 1995) can handle both wide-angle propagation and lateral velocity variations, but the imaging becomes less accurate when the lateral velocity variations are strong. The FD methods can easily handle strong lateral velocity variations. When implicit extrapolators are used in FD methods, the one-way wave equation is solved in the frequency-space domain, and the square root of the wave operator is approximated using continued fractions expansions (Claerbout 1985). The essential shortcoming * Now at: Total E&P USA Inc., 800 Gessner, Suite 700, Houston, TX 77024, USA. of this method is that it is not efficient for wide-angle propagation. High-order approximations to the square root operators are required for imaging of steep dips. When explicit extrapolators are used (Holberg 1988;Hale 1991), the exponential operator is approximated by finite length spatial filters. The disadvantage of explicit methods is that their stability is not guaranteed if the filter is not designed carefully.In 1994, Ristow and Ruhl proposed a Fourier finite-difference method (FFD) which combined a phase-shift method in the frequency-wavenumber domain and an FD method ...

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Data parallel implementation of 3‐D PSPI

Cited by 21 publications

References 5 publications

Kinematic characteristics and the influence of reference velocities of phase‐shift‐plus‐interpolation and extended‐split‐step‐Fourier migration methods

Kinematic characteristics and the influence of reference velocities of phase‐shift‐plus‐interpolation and extended‐split‐step‐Fourier migration methods

Migração PSPI baseada nas equações da onda unidirecionais com amplitude verdadeira

Split-step complex Padé-Fourier depth migration

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