Vertical image waves in elliptically anisotropic media

Schleicher, Jörg; Novais, Amélia; Costa, Jessé C.

doi:10.1007/s11200-008-0008-0

Cited by 5 publications

(1 citation statement)

References 23 publications

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“…Esta onda imagem pode ser aplicada em cada traço individualmente em uma seção de afastamento comum com h > 0, diferentes dos outros que são aplicados em seções sísmicas. Note a semelhança com a equação da onda imagem para remigração na velocidade vertical em meios elipticamente anisotrópicos (Schleicher et al, 2008). A equação (4.28) pode ser resolvida numericamente de modo similar à equação discutida por estes autores, permitindo a comparação direta da seção simulada com a seção adquirida.…”

Section: Onda Imagem Para Continuação Da Velocidade Mcounclassified

Solução da equação da onda imagem para continuação do afastamento mediante o metodo das caracteristicas

Coimbra¹,

Schleicher²

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The dislocation of a seismic event under the so-called Offset Continuation Operation (OCO) can be described by a second-order partial differential equation, which has been called the OCO image-wave equation. By substitution of a ray-like trial solution, an OCO image-wave eikonal equation is obtained that describes the kinematic aspects of OCO imagewave propagation. In this work, we solve the OCO image-wave eikonal equation by means of the method of characteristics. The characteristics of this equation are the OCO trajectories that describe the path of dislocation of a seismic event under variation of the source-receiver offset. The set of endpoints of several OCO trajectories traced from the same initial to the same final offset under varying values for the medium velocity defines the OCO velocity ray or briefly OCO ray. This OCO ray can be employed for velocity analysis. The algorithm consists of OCO ray tracing an then finding the intersection point of the OCO ray with the seismic reflection event in the final common-offset section. The procedure has the advantage over conventional velocity analysis that it is based on a comparison of simulated and acquired data rather than two sets of simulated data. Numerical examples demonstrate that the OCO ray tracing can be accurately executed and that the resulting velocity analysis yields reliable velocities. Moreover, based on the analytic expressions for the OCO rays starting from zerooffset (migraton to common offset, MCO), we derived an image-wave equation for MCO velocity continuation. We demonstrate that in many practical situations this equation can be directly employed for OCO, thus avoiding the need to trace OCO trajectories and OCO rays.

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Section: Onda Imagem Para Continuação Da Velocidade Mcounclassified

Solução da equação da onda imagem para continuação do afastamento mediante o metodo das caracteristicas

Coimbra¹,

Schleicher²

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Azimuthally Anisotropic 3D Velocity Continuation

Burnett

Fomel

2011

International Journal of Geophysics

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We extend time-domain velocity continuation to the zero-offset 3D azimuthally anisotropic case. Velocity continuation describes how a seismic image changes given a change in migration velocity. This description turns out to be of a wave propagation process, in which images change along a velocity axis. In the anisotropic case, the velocity model is multiparameter. Therefore, anisotropic image propagation is multidimensional. We use a three-parameter slowness model, which is related to azimuthal variations in velocity, as well as their principal directions. This information is useful for fracture and reservoir characterization from seismic data. We provide synthetic diffraction imaging examples to illustrate the concept and potential applications of azimuthal velocity continuation and to analyze the impulse response of the 3D velocity continuation operator.

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Time-migration velocity analysis by image-wave propagation of common-image gathers

2008

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Image-wave propagation or velocity continuation describes the variation of the migrated position of a seismic event as a function of migration velocity. Image-wave propagation in the common-image gather (CIG) domain can be combined with residual-moveout analysis for iterative migration velocity analysis (MVA). Velocity continuation of CIGs leads to a detection of those velocities in which events flatten. Although image-wave continuation is based on the assumption of a constant migration velocity, the procedure can be applied in inhomogeneous media. For this purpose, CIGs obtained by migration with an inhomogeneous macrovelocity model are continued starting from a constant reference velocity. The interpretation of continued CIGs, as if they were obtained from residual migrations, leads to a correction formula that translates residual flattening velocities into absolute time-migration velocities. In this way, the migration velocity model can be improved iteratively until a satisfactory result is reached. With a numerical example, we found that MVA with iterative image continuation applied exclusively to selected CIGs can construct a reasonable migration velocity model from scratch, without the need to build an initial model from a previous conventional normal-moveout/dip-moveout velocity analysis.

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Vertical image waves in elliptically anisotropic media

Cited by 5 publications

References 23 publications

Solução da equação da onda imagem para continuação do afastamento mediante o metodo das caracteristicas

Solução da equação da onda imagem para continuação do afastamento mediante o metodo das caracteristicas

Azimuthally Anisotropic 3D Velocity Continuation

Time-migration velocity analysis by image-wave propagation of common-image gathers

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