Element-free reverse-time migration in frequency domain

2016 ◽  
Author(s):  
Xiaodong Qiang* ◽  
Xiaofeng Jia
Keyword(s):  
Frequency Domain ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Element Free

An efficient vector elastic reverse time migration method in the hybrid time and frequency domain for anisotropic media

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S511-S522 ◽  
Author(s):  
Kai Gao ◽  
Lianjie Huang
Keyword(s):  
Frequency Domain ◽  
Anisotropic Media ◽  
Reverse Time ◽  
Computationally Efficient ◽  
Reverse Time Migration ◽  
Computational Costs ◽  
Time Migration ◽  
Migration Imaging ◽  
Efficient Vector ◽  
Wave Migration

Vector elastic reverse time migration (ERTM) produces subsurface elastic images with correct polarities using multicomponent seismic data. However, the decomposition of elastic wavefields into vector P- and S-wavefields is computationally expensive, particularly in heterogeneous and complex anisotropic media. We have developed a computationally efficient vector ERTM method in the hybrid time and frequency domain by combining three existing techniques. Rather than decomposing elastic wavefields into vector qP- and qS-wavefields during time-domain wavefield propagation, we conduct the wavefield decomposition in the frequency domain for several selected frequencies. In general, the number of selected frequencies needed for migration imaging is much smaller than the number of time steps during forward and backward wavefield propagation, leading to greatly reduced computational costs associated with the qP-/qS-wavefield vector separation in complex heterogeneous anisotropic media. We further combine an implicit directional wavefield separation into the vector ERTM to enhance the image quality. The numerical results demonstrate that our method produces high-quality elastic-wave migration images with notably reduced computational costs compared to the conventional vector ERTM method.

scholarly journals REVERSE TIME MIGRATION IN THE FREQUENCY DOMAIN BY THE RAPID EXPANSION METHOD

2017 ◽  
Vol 35 (4) ◽  
pp. 287
Author(s):  
Protásio Nery Andrade ◽  
Reynam Cruz Pestana ◽  
Daniel E. Revelo
Keyword(s):  
Frequency Domain ◽  
Expansion Method ◽  
Frequency Component ◽  
Rapid Expansion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
High Quality ◽  
Depth Migration ◽  
Time Migration ◽  
Seismic Images

ABSTRACT.  This paper proposes and describes the implementation of a new depth migration method in the frequency domain. The method, based in the reverse time migration (RTM) technique, extrapolates wavefields from the source and receivers to obtain migrated seismic images that are built directly into the frequency domain. In the proposed method, wavefields are propagated in the time domain and are then transformed into the frequency domain at each time extrapolation step through the discrete Fourier transform. Neither the forward nor backward wavefield is needed to be stored in memory or read from disk storage. To speed up the migration algorithm, the discrete Fourier transform kernel for each frequency is computed and salved before the time extrapolation procedure. At the imaging condition phase, both source and receiver wavefields are at the same frequency, so that, the construction of the image occurs by multiplying the forward source propagated wavefield with the backward propagated of the receivers wavefield for each frequency component. Subsequently, saving the source field at each step to later correlate it with the backpropagated receiver wave field, usually done in conventional RTM, becomes unnecessary. Nor is it necessary to invert a matrix for each frequency component, which is done in the migration technique that uses the Helmholtz equation solution in the frequency domain. Thus, the migration procedure in the frequency domain being proposed is more efficient from a computational point of view, and can also produce high quality migrated images as those produced by conventional RTM. The rapid expansion method (REM) is used for seismic forward modeling, which extrapolated data with good precision and free of numerical dispersion. Thus, with the transformed data at each step in the frequency domain, it is possible to construct high quality, in-depth seismic images at a lower computational cost. Moreover, this frequency domain migration with REM is an atractive strategy to design robust inverse algorithms, especially for 3D problems. To demonstrate the efficiency and applicability of the proposed method, two synthetic models were used and their results showed high quality images equivalent to those obtained by conventional RTM and thus proving the vality of the method. Keywords: wave equation migration, depth migration, imaging condition, frequency domain migration. RESUMO. Um método de migração em profundidade no domínio da frequência é proposto e implementado. O método consiste na extrapolação dos campos de ondas da fonte e dos receptores e baseia-se na técnica de migração reversa no tempo (da sigla em inglês, RTM), obtendo imagens sísmicas migradas, construídas diretamente no domínio da frequência. No método que estamos propondo, os campos de ondas são propagados no domínio do tempo e a cada passo de extrapolação são transformados para o domínio da frequência, através da transformada de Fourier discreta (do inglês, on-the-fly transform). Para acelerar o algoritmo de migração, o kernel da transformada de Fourier é calculado fora do loop do tempo. Além disso, na etapa de condição da imagem, os campos de onda, tanto da fonte como dos receptores, são calculados no mesmo instante de tempo, ou seja, a construção da imagem se dá através da multiplicação do campo de onda da fonte com o campo retropropagado dos receptores, para cada componente de frequência. Portanto, não precisamos salvar o campo da fonte a cada passo no tempo para posteriormente correlacionar com o campo de onda retropropagado dos receptores, como é usualmente feito na RTM convencional, nem é preciso inverter uma matriz para cada componente de frequência, como é realizado normalmente pela técnica de migração no domínio da frequência, utilizando a solução da equação de Helmholtz. Desta forma, o procedimento de migração no domínio da frequência que estamos propondo se torna mais eficiente do ponto de vista computacional, podendo produzir imagens migradas de alta qualidade, quando comparadas às obtidas através da RTM convencional no domínio do tempo. Para a extrapolação dos campos de ondas no tempo foi empregado o método de expansão rápida (da sigla em inglês, REM), que permite a extrapolação dos dados com boa precisão e livres de dispersão numérica. Desta forma, com os dados transformados para o domínio da frequência, a cada passo no tempo, é possível a construção de imagens sísmicas em profundidade de boa qualidade e a um menor custo computacional. Para demonstrar a eficiência e aplicabilidade do método proposto, dois modelos sintéticos foram usados e seus resultados apresentaram imagens de alta qualidade equivalentes às obtidas pela RTM convencional. Palavras-chave: equação de migração da onda, migração, condição de imagem, migração no domínio da frequência.

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