A stable approach for Q-compensated viscoelastic reverse time migration using excitation amplitude imaging condition

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. S459-S476 ◽  
Author(s):  
Xuebin Zhao ◽  
Hui Zhou ◽  
Yufeng Wang ◽  
Hanming Chen ◽  
Zheng Zhou ◽  
...  
Keyword(s):  
Excitation Amplitude ◽  
Frequency Noise ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Migration ◽  
Free Data ◽  
Text Filtering ◽  
Low Pass ◽  
Compensation Approach

The earth [Formula: see text] filtering causes poor illumination of the subsurface. Compensating for the attenuated amplitude and distorted phase is crucial during elastic reverse time migration (ERTM) to improve the imaging quality. Conventional [Formula: see text]-compensated ERTM ([Formula: see text]-ERTM) methods tend to boost the attenuated energy to inverse the [Formula: see text] effects. These methods usually suffer from severe numerical instability because of the unlimited amplification of the high-frequency noise. Low-pass filtering is generally used to stabilize the process, however, at the expense of precision. We have developed a stable compensation approach in this paper. Based on the decoupled fractional Laplacians viscoelastic wave equation, two compensation operators are obtained by extrapolating wavefield in the dispersion-only and viscoelastic media. Because no explicit amplification is included, these two operators are absolutely stable for implementation. To improve the division morbidity for calculating the compensation operators, we use the excitation amplitude criterion and embed the operators into a vector-based [Formula: see text]-compensated excitation amplitude imaging condition. With the derived imaging condition, we could compensate for the absorption accurately without needing to concern the stability issue. The [Formula: see text]-ERTM results for noise-free data are carried out over a simple layered model and a more realistic Marmousi model with an attenuating area to verify the feasibility of the proposed approach. The migration results for noisy data from the Marmousi model further prove that the proposed method performs better fidelity, adaptability, and antinoise performance compared with conventional compensation method with low-pass filtering.

scholarly journals LAGUERRE-GAUSS FILTERS IN REVERSE TIME MIGRATION IMAGE RECONSTRUCTION

2018 ◽  
Vol 35 (2) ◽  
Author(s):  
Juan Guillermo Paniagua Castrillón ◽  
Olga Lucia Quintero Montoya ◽  
Daniel Sierra-Sosa
Keyword(s):  
Cross Correlation ◽  
Synthetic Data ◽  
Low Frequency ◽  
Frequency Noise ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Migration ◽  
Migration Imaging ◽  
Gauss Transform

ABSTRACT. Reverse time migration (RTM) solves the acoustic or elastic wave equation by means of the extrapolation from source and receiver wavefield in time. A migrated image is obtained by applying a criteria known as imaging condition. The cross-correlation between source and receiver wavefields is the commonly used imaging condition. However, this imaging condition produces spatial low-frequency noise, called artifacts, due to the unwanted correlation of the diving, head and backscattered waves. Several techniques have been proposed to reduce the artifacts occurrence. Derivative operators as Laplacian are the most frequently used. In this work, we propose a technique based on a spiral phase filter ranging from 0 to 2π, and a toroidal amplitude bandpass filter, known as Laguerre-Gauss transform. Through numerical experiments we present the application of this particular filter on three synthetic data sets. In addition, we present a comparative spectral study of images obtained by the zero-lag cross-correlation imaging condition, the Laplacian filtering and the Laguerre-Gauss filtering, showing their frequency features. We also present evidences not only with simulated noisy velocity fields but also by comparison with the model velocity field gradients that this method improves the RTM images by reducing the artifacts and notably enhance the reflective events. Keywords: Laguerre-Gauss transform, zero-lag cross-correlation, seismic migration, imaging condition. RESUMO. A migração reversa no tempo (RTM) resolve a equação de onda acústica ou elástica por meio da extrapolação a partir do campo de onda da fonte e do receptor no tempo. Uma imagem migrada é obtida aplicando um critério conhecido como condição de imagem. A correlação cruzada entre campos de onda de fonte e receptor é a condição de imagem comumente usada. No entanto, esta condição de imagem produz ruído espacial de baixa frequência, chamados artefatos, devido à correlação indesejada das ondas de mergulho, cabeça e retrodifusão. Várias técnicas têm sido propostas para reduzir a ocorrência de artefatos. Operadores derivados como Laplaciano são os mais utilizados. Neste trabalho, propomos uma técnica baseada em um filtro de fase espiral que varia de 0 a 2π, e um filtro passabanda de amplitude toroidal, conhecido como transformada de Laguerre-Gauss. Através de experimentos numéricos, apresentamos a aplicação deste filtro particular em três conjuntos de dados sintéticos. Além disso, apresentamos um estudo comparativo espectral de imagens obtidas pela condição de imagem de correlação cruzada atraso zero, a filtragem de Laplaciano e a filtragem Laguerre-Gauss, mostrando suas características de frequência. Apresentamos evidências não somente com campos simulados de velocidade ruidosa, mas também por comparação com os gradientes de campo de velocidade do modelo que este método melhora as imagens RTM, reduzindo os artefatos e aumentando notavelmente os eventos reflexivos. Palavras-chave: Transformação de Laguerre-Gauss, correlação cruzada atraso zero, migração sísmica, condição de imagem.

scholarly journals Common-image gathers using the excitation amplitude imaging condition

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. S261-S269 ◽  
Author(s):  
Mahesh Kalita ◽  
Tariq Alkhalifah
Keyword(s):  
Computational Cost ◽  
Velocity Model ◽  
Excitation Amplitude ◽  
Time Lags ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Disk Storage ◽  
Time Migration ◽  
Migration Velocity Analysis

Common-image gathers (CIGs) are extensively used in migration velocity analysis. Any defocused events in the subsurface offset domain or equivalently nonflat events in angle-domain CIGs are accounted for revising the migration velocities. However, CIGs from wave-equation methods such as reverse time migration are often expensive to compute, especially in 3D. Using the excitation amplitude imaging condition that simplifies the forward-propagated source wavefield, we have managed to extract extended images for space and time lags in conjunction with prestack reverse time migration. The extended images tend to be cleaner, and the memory cost/disk storage is extensively reduced because we do not need to store the source wavefield. In addition, by avoiding the crosscorrelation calculation, we reduce the computational cost. These features are demonstrated on a linear [Formula: see text] model, a two-layer velocity model, and the Marmousi model.

Polarity-consistent excitation amplitude imaging condition for elastic reverse time migration

2014 ◽  
Vol 12 (1) ◽  
pp. 33-44 ◽  
Author(s):  
Qizhen Du ◽  
Mingqiang Zhang ◽  
Xufei Gong ◽  
Xiaoran Chen
Keyword(s):  
Excitation Amplitude ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Migration

A stable and efficient approach of Q reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S557-S567 ◽  
Author(s):  
Yan Zhao ◽  
Ningbo Mao ◽  
Zhiming Ren
Keyword(s):  
Wave Equation ◽  
Computational Efficiency ◽  
High Frequency ◽  
Frequency Noise ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
High Frequency Noise ◽  
Time Migration ◽  
Low Pass ◽  
Wavefield Extrapolation

Amplitude energy attenuation and phase distortion of seismic waves caused by formation viscoelasticity reduce the resolution of reverse time migration (RTM) images. Q-RTM often is used to compensate the attenuation effects and improve the resolution of seismic imaging. However, serious high-frequency noise and tremendous amplitude will be produced during the wavefield extrapolation of Q-RTM, resulting in its inability to be imaged. Many Q-RTM algorithms solve the problem of instability through low-pass filtering in the wavenumber domain, but the method is less efficient in computation and has a truncation effect in the wavefield. We have developed a stable and efficient Q-RTM method, in which a regularization term was introduced into the viscoacoustic wave equation to suppress the high-frequency noise, and the finite-difference method was used to solve the viscoacoustic wave equation with a regularization term. We used the model example to visually demonstrate the instability of wavefield extrapolation in Q-RTM and compared the effect and computational efficiency of the two stabilization processing methods, low-pass filtering and regularization. Meanwhile, our method is not involved in solving the fractional derivatives by using the pseudo-spectral method, the computational efficiency also can be improved. We tested the Q-RTM approach on a simple layered model, Marmousi model, and real seismic data. The results of numerical examples demonstrated that the Q-RTM method can solve the problem of instability effectively and obtain a higher resolution image with lower computational cost.

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