Viscoacoustic reverse-time migration with a robust space-wavenumber domain attenuation compensation operator

Geophysics ◽  
2021 ◽  
pp. 1-95
Author(s):  
Jidong Yang ◽  
Jianping Huang ◽  
Hejun Zhu ◽  
Zhenchun Li ◽  
Nanxun Dai
Keyword(s):  
Time Window ◽  
Back Propagation ◽  
Homogeneous Medium ◽  
Frequency Noise ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Frequency ◽  
Attenuation Compensation ◽  
Time Migration ◽  
Wavefield Extrapolation

Intrinsic attenuation gives rise to phase dispersion and amplitude loss during seismic wave propagation. Not correcting these effects in seismic imaging can result in inaccurate reflector locations, dimmed amplitudes and degraded spatial resolution. In reverse-time migration (RTM), attenuation compensation can be implemented by reversing the sign of the dissipation term and keeping the dispersion term unchanged for backward wavefield extrapolation. Although this Q-compensated RTM scheme can effectively correct attenuation effects, amplitude amplification during back-propagation might lead to numerical instabilities, especially for field data with strong high-frequency noise. To mitigate this problem, we develop a robust space-wavenumber compensation operator, and apply it to viscoacoustic RTM. By analyzing the dispersion-only and viscoacoustic Green’s functions, we obtain an analytical solution for the attenuation compensation operator in a homogeneous medium. Because it is a time-frequency operator, to apply it directly in viscoacoustic RTM requires access to the extrapolated wavefields within a certain time window. To avoid storing the wavefields and improve computational efficiency, we use an approximated dispersion relation and convert the time-frequency operator to an equivalent space-wavenumber operator, which allows us to implement attenuation compensation on the fly during wavefield extrapolation. The hybrid-domain property of the operator enables us to account for the wavenumber-dependent compensation. A similar strategy can also be applied to the migrated images as a poststack processing approach, which is more efficient than the prestack compensation. Two synthetic and one land field dataset examples demonstrate the feasibility and adaptability of the proposed method.

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.

An implicit stabilization strategy for Q-compensated reverse time migration

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. S169-S183
Author(s):  
Hanming Chen ◽  
Hui Zhou ◽  
Ying Rao
Keyword(s):  
Robust Stabilization ◽  
Synthetic Data ◽  
Frequency Noise ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Time Migration ◽  
Wavefield Extrapolation ◽  
Amplitude Compensation ◽  
Seismic Images

Reverse time migration with [Formula: see text] compensation ([Formula: see text]-RTM) is an effective approach to enhance the resolution of seismic images because it retrieves the amplitude loss and phase distortion induced by the viscosity of media. According to the crosscorrelation imaging condition, [Formula: see text]-RTM requires compensation for the amplitude loss in the propagation paths of source and receiver wavefields, which can be realized by solving an amplitude-boosted wave equation. However, the amplitude-boosted simulations suffer from numerical instability due to the amplification of high-frequency noise. We have developed a robust stabilization strategy for [Formula: see text]-RTM by incorporating a time-variant filter into the amplitude-boosted wavefield extrapolation step. We modify the Fourier spectrum of the operator that controls the amplitude compensation to be time variant, and we add to the spectrum a stabilization factor. Doing so, we integrate the time-variant filter into the viscoacoustic wave propagator implicitly, and we avoid any explicit filtering operation in [Formula: see text]-RTM. We verify the robustness of this stabilized [Formula: see text]-RTM with two synthetic data examples. We also apply this technique to a field data set to demonstrate the imaging improvements compared to an acoustic RTM and a more traditional [Formula: see text]-RTM method.

An efficient local operator-based Q-compensated reverse time migration algorithm with multistage optimization

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S249-S259 ◽  
Author(s):  
Tong Zhou ◽  
Wenyi Hu ◽  
Jieyuan Ning
Keyword(s):  
Seismic Attenuation ◽  
Depth Information ◽  
Frequency Noise ◽  
Processing Unit ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Time Migration ◽  
Imaging Results

Most existing [Formula: see text]-compensated reverse time migration ([Formula: see text]-RTM) algorithms are based on pseudospectral methods. Because of the global nature of pseudospectral operators, these methods are not ideal for efficient parallelization, implying that they may suffer from high computational cost and inefficient memory usage for large-scale industrial problems. In this work, we reported a novel [Formula: see text]-RTM algorithm — the multistage optimized [Formula: see text]-RTM method. This [Formula: see text]-RTM algorithm uses a finite-difference method to compensate the amplitude and the phase simultaneously by uniquely combining two techniques: (1) a negative [Formula: see text] method for amplitude compensation and (2) a multistage dispersion optimization technique for phase correction. To prevent high-frequency noise from growing exponentially and ruining the imaging results, we apply a finite impulse response low-pass filter using the Kaiser window. The theoretical analyses and numerical experiments demonstrate that this [Formula: see text]-RTM algorithm precisely recovers the decayed amplitude and corrects the distorted phase caused by seismic attenuation effects, and hence produces higher resolution subsurface images with the correct structural depth information. This new method performs best in the frequency range of 10–70 Hz. Compared with pseudospectral [Formula: see text]-RTM methods, this [Formula: see text]-RTM approach offers nearly identical imaging quality. Based on local numerical differential operators, this [Formula: see text]-RTM method is very suitable for parallel computing and graphic processing unit implementation, an important feature for large 3D seismic surveys.

Viscoacoustic reverse time migration of joint primaries and different-order multiples

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. S71-S87
Author(s):  
Yingming Qu ◽  
Jinli Li ◽  
Zhe Guan ◽  
Zhenchun Li
Keyword(s):  
Vertical Direction ◽  
Seismic Attenuation ◽  
Frequency Noise ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Sea Bottom ◽  
Multiple Imaging ◽  
Propagation Paths ◽  
Different Order

Compared to primary arrivals, multiples have longer propagation paths and smaller reflection angles, leading to a wider illumination area in the horizontal direction and higher resolution in the vertical direction. Hence, it is better to make full use of the multiples rather than suppressing them. However, seismic attenuation exists widely in the subsurface medium, especially directly below the deep sea bottom. Therefore, to compensate for the attenuation effect during multiple imaging, we have developed a viscoacoustic reverse time migration (RTM) method of different-order multiples. Following the multiple propagation paths, we compensate for the attenuation during source wavefield forward propagation and receiver backward propagation, and we introduce a regularization operator to automatically eliminate the exponential high-frequency noise during the attenuation compensation process. Taking advantage of the full wavefield information, we jointly use the different-order multiples and primaries when implementing viscoacoustic RTM. In numerical examples, we validate the viscoacoustic RTM of different-order multiples in a three-layer attenuation model and an attenuating Sigsbee2B model. Our results suggest that our method can image the models using different-order multiples separately, which suppresses crosstalk artifacts, balances energy, raises resolution, and improves subsalt images dramatically.

scholarly journals Q-compensated least-squares reverse time migration using low-rank one-step wave extrapolation

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. S271-S279 ◽  
Author(s):  
Junzhe Sun ◽  
Sergey Fomel ◽  
Tieyuan Zhu ◽  
Jingwei Hu
Keyword(s):  
Convergence Rate ◽  
Least Squares ◽  
Seismic Attenuation ◽  
Low Rank ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Attenuation Compensation ◽  
Time Migration ◽  
Rank One ◽  
One Step

Attenuation of seismic waves needs to be taken into account to improve the accuracy of seismic imaging. In viscoacoustic media, reverse time migration (RTM) can be performed with [Formula: see text]-compensation, which is also known as [Formula: see text]-RTM. Least-squares RTM (LSRTM) has also been shown to be able to compensate for attenuation through linearized inversion. However, seismic attenuation may significantly slow down the convergence rate of the least-squares iterative inversion process without proper preconditioning. We have found that incorporating attenuation compensation into LSRTM can improve the speed of convergence in attenuating media, obtaining high-quality images within the first few iterations. Based on the low-rank one-step seismic modeling operator in viscoacoustic media, we have derived its adjoint operator using nonstationary filtering theory. The proposed forward and adjoint operators can be efficiently applied to propagate viscoacoustic waves and to implement attenuation compensation. Recognizing that, in viscoacoustic media, the wave-equation Hessian may become ill-conditioned, we propose to precondition LSRTM with [Formula: see text]-compensated RTM. Numerical examples showed that the preconditioned [Formula: see text]-LSRTM method has a significantly faster convergence rate than LSRTM and thus is preferable for practical applications.

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.

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