Q-compensated viscoelastic reverse time migration using mode-dependent adaptive stabilization scheme

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. S301-S315 ◽  
Author(s):  
Yufeng Wang ◽  
Hui Zhou ◽  
Xuebin Zhao ◽  
Qingchen Zhang ◽  
Yangkang Chen
Keyword(s):  
Staggered Grid ◽  
Data Sets ◽  
Adaptive Stabilization ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Text Filtering ◽  
Low Pass ◽  
Filtering Effect ◽  
Wavefield Decomposition

The [Formula: see text]-compensated viscoelastic reverse time migration ([Formula: see text]-ERTM) method counteracts the subsurface quality-factor ([Formula: see text]) filtering effect for attenuated multicomponent seismic data to produce high-quality migrated images. Compared with [Formula: see text]-compensated viscoacoustic reverse time migration ([Formula: see text]-ARTM), [Formula: see text]-ERTM provides more informative geologic and structural characterization of the subsurface, but it poses greater challenges on viscoelastic wavefield decomposition and stabilization. On the basis of our previously proposed stabilization operator for [Formula: see text]-ARTM, we have developed a mode-dependent adaptive stabilization scheme for [Formula: see text]-ERTM, which has the ability to handle the numerical instability issue arising from viscoelastic compensation. The stabilization scheme exhibits superior properties of time variance and [Formula: see text] dependence over the commonly used low-pass filtering method. In the context of the viscoelastic wave equation with decoupled fractional Laplacians, we have thoroughly investigated the staggered-grid pseudospectral approach for viscoelastic simulation, vector-based wavefield decomposition for imaging, and mode-dependent adaptive stabilization for compensation. These indispensable modules eventually form the whole framework for stable and accurate [Formula: see text]-ERTM. The [Formula: see text]-ERTM results including PP- and PS-images from synthetic and field data sets are provided to verify the feasibility and superiority of our approach in terms of fidelity and stability.

Adaptive stabilization for Q-compensated reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. S15-S32 ◽  
Author(s):  
Yufeng Wang ◽  
Hui Zhou ◽  
Hanming Chen ◽  
Yangkang Chen
Keyword(s):  
Wave Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Numerical Instability ◽  
Adaptive Stabilization ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Gas Chimney ◽  
Low Pass

Reverse time migration (RTM) for attenuating media should take amplitude compensation and phase correction into consideration. However, attenuation compensation during seismic propagation suffers from numerical instability because of the boosted high-frequency ambient noise. We have developed a novel adaptive stabilization method for [Formula: see text]-compensated RTM ([Formula: see text]-RTM), which exhibits superior properties of time variance and [Formula: see text] dependence over conventional low-pass filtering-based method. We derive the stabilization operator by first analytically deriving [Formula: see text]-space Green’s functions for a constant-[Formula: see text] wave equation with decoupled fractional Laplacians and its compensated equation. The time propagator of Green’s function for the viscoacoustic wave equation decreases exponentially, whereas that of the compensated equation is exponentially divergent at a high wavenumber, and it is not stable after the wave is extrapolated for a long time. Therefore, the Green’s functions theoretically explain how the numerical instability existing in [Formula: see text]-RTM arises and shed light on how to overcome this problem pertinently. The stabilization factor required in the proposed method can be explicitly identified by the specified gain limit according to an empirical formula. The [Formula: see text]-RTM results for noise-free data using low-pass filtering and adaptive stabilization are compared over a simple five-layer model and the BP gas chimney model to verify the superiority of the proposed approach in terms of fidelity and stability. The [Formula: see text]-RTM result for noisy data from the BP gas chimney model further demonstrates that our method enjoys a better antinoise performance and helps significantly to enhance the resolution of seismic images.

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.

Reverse time migration

Geophysics ◽  
1983 ◽  
Vol 48 (11) ◽  
pp. 1514-1524 ◽  
Author(s):  
Edip Baysal ◽  
Dan D. Kosloff ◽  
John W. C. Sherwood
Keyword(s):  
Wave Amplitude ◽  
Synthetic Data ◽  
Data Sets ◽  
Field Observations ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Method ◽  
Zero Offset ◽  
Time Extrapolation

Migration of stacked or zero‐offset sections is based on deriving the wave amplitude in space from wave field observations at the surface. Conventionally this calculation has been carried out through a depth extrapolation. We examine the alternative of carrying out the migration through a reverse time extrapolation. This approach may offer improvements over existing migration methods, especially in cases of steeply dipping structures with strong velocity contrasts. This migration method is tested using appropriate synthetic data sets.

First-order particle velocity equations of decoupled P- and S-wavefields and their application in elastic reverse time migration

Geophysics ◽  
2021 ◽  
pp. 1-78
Author(s):  
Zhiyuan Li ◽  
Youshan Liu ◽  
Guanghe Liang ◽  
Guoqiang Xue ◽  
Runjie Wang
Keyword(s):  
Particle Velocity ◽  
Computational Cost ◽  
Staggered Grid ◽  
Additional Stress ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Computational Accuracy ◽  
First Order ◽  
Time Migration ◽  
Stress Variable

The separation of P- and S-wavefields is considered to be an effective approach for eliminating wave-mode cross-talk in elastic reverse-time migration. At present, the Helmholtz decomposition method is widely used for isotropic media. However, it tends to change the amplitudes and phases of the separated wavefields compared with the original wavefields. Other methods used to obtain pure P- and S-wavefields include the application of the elastic wave equations of the decoupled wavefields. To achieve a high computational accuracy, staggered-grid finite-difference (FD) schemes are usually used to numerically solve the equations by introducing an additional stress variable. However, the computational cost of this method is high because a conventional hybrid wavefield (P- and S-wavefields are mixed together) simulation must be created before the P- and S-wavefields can be calculated. We developed the first-order particle velocity equations to reduce the computational cost. The equations can describe four types of particle velocity wavefields: the vector P-wavefield, the scalar P-wavefield, the vector S-wavefield, and the vector S-wavefield rotated in the direction of the curl factor. Without introducing the stress variable, only the four types of particle velocity variables are used to construct the staggered-grid FD schemes, so the computational cost is reduced. We also present an algorithm to calculate the P and S propagation vectors using the four particle velocities, which is simpler than the Poynting vector. Finally, we applied the velocity equations and propagation vectors to elastic reverse-time migration and angle-domain common-image gather computations. These numerical examples illustrate the efficiency of the proposed methods.

Reducing artifacts of elastic reverse time migration by the deprimary technique

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S569-S577 ◽  
Author(s):  
Yang Zhao ◽  
Houzhu Zhang ◽  
Jidong Yang ◽  
Tong Fei
Keyword(s):  
Complex Function ◽  
Noise Removal ◽  
Pure Mode ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Imaging Condition ◽  
Velocity Models ◽  
Time Migration ◽  
Wavefield Decomposition

Using the two-way elastic-wave equation, elastic reverse time migration (ERTM) is superior to acoustic RTM because ERTM can handle mode conversions and S-wave propagations in complex realistic subsurface. However, ERTM results may not only contain classical backscattering noises, but they may also suffer from false images associated with primary P- and S-wave reflections along their nonphysical paths. These false images are produced by specific wave paths in migration velocity models in the presence of sharp interfaces or strong velocity contrasts. We have addressed these issues explicitly by introducing a primary noise removal strategy into ERTM, in which the up- and downgoing waves are efficiently separated from the pure-mode vector P- and S-wavefields during source- and receiver-side wavefield extrapolation. Specifically, we investigate a new method of vector wavefield decomposition, which allows us to produce the same phases and amplitudes for the separated P- and S-wavefields as those of the input elastic wavefields. A complex function involved with the Hilbert transform is used in up- and downgoing wavefield decomposition. Our approach is cost effective and avoids the large storage of wavefield snapshots that is required by the conventional wavefield separation technique. A modified dot-product imaging condition is proposed to produce multicomponent PP-, PS-, SP-, and SS-images. We apply our imaging condition to two synthetic models, and we demonstrate the improvement on the image quality of ERTM.

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