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 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.

Fast image-domain target-oriented least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. A81-A86 ◽  
Author(s):  
Zeyu Zhao ◽  
Mrinal K. Sen
Keyword(s):  
Plane Wave ◽  
Least Squares ◽  
Large Scale ◽  
Green's Functions ◽  
Green’S Functions ◽  
Hessian Matrix ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Image Domain ◽  
Time Migration

We have developed a fast image-domain target-oriented least-squares reverse time migration (LSRTM) method based on applying the inverse or pseudoinverse of a target-oriented Hessian matrix to a migrated image. The image and the target-oriented Hessian matrix are constructed using plane-wave Green’s functions that are computed by solving the two-way wave equation. Because the number of required plane-wave Green’s functions is small, the proposed method is highly efficient. We exploit the sparsity of the Hessian matrix by computing only a couple of off-diagonal terms for the target-oriented Hessian, which further improves the computational efficiency. We examined the proposed LSRTM method using the 2D Marmousi model. We demonstrated that our method correctly recovers the reflectivity model, and the retrieved results have more balanced illumination and higher spatial resolution than traditional images. Because of the low cost of computing the target-oriented Hessian matrix, the proposed method has the potential to be applied to large-scale problems.

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.

Double-plane-wave reverse time migration in the frequency domain

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. S367-S382 ◽  
Author(s):  
Zeyu Zhao ◽  
Mrinal K. Sen ◽  
Paul L. Stoffa
Keyword(s):  
Plane Wave ◽  
Frequency Domain ◽  
Green's Functions ◽  
Green’S Functions ◽  
Plane Waves ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Time Migration ◽  
Double Plane

We have developed an efficient, accurate, and flexible plane-wave migration algorithm in the frequency domain by using a compressed and coupled-plane-wave data set, known as the double-plane-wave (DPW) data set. The DPW data set obtained by slant stacking of seismic shot profiles over source and receiver/offset represents seismic data in a fully decomposed plane-wave domain, which is called the DPW domain. A new DPW migration algorithm is derived under the Born approximation in the frequency domain, and it is referred to as the frequency-domain DPW reverse time migration (RTM). Frequency plane-wave Green’s functions need to be constructed and used during the migration. Time dips in shot profiles help to estimate the range of plane-wave decomposition. Therefore, the number of frequency plane-wave Green’s functions required for migration is limited. Furthermore, frequency plane-wave Green’s functions can be used for imaging each set of plane waves — either source or receiver/offset plane waves. As a result, the computational burden of computing Green’s function is substantially reduced; this results in increasing the migration efficiency. A selected range of plane-wave components can be migrated independently to image specific targets. Ray-parameter common-image gathers can be generated after migration without extra effort. The algorithm was tested on several synthetic data sets to show its feasibility and usefulness. The frequency-domain DPW RTM can also include anisotropy by constructing plane-wave Green’s function in anisotropic media.

scholarly journals Depth-Extrapolation-Based True-Amplitude Full-Wave-Equation Migration from Topography

2021 ◽  
Vol 11 (7) ◽  
pp. 3010
Author(s):  
Hao Liu ◽  
Xuewei Liu
Keyword(s):  
Wave Equation ◽  
Partial Derivative ◽  
Model Experiment ◽  
Surface Velocity ◽  
Seismic Exploration ◽  
Initial Condition ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Full Wave ◽  
Time Migration

The lack of an initial condition is one of the major challenges in full-wave-equation depth extrapolation. This initial condition is the vertical partial derivative of the surface wavefield and cannot be provided by the conventional seismic acquisition system. The traditional solution is to use the wavefield value of the surface to calculate the vertical partial derivative by assuming that the surface velocity is constant. However, for seismic exploration on land, the surface velocity is often not uniform. To solve this problem, we propose a new method for calculating the vertical partial derivative from the surface wavefield without making any assumptions about the surface conditions. Based on the calculated derivative, we implemented a depth-extrapolation-based full-wave-equation migration from topography using the direct downward continuation. We tested the imaging performance of our proposed method with several experiments. The results of the Marmousi model experiment show that our proposed method is superior to the conventional reverse time migration (RTM) algorithm in terms of imaging accuracy and amplitude-preserving performance at medium and deep depths. In the Canadian Foothills model experiment, we proved that our method can still accurately image complex structures and maintain amplitude under topographic scenario.

Q least-squares reverse time migration based on the first-order viscoacoustic quasidifferential equations

Geophysics ◽  
2021 ◽  
pp. 1-65
Author(s):  
Yingming Qu ◽  
Yixin Wang ◽  
Zhenchun Li ◽  
Chang Liu
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Surface Topography ◽  
Density Perturbation ◽  
Second Order ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Time Migration ◽  
Grid Scheme

Seismic wave attenuation caused by subsurface viscoelasticity reduces the quality of migration and the reliability of interpretation. A variety of Q-compensated migration methods have been developed based on the second-order viscoacoustic quasidifferential equations. However, these second-order wave-equation-based methods are difficult to handle with density perturbation and surface topography. In addition, the staggered grid scheme, which has an advantage over the collocated grid scheme because of its reduced numerical dispersion and enhanced stability, works in first-order wave-equation-based methods. We have developed a Q least-squares reverse time migration method based on the first-order viscoacoustic quasidifferential equations by deriving Q-compensated forward-propagated operators, Q-compensated adjoint operators, and Q-attenuated Born modeling operators. Besides, our method using curvilinear grids is available even when the attenuating medium has surface topography and can conduct Q-compensated migration with density perturbation. The results of numerical tests on two synthetic and a field data sets indicate that our method improves the imaging quality with iterations and produces better imaging results with clearer structures, higher signal-to-noise ratio, higher resolution, and more balanced amplitude by correcting the energy loss and phase distortion caused by Q attenuation. It also suppresses the scattering and diffracted noise caused by the surface topography.

Angle-Domain Gathers Computation Using Poynting Vector of Two-Way Acoustic Wave Equation

2014 ◽  
Vol 962-965 ◽  
pp. 2984-2987
Author(s):  
Jia Jia Yang ◽  
Bing Shou He ◽  
Ting Chen
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Real Data ◽  
Flow Density ◽  
Acoustic Wave Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wave Fields ◽  
Time Migration ◽  
Source Wave

Based on two-way acoustic wave equation, we present a method for computing angle-domain common-image gathers for reverse time migration. The method calculates the propagation direction of source wave-fields and receiver wave-fields according to expression of energy flow density vectors (Poynting vectors) of acoustic wave equation in space-time domain to obtain the reflection angle, then apply the normalized cross-correlation imaging condition to achieve the angle-domain common-image gathers. The angle gathers obtained can be used for migration velocity analysis, AVA analysis and so on. Numerical examples and real data examples demonstrate the effectiveness of this method.

Implicit interpolation in reverse‐time migration

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 906-917 ◽  
Author(s):  
Jinming Zhu ◽  
Larry R. Lines
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Real Data ◽  
Seismic Sources ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Difference Wave ◽  
Time Migration ◽  
Seismic Acquisition ◽  
Recorded Data

Reverse‐time migration applies finite‐difference wave equation solutions by using unaliased time‐reversed recorded traces as seismic sources. Recorded data can be sparsely or irregularly sampled relative to a finely spaced finite‐difference mesh because of the nature of seismic acquisition. Fortunately, reliable interpolation of missing traces is implicitly included in the reverse‐time wave equation computations. This implicit interpolation is essentially based on the ability of the wavefield to “heal itself” during propagation. Both synthetic and real data examples demonstrate that reverse‐time migration can often be performed effectively without the need for explicit interpolation of missing traces.

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