Least-squares inversion-based elastic reverse time migration with PP- and PS-angle-domain common-imaging gathers

Geophysics ◽  
2021 ◽  
Vol 86 (1) ◽  
pp. S29-S44
Author(s):  
Bingluo Gu ◽  
Jianping Huang ◽  
Jianguang Han ◽  
Zhiming Ren ◽  
Zhenchun Li
Keyword(s):  
Adjoint Operator ◽  
Optimization Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
Velocity Information ◽  
The Difference ◽  
Amplitude Variation With Angle

Elastic angle-domain common-imaging gathers (ADCIGs) extracted from elastic reverse time migration (ERTM) play a pivotal part in elastic migration velocity analysis, elastic amplitude variation with angle, and attribute interpretation. In practice, however, elastic ADCIGs often suffer from unbalanced amplitude behavior, poor resolution, and low-wavenumber artifacts because of insufficient velocity information, limited recording aperture, uneven illumination, and other inaccuracies of the migration operator. We have developed a new method to improve the quality of elastic ADCIGs extracted from ERTM by posing ERTM imaging as an inverse problem whose misfit function measures the difference between simulated and observed data. The misfit function can be minimized by updating elastic offset-domain common-imaging gathers (ODCIGs) using an optimization method. Based on the transformation between ADCIGs and ODCIGs, the forward operator generates multicomponent seismic data from elastic ODCIGs by applying a scattering condition, and the adjoint operator generates elastic ODCIGs from ERTM using a subsurface space-shift imaging condition. Compared with elastic ODCIGs extracted from ERTM, our method effectively improves the focusing of elastic ODCIGs to produce elastic ADCIGs with higher resolution, fewer artifacts, and improved amplitude coherency across different reflection angles. Several synthetic examples were used to validate the effectiveness of the method.

Multidirectional slowness vector for computing angle gathers from reverse time migration

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. S55-S68 ◽  
Author(s):  
Chen Tang ◽  
George A. McMechan
Keyword(s):  
Fourier Transforms ◽  
Grid Point ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Slowness Vector ◽  
Migration Velocity Analysis ◽  
Wavefield Decomposition ◽  
Complex Valued

Angle gathers are important for true-amplitude migration, migration velocity analysis, and angle-dependent inversion. Among existing methods, calculating the [Formula: see text] direction vector is efficient, but it can give only one direction per grid point and fails to give multiple directions for overlapping wavefields associated with multipaths and reflections. The slowness vectors (SVs) in [Formula: see text] and [Formula: see text] can be connected by Fourier transforms (FTs); the forward FT from [Formula: see text] to [Formula: see text] decomposes the wavefields into different vector components, and the inverse FT sums these components into a unique direction. Therefore, the SV has multiple directions in [Formula: see text], but it has only one direction in [Formula: see text]. Based on this relation, we have separated the computation of propagation direction into two steps: First, we used the forward FT, [Formula: see text] binning, and several inverse FTs to separate the wavefields into vector subsets with different approximate propagation angles, which contained much less wave overlapping; then, we computed [Formula: see text] SVs for each separated wavefield, and the set of these single-direction SVs constituted a multidirectional SV (MSV). In this process, the FTs between [Formula: see text] and [Formula: see text] domains required a large input/output (I/O) time. We prove the conjugate relation between the decomposition results using positive- and negative-frequency wavefields, and we use complex-valued modeling to obtain the positive-frequency wavefields. Thus, we did wavefield decomposition in [Formula: see text] instead of [Formula: see text], and avoided the huge I/O caused by the FT between the [Formula: see text] and [Formula: see text] domains. Our tests demonstrated that the MSV can give multiple directions for overlapping wavefields and improve the quality of angle gathers.

Plane-wave least-squares reverse time migration with a preconditioned stochastic conjugate gradient method

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. S33-S46 ◽  
Author(s):  
Chuang Li ◽  
Jianping Huang ◽  
Zhenchun Li ◽  
Rongrong Wang
Keyword(s):  
Plane Wave ◽  
Least Squares ◽  
Conjugate Gradient ◽  
Sampling Method ◽  
Singular Spectrum Analysis ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Numerical Tests ◽  
Time Migration

This study derives a preconditioned stochastic conjugate gradient (CG) method that combines stochastic optimization with singular spectrum analysis (SSA) denoising to improve the efficiency and image quality of plane-wave least-squares reverse time migration (PLSRTM). This method reduces the computational costs of PLSRTM by applying a controlled group-sampling method to a sufficiently large number of plane-wave sections and accelerates the convergence using a hybrid of stochastic descent (SD) iteration and CG iteration. However, the group sampling also produces aliasing artifacts in the migration results. We use SSA denoising as a preconditioner to remove the artifacts. Moreover, we implement the preconditioning on the take-off angle-domain common-image gathers (CIGs) for better results. We conduct numerical tests using the Marmousi model and Sigsbee2A salt model and compare the results of this method with those of the SD method and the CG method. The results demonstrate that our method efficiently eliminates the artifacts and produces high-quality images and CIGs.

An exact adjoint operation pair in time extrapolation and its application in least-squares reverse-time migration

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. H27-H33 ◽  
Author(s):  
Jun Ji
Keyword(s):  
Least Squares ◽  
Adjoint Operator ◽  
Synthetic Data ◽  
Forward Modeling ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Product Test ◽  
Least Squares Migration ◽  
Time Extrapolation

To reduce the migration artifacts arising from incomplete data or inaccurate operators instead of migrating data with the adjoint of the forward-modeling operator, a least-squares migration often is considered. Least-squares migration requires a forward-modeling operator and its adjoint. In a derivation of the mathematically correct adjoint operator to a given forward-time-extrapolation modeling operator, the exact adjoint of the derived operator is obtained by formulating an explicit matrix equation for the forward operation and transposing it. The programs that implement the exact adjoint operator pair are verified by the dot-product test. The derived exact adjoint operator turns out to differ from the conventional reverse-time-migration (RTM) operator, an implementation of wavefield extrapolation backward in time. Examples with synthetic data show that migration using the exact adjoint operator gives similar results for a conventional RTM operator and that least-squares RTM is quite successful in reducing most migration artifacts. The least-squares solution using the exact adjoint pair produces a model that fits the data better than one using a conventional RTM operator pair.

Reverse time migration of phase encoded all-order multiples

Geophysics ◽  
2021 ◽  
pp. 1-42
Author(s):  
Yike Liu ◽  
Yanbao Zhang ◽  
Yingcai Zheng
Keyword(s):  
Virtual Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Phase Encoding ◽  
Seismic Migration ◽  
Computational Costs ◽  
Time Migration ◽  
Source Data ◽  
Decomposition Strategies

Multiples follow long paths and carry more information on the subsurface than primary reflections, making them particularly useful for imaging. However, seismic migration using multiples can generate crosstalk artifacts in the resulting images because multiples of different orders interfere with each others, and crosstalk artifacts greatly degrade the quality of an image. We propose to form a supergather by applying phase-encoding functions to image multiples and stacking several encoded controlled-order multiples. The multiples are separated into different orders using multiple decomposition strategies. The method is referred to as the phase-encoded migration of all-order multiples (PEM). The new migration can be performed by applying only two finite-difference solutions to the wave equation. The solutions include backward-extrapolating the blended virtual receiver data and forward-propagating the summed virtual source data. The proposed approach can significantly attenuate crosstalk artifacts and also significantly reduce computational costs. Numerical examples demonstrate that the PEM can remove relatively strong crosstalk artifacts generated by multiples and is a promising approach for imaging subsurface targets.

Angle-domain common-image gathers from plane-wave least-squares reverse time migration

Geophysics ◽  
2021 ◽  
pp. 1-60
Author(s):  
Chuang Li ◽  
Zhaoqi Gao ◽  
Jinghuai Gao ◽  
Feipeng Li ◽  
Tao Yang
Keyword(s):  
Inverse Problem ◽  
Plane Wave ◽  
Least Squares ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
Amplitude Versus

Angle-domain common-image gathers (ADCIGs) that can be used for migration velocity analysis and amplitude versus angle analysis are important for seismic exploration. However, because of limited acquisition geometry and seismic frequency band, the ADCIGs extracted by reverse time migration (RTM) suffer from illumination gaps, migration artifacts, and low resolution. We have developed a reflection angle-domain pseudo-extended plane-wave least-squares RTM method for obtaining high-quality ADCIGs. We build the mapping relations between the ADCIGs and the plane-wave sections using an angle-domain pseudo-extended Born modeling operator and an adjoint operator, based on which we formulate the extraction of ADCIGs as an inverse problem. The inverse problem is iteratively solved by a preconditioned stochastic conjugate gradient method, allowing for reduction in computational cost by migrating only a subset instead of the whole dataset and improving image quality thanks to preconditioners. Numerical tests on synthetic and field data verify that the proposed method can compensate for illumination gaps, suppress migration artifacts, and improve resolution of the ADCIGs and the stacked images. Therefore, compared with RTM, the proposed method provides a more reliable input for migration velocity analysis and amplitude versus angle analysis. Moreover, it also provides much better stacked images for seismic interpretation.

Periodic plane-wave least-squares reverse time migration for diffractions

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. S185-S198
Author(s):  
Chuang Li ◽  
Jinghuai Gao ◽  
Zhaoqi Gao ◽  
Rongrong Wang ◽  
Tao Yang
Keyword(s):  
Inverse Problem ◽  
Image Quality ◽  
Plane Wave ◽  
Least Squares ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Diffraction Imaging ◽  
Periodic Plane

Diffraction imaging is important for high-resolution characterization of small subsurface heterogeneities. However, due to geometry limitations and noise distortion, conventional diffraction imaging methods may produce low-quality images. We have adopted a periodic plane-wave least-squares reverse time migration method for diffractions to improve the image quality of heterogeneities. The method reformulates diffraction imaging as an inverse problem using the Born modeling operator and its adjoint operator derived in the periodic plane-wave domain. The inverse problem is implemented for diffractions separated by a plane-wave destruction filter from the periodic plane-wave sections. Because the plane-wave destruction filter may fail to eliminate hyperbolic reflections and noise, we adopt a hyperbolic misfit function to minimize a weighted residual using an iteratively reweighted least-squares algorithm and thereby reduce residual reflections and noise. Synthetic and field data tests show that the adopted method can significantly improve the image quality of subsalt and deep heterogeneities. Compared with reverse time migration, it produces better images with fewer artifacts, higher resolution, and more balanced amplitude. Therefore, the adopted method can accurately characterize small heterogeneities and provide a reliable input for seismic interpretation in the prediction of hydrocarbon reservoirs.

scholarly journals Sparse Constrained Least-Squares Reverse Time Migration Based on Kirchhoff Approximation

2021 ◽  
Vol 9 ◽  
Author(s):  
Xu Hong-Qiao ◽  
Wang Xiao-Yi ◽  
Wang Chen-Yuan ◽  
Zhang Jiang-Jie
Keyword(s):  
Least Squares ◽  
Kirchhoff Approximation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
L1 Norm ◽  
Constrained Least Squares ◽  
Geological Structures ◽  
Numerical Examples ◽  
Time Migration ◽  
The Difference

Least-squares reverse time migration (LSRTM) is powerful for imaging complex geological structures. Most researches are based on Born modeling operator with the assumption of small perturbation. However, studies have shown that LSRTM based on Kirchhoff approximation performs better; in particular, it generates a more explicit reflected subsurface and fits large offset data well. Moreover, minimizing the difference between predicted and observed data in a least-squares sense leads to an average solution with relatively low quality. This study applies L1-norm regularization to LSRTM (L1-LSRTM) based on Kirchhoff approximation to compensate for the shortcomings of conventional LSRTM, which obtains a better reflectivity image and gets the residual and resolution in balance. Several numerical examples demonstrate that our method can effectively mitigate the deficiencies of conventional LSRTM and provide a higher resolution image profile.

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