scholarly journals Least-Squares Reverse Time Migration Using the Gradient Preconditioning Based on Transmitted Wave Energy

2021 ◽  
Vol 9 ◽  
Author(s):  
Chuang Xie ◽  
Peng Song ◽  
Xishuang Li ◽  
Jun Tan ◽  
Shaowen Wang ◽  
...  
Keyword(s):  
Least Squares ◽  
Wave Energy ◽  
Hessian Matrix ◽  
Transmitted Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Reflected Waves ◽  
Time Migration ◽  
Acoustic Equation ◽  
And Storage

A gradient preconditioning approach based on transmitted wave energy for least-squares reverse time migration (LSRTM) is proposed in this study. The gradient is preconditioned by using the energy of “approximate transmission wavefield,” which is calculated based on the non-reflecting acoustic equation. The proposed method can effectively avoid a huge amount of calculation and storage required by the Hessian matrix or approximated Hessian matrix and can overcome the influence of reflected waves, multiples, and other wavefields on the gradient in gradient preconditioning based on seismic wave energy (GPSWE). The numerical experiments, compared with that using GPSWE, show that LSRTM using the gradient preconditioning based on transmitted wave energy (GPTWE) can significantly improve the imaging accuracy of deep target and accelerate the convergence rate without trivial increased calculation.

Least-squares reverse time migration method using the factorization of the Hessian matrix

2021 ◽  
Vol 18 (1) ◽  
pp. 94-100
Author(s):  
Sun Xiao-Dong ◽  
Teng Hou-Hua ◽  
Ren Li-Juan ◽  
Wang Wei-Qi ◽  
Li Zhen-Chun
Keyword(s):  
Least Squares ◽  
Hessian Matrix ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Method

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.

From acoustic to elastic inverse extended Born modeling: a first insight in the marine environment

Geophysics ◽  
2021 ◽  
pp. 1-73
Author(s):  
Milad Farshad ◽  
Hervé Chauris
Keyword(s):  
Least Squares ◽  
Marine Environment ◽  
Computational Cost ◽  
Physical Parameters ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Physical Density ◽  
Acoustic Approximation

Elastic least-squares reverse time migration is the state-of-the-art linear imaging technique to retrieve high-resolution quantitative subsurface images. A successful application requires many migration/modeling cycles. To accelerate the convergence rate, various pseudoinverse Born operators have been proposed, providing quantitative results within a single iteration, while having roughly the same computational cost as reverse time migration. However, these are based on the acoustic approximation, leading to possible inaccurate amplitude predictions as well as the ignorance of S-wave effects. To solve this problem, we extend the pseudoinverse Born operator from acoustic to elastic media to account for the elastic amplitudes of PP reflections and provide an estimate of physical density, P- and S-wave impedance models. We restrict the extension to marine environment, with the recording of pressure waves at the receiver positions. Firstly, we replace the acoustic Green's functions by their elastic version, without modifying the structure of the original pseudoinverse Born operator. We then apply a Radon transform to the results of the first step to calculate the angle-dependent response. Finally, we simultaneously invert for the physical parameters using a weighted least-squares method. Through numerical experiments, we first illustrate the consequences of acoustic approximation on elastic data, leading to inaccurate parameter inversion as well as to artificial reflector inclusion. Then we demonstrate that our method can simultaneously invert for elastic parameters in the presence of complex uncorrelated structures, inaccurate background models, and Gaussian noisy data.

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.

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.

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