Adjoint-based least-squares reverse time migration for viscoelastic media

2017 ◽  
Author(s):  
Peng Guo ◽  
George McMechan
Keyword(s):  
Least Squares ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Viscoelastic Media ◽  
Time Migration

Compensating Q effects in viscoelastic media by adjoint-based least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. S151-S172 ◽  
Author(s):  
Peng Guo ◽  
George A. McMechan
Keyword(s):  
Least Squares ◽  
Adjoint Operator ◽  
Seismic Attenuation ◽  
Quality Factors ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Viscoelastic Media ◽  
Time Migration ◽  
Attenuation Loss

Low values of P- and S-wave quality factors [Formula: see text] and [Formula: see text] result in strong intrinsic seismic attenuation in seismic modeling and imaging. We use a linearized waveform inversion approach, by generalizing least-squares reverse time migration (LSRTM) for viscoelastic media ([Formula: see text]-LSRTM), to compensate for the attenuation loss for P- and S-images. We use the first-order particle velocity, stress, and memory variable equations, with explicit [Formula: see text] in the formulations, based on the generalized standard linear solid, as the forward-modeling operator. The linearized two-way viscoelastic modeling operator is obtained with modulus perturbations introduced for the relaxed P- and S-moduli. The viscoelastic adjoint operator and the P- and S-imaging conditions for modulus perturbations are derived using the adjoint-state method and an augmented Lagrangian functional. [Formula: see text]-LSRTM solves the viscoelastic linearized modeling operator for generating synthetic data, and the adjoint operator is used for back propagating the data residual. With the correct background velocity model, and with the inclusion of [Formula: see text] in the modeling and imaging, [Formula: see text]-LSRTM is capable of iteratively updating the P- and S-modulus perturbations, and compensating the attenuation loss caused by [Formula: see text] and [Formula: see text], in the direction of minimizing the data residual between the observed and predicted data. Compared with elastic LSRTM results, the P- and S-modulus perturbation images from [Formula: see text]-LSRTM have stronger (closer to the true modulus perturbation), and more continuous, amplitudes for the structures in and beneath low-[Formula: see text] zones. The residuals in the image space obtained using the correctly parameterized [Formula: see text]-LSRTM are much smaller than those obtained using the incorrectly parameterized elastic LSRTM. However, the data residuals from [Formula: see text]-LSRTM and elastic LSRTM are similar because elastic Born modeling with a weak reflector in the image produces similar reflection amplitudes with viscoelastic Born modeling with a strong reflector.

Correlative least-squares reverse time migration in viscoelastic media

2021 ◽  
Vol 185 ◽  
pp. 104256
Author(s):  
Wei Zhang ◽  
Jinghuai Gao ◽  
Feipeng Li ◽  
Ying Shi ◽  
Xuan Ke
Keyword(s):  
Least Squares ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Viscoelastic Media ◽  
Time Migration

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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