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.

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.

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.

scholarly journals Q-compensated least-squares reverse time migration using low-rank one-step wave extrapolation

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. S271-S279 ◽  
Author(s):  
Junzhe Sun ◽  
Sergey Fomel ◽  
Tieyuan Zhu ◽  
Jingwei Hu
Keyword(s):  
Convergence Rate ◽  
Least Squares ◽  
Seismic Attenuation ◽  
Low Rank ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Attenuation Compensation ◽  
Time Migration ◽  
Rank One ◽  
One Step

Attenuation of seismic waves needs to be taken into account to improve the accuracy of seismic imaging. In viscoacoustic media, reverse time migration (RTM) can be performed with [Formula: see text]-compensation, which is also known as [Formula: see text]-RTM. Least-squares RTM (LSRTM) has also been shown to be able to compensate for attenuation through linearized inversion. However, seismic attenuation may significantly slow down the convergence rate of the least-squares iterative inversion process without proper preconditioning. We have found that incorporating attenuation compensation into LSRTM can improve the speed of convergence in attenuating media, obtaining high-quality images within the first few iterations. Based on the low-rank one-step seismic modeling operator in viscoacoustic media, we have derived its adjoint operator using nonstationary filtering theory. The proposed forward and adjoint operators can be efficiently applied to propagate viscoacoustic waves and to implement attenuation compensation. Recognizing that, in viscoacoustic media, the wave-equation Hessian may become ill-conditioned, we propose to precondition LSRTM with [Formula: see text]-compensated RTM. Numerical examples showed that the preconditioned [Formula: see text]-LSRTM method has a significantly faster convergence rate than LSRTM and thus is preferable for practical applications.

Preconditioned acoustic least-squares two-way wave-equation migration with exact adjoint operator

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. S1-S13 ◽  
Author(s):  
Linan Xu ◽  
Mauricio D. Sacchi
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Adjoint Operator ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Product Test ◽  
Dot Product ◽  
The Time Domain ◽  
Adjoint Operators

We have investigated the problem of designing the forward operator and its exact adjoint for two-way wave-equation least-squares migration. We study the problem in the time domain and pay particular attention to the individual operators that are required by the algorithm. We derive our algorithm using the language of linear algebra and establish a simple path to design forward and adjoint operators that pass the dot-product test. We also found that the exact adjoint operator is not equal to the classic reverse time migration algorithm. For instance, one must pay particular attention to boundary conditions to compute the exact adjoint that accurately passes the dot-product test. Forward and adjoint operators are adopted to solve the so-called least-squares reverse time migration problem via the method of conjugate gradients. We also examine a preconditioning strategy to invert extended images.

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

Elastic least-squares reverse time migration with hybrid l1/l2 misfit function

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. S271-S291 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Peng Yang ◽  
Wencai Xu ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Adjoint Equations ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Wave Image

We have developed the theory and synthetic tests of elastic least-squares reverse time migration (ELSRTM). In this method, a least-squares reverse time migration algorithm is used to image multicomponent seismic data based on the first-order elastic velocity-stress wave equation, in which the linearized elastic modeling equations are used for forward modeling and its adjoint equations are derived based on the adjoint-state method for back propagating the data residuals. Also, we have developed another ELSRTM scheme based on the wavefield separation technique, in which the P-wave image is obtained using P-wave forward and adjoint wavefields and the S-wave image is obtained using P-wave forward and S-wave adjoint wavefields. In this way, the crosstalk artifacts can be minimized to a significant extent. In general, seismic data inevitably contain noise. We apply the hybrid [Formula: see text] misfit function to the ELSRTM algorithm to improve the robustness of our ELSRTM to noise. Numerical tests on synthetic data reveal that our ELSRTM, when compared with elastic reverse time migration, can produce images with higher spatial resolution, more-balanced amplitudes, and fewer artifacts. Moreover, the hybrid [Formula: see text] misfit function makes the ELSRTM more robust than the [Formula: see text] misfit function in the presence of noise.

Estimating Subsurface P- and S-wave Reflectivities using Elastic TTI Least-Squares Reverse-Time Migration

2021 ◽  
Author(s):  
J. Yang ◽  
B. Hua ◽  
P. Williamson ◽  
H. Zhu ◽  
G. McMechan ◽  
...  
Keyword(s):  
Least Squares ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration

Elastic least-squares reverse time migration with density variations

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S533-S547 ◽  
Author(s):  
Minao Sun ◽  
Liangguo Dong ◽  
Jizhong Yang ◽  
Chao Huang ◽  
Yuzhu Liu
Keyword(s):  
Least Squares ◽  
Wave Velocity ◽  
Constant Density ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Velocity Images ◽  
Density Image ◽  
Elastic Impedance

Elastic least-squares reverse time migration (ELSRTM) is a powerful tool to retrieve high-resolution subsurface images of the earth’s interior. By minimizing the differences between synthetic and observed data, ELSRTM can improve spatial resolution and reduce migration artifacts. However, conventional ELSRTM methods usually assume constant density models, which cause inaccurate amplitude performance in resulting images. To partially remedy this problem, we have developed a new ELSRTM method that considers P- and S-wave velocity and density variations. Our method can simultaneously obtain P- and S-wave velocity and density images with enhanced amplitude fidelity and suppressed parameter crosstalk. In addition, it can provide subsurface elastic impedance images by summing the inverted velocity images with the density image. Compared with the conventional ELSRTM method, our method can improve the quality of final images and provide more accurate reflectivity estimates. Numerical experiments on a horizontal reflector model and a Marmousi-II model demonstrate the effectiveness of this method.

Sign in / Sign up

Export Citation Format

Share Document