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

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.

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.

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.

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.

A wavefield-separation-based elastic least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S279-S297 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Synthetic Data ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
S Waves ◽  
Numerical Tests ◽  
Time Migration

Elastic least-squares reverse time migration (ELSRTM) has the potential to provide improved subsurface reflectivity estimation. Compared with elastic RTM (ERTM), ELSRTM can produce images with higher spatial resolution, more balanced amplitudes, and fewer artifacts. However, the crosstalk between P- and S-waves can significantly degrade the imaging quality of ELSRTM. We have developed an ELSRTM method to suppress the crosstalk artifacts. This method includes three crucial points. The first is that the forward and backward wavefields are extrapolated based on the separated elastic velocity-stress equation of P- and S-waves. The second is that the separated vector P- and S-wave residuals are migrated to form reflectivity images of Lamé constants [Formula: see text] and [Formula: see text] independently. The third is that the reflectivity images of [Formula: see text] and [Formula: see text] are obtained by the vector P-wave wavefields achieved in the backward extrapolation of the separated vector P-wave residuals and the vector S-wave wavefields achieved in the backward extrapolation of the separated vector S-wave residuals, respectively. Numerical tests with synthetic data demonstrate that our ELSRTM method can produce images free of crosstalk artifacts. Compared with ELSRTM based on the coupled wavefields, our ELSRTM method has better convergence and higher accuracy.

scholarly journals Elastic least-squares reverse time migration

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. S143-S157 ◽  
Author(s):  
Zongcai Feng ◽  
Gerard T. Schuster
Keyword(s):  
Least Squares ◽  
Synthetic Data ◽  
Adjoint Equations ◽  
Accurate Estimation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Velocity Models ◽  
Time Migration ◽  
Wave Migration

We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTM solves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional least-squares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTM will produce migration noise stronger than that seen in the RTM images.

Elastic least-squares reverse time migration of steeply dipping structures using prismatic reflections

Geophysics ◽  
2022 ◽  
pp. 1-130
Author(s):  
Zheng Wu ◽  
Yuzhu Liu ◽  
Jizhong Yang
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Oil And Gas ◽  
Normal Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Multicomponent Seismic ◽  
Imaging Conditions

The migration of prismatic reflections can be used to delineate steeply dipping structures, which is crucial for oil and gas exploration and production. Elastic least-squares reverse time migration (ELSRTM), which considers the effects of elastic wave propagation, can be used to obtain reasonable subsurface reflectivity estimations and interpret multicomponent seismic data. In most cases, we can only obtain a smooth migration model. Thus, conventional ELSRTM, which is based on the first-order Born approximation, considers only primary reflections and cannot resolve steeply dipping structures. To address this issue, we develop an ELSRTM framework, called Pris-ELSRTM, which can jointly image primary and prismatic reflections in multicomponent seismic data. When Pris-ELSRTM is directly applied to multicomponent records, near-vertical structures can be resolved. However, the application of imaging conditions established for prismatic reflections to primary reflections destabilizes the process and leads to severe contamination of the results. Therefore, we further improve the Pris-ELSRTM framework by separating prismatic reflections from recorded multicomponent data. By removing artificial imaging conditions from the normal equation, primary and prismatic reflections can be imaged based on unique imaging conditions. The results of synthetic tests and field data applications demonstrate that the improved Pris-ELSRTM framework produces high-quality images of steeply dipping P- and S-wave velocity structures. However, it is difficult to delineate steep density structures because of the insensitivity of the density to prismatic reflections.

scholarly journals Elastic least-squares reverse time migration via linearized elastic full-waveform inversion with pseudo-Hessian preconditioning

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. S341-S358 ◽  
Author(s):  
Ke Chen ◽  
Mauricio D. Sacchi
Keyword(s):  
Least Squares ◽  
Waveform Inversion ◽  
Wave Impedance ◽  
Full Waveform Inversion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Full Waveform ◽  
Time Migration ◽  
Hessian Operator

Time-domain elastic least-squares reverse time migration (LSRTM) is formulated as a linearized elastic full-waveform inversion problem. The elastic Born approximation and elastic reverse time migration (RTM) operators are derived from the time-domain continuous adjoint-state method. Our approach defines P- and S-wave impedance perturbations as unknown elastic images. Our algorithm is obtained using continuous functional analysis in which the problem is discretized at the final stage (optimize-before-discretize approach). The discretized numerical versions of the elastic Born operator and its adjoint (elastic RTM operator) pass the dot-product test. The conjugate gradient least-squares method is used to solve the least-squares migration quadratic optimization problem. In other words, the Hessian operator for elastic LSRTM is implicitly inverted via a matrix-free algorithm that only requires the action of forward and adjoint operators on vectors. The diagonal of the pseudo-Hessian operator is used to design a preconditioning operator to accelerate the convergence of the elastic LSRTM. The elastic LSRTM provides higher resolution images with fewer artifacts and a superior balance of amplitudes when compared with elastic RTM. More important, elastic LSRTM can mitigate crosstalk between the P- and S-wave impedance perturbations given that the off-diagonal elements of the Hessian are attenuated via the inversion.

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