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.

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.

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.

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.

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.

Least-squares reverse time migration via linearized waveform inversion using a Wasserstein metric

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. S411-S423
Author(s):  
Peng Yong ◽  
Jianping Huang ◽  
Zhenchun Li ◽  
Wenyuan Liao ◽  
Luping Qu
Keyword(s):  
Least Squares ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Gradient Algorithm ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wasserstein Metric ◽  
Time Migration ◽  
Imaging Results ◽  
Primal Dual

Least-squares reverse time migration (LSRTM), an effective tool for imaging the structures of the earth from seismograms, can be characterized as a linearized waveform inversion problem. We have investigated the performance of three minimization functionals as the [Formula: see text] norm, the hybrid [Formula: see text] norm, and the Wasserstein metric ([Formula: see text] metric) for LSRTM. The [Formula: see text] metric used in this study is based on the dynamic formulation of transport problems, and a primal-dual hybrid gradient algorithm is introduced to efficiently compute the [Formula: see text] metric between two seismograms. One-dimensional signal analysis has demonstrated that the [Formula: see text] metric behaves like the [Formula: see text] norm for two amplitude-varied signals. Unlike the [Formula: see text] norm, the [Formula: see text] metric does not suffer from the differentiability issue for null residuals. Numerical examples of the application of three misfit functions to LSRTM on synthetic data have demonstrated that, compared to the [Formula: see text] norm, the hybrid [Formula: see text] norm and [Formula: see text] metric can accelerate LSRTM and are less sensitive to non-Gaussian noise. For the field data application, the [Formula: see text] metric produces the most reliable imaging results. The hybrid [Formula: see text] norm requires tedious trial-and-error tests for the judicious threshold parameter selection. Hence, the more automatic [Formula: see text] metric is recommended as a robust alternative to the customary [Formula: see text] norm for time-domain LSRTM.

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.

3-D prestack migration in anisotropic media

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 79-90 ◽  
Author(s):  
Zhengxin Dong ◽  
George A. McMechan
Keyword(s):  
A Priori ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Anisotropic Media ◽  
P Wave ◽  
Common Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Prestack Migration ◽  
Time Migration

A three‐dimensional (3-D) prestack reverse‐time migration algorithm for common‐source P‐wave data from anisotropic media is developed and illustrated by application to synthetic data. Both extrapolation of the data and computation of the excitation‐time imaging condition are implemented using a second‐order finite‐ difference solution of the 3-D anisotropic scalar‐wave equation. Poorly focused, distorted images are obtained if data from anisotropic media are migrated using isotropic extrapolation; well focused, clear images are obtained using anisotropic extrapolation. A priori estimation of the 3-D anisotropic velocity distribution is required. Zones of anomalous, directionally dependent reflectivity associated with anisotropic fracture zones are detectable in both the 3-D common‐ source data and the corresponding migrated images.

Least-squares reverse time migration in TTI media using a pure qP-wave equation

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. S199-S216
Author(s):  
Xinru Mu ◽  
Jianping Huang ◽  
Jidong Yang ◽  
Xu Guo ◽  
Yundong Guo
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Seismic Imaging ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
The Matrix ◽  
The Stability

Anisotropy is a common phenomenon in subsurface strata and should be considered in seismic imaging and inversion. Seismic imaging in a vertical transversely isotropic (VTI) medium does not take into account the effects of the tilt angles, which can lead to degraded migrated images in areas with strong anisotropy. To correct such waveform distortion, reduce related image artifacts, and improve migration resolution, a tilted transversely isotropic (TTI) least-squares reverse time migration (LSRTM) method is presented. In the LSRTM, a pure qP-wave equation is used and solved with the finite-difference method. We have analyzed the stability condition for the pure qP-wave equation using the matrix method, which is used to ensure the stability of wave propagation in the TTI medium. Based on this wave equation, we derive a corresponding demigration (Born modeling) and adjoint migration operators to implement TTI LSRTM. Numerical tests on the synthetic data show the advantages of TTI LSRTM over VTI RTM and VTI LSRTM when the recorded data contain strong effects caused by large tilt angles. Our numerical experiments illustrate that the sensitivity of the adopted TTI LSRTM to the migration velocity errors is much higher than that to the anisotropic parameters (including epsilon, delta, and tilted angle parameters), and its sensitivity to the epsilon model and tilt angle is higher than that to the delta model.

Elastic inversion of near- and postcritical reflections using phase variation with angle

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. R149-R159 ◽  
Author(s):  
Xinfa Zhu ◽  
George A. McMechan
Keyword(s):  
Wave Velocity ◽  
Spherical Wave ◽  
Phase Variation ◽  
P Wave ◽  
Wide Angle ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Elastic Inversion

Near- and postcritical (wide-angle) reflections provide the potential for velocity and density inversion because of their large amplitudes and phase-shifted waveforms. We tested using phase variation with angle (PVA) data in addition to, or instead of, amplitude variation with angle (AVA) data for elastic inversion. Accurate PVA test data were generated using the reflectivity method. Two other forward modeling methods were also investigated, including plane-wave and spherical-wave reflection coefficients. For a two half-space model, linearized least squares was used to invert PVA and AVA data for the P-wave velocity, S-wave velocity, and the density of the lower space and the S-wave velocity of the upper space. Inversion tests showed the feasibility and robustness of PVA inversion. A reverse-time migration test demonstrated better preservation of PVA information than AVA information during wavefield propagation through a layered overburden. Phases of deeper reflections were less affected than amplitudes by the transmission losses, which makes the results of PVA inversion more accurate than AVA inversion in multilayered media. PVA brings useful information to the elastic inversion of wide-angle reflections.

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