Elastic reverse time migration using acoustic propagators

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. S399-S408 ◽  
Author(s):  
Yunyue Elita Li ◽  
Yue Du ◽  
Jizhong Yang ◽  
Arthur Cheng ◽  
Xinding Fang
Keyword(s):  
Wave Equations ◽  
Mode Conversion ◽  
Computational Cost ◽  
Body Waves ◽  
Constant Density ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Isotropic Constant ◽  
Time Migration

Elastic wave imaging has been a significant challenge in the exploration industry due to the complexities in wave physics and numerical implementation. We have separated the governing equations for P- and S-wave propagation without the assumptions of homogeneous Lamé parameters to capture the mode conversion between the two body waves in an isotropic, constant-density medium. The resulting set of two coupled second-order equations for P- and S-potentials clearly demonstrates that mode conversion only occurs at the discontinuities of the shear modulus. Applying the Born approximation to the new equations, we derive the PP, PS, SP, and SS imaging conditions from the first gradients of waveform matching objective functions. The resulting images are consistent with the physical perturbations of the elastic parameters, and, hence, they are automatically free of the polarity reversal artifacts in the converted images. When implementing elastic reverse time migration (RTM), we find that scalar wave equations can be used to back propagate the recorded P-potential, as well as individual components in the vector field of the S-potential. Compared with conventional elastic RTM, the proposed elastic RTM implementation using acoustic propagators not only simplifies the imaging condition, it but also reduces the computational cost and the artifacts in the images. We have determined the accuracy of our method using 2D and 3D numerical examples.

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.

Surface-offset gathers from elastic reverse time migration and velocity analysis

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. S47-S64
Author(s):  
Yang Zhao ◽  
Tao Liu ◽  
Xueyi Jia ◽  
Hongwei Liu ◽  
Zhiguang Xue ◽  
...  
Keyword(s):  
Velocity Ratio ◽  
Computational Cost ◽  
Cost Effective ◽  
Velocity Estimation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
The Common ◽  
Wave Decomposition

Angle-domain common-image gathers (ADCIGs) from elastic reverse time migration (ERTM) are valuable tools for seismic elastic velocity estimation. Traditional ADCIGs are based on the concept of common-offset domains, but common-shot domain implementations are often favored for computational cost considerations. Surface-offset gathers (SOGs) built from common-offset migration may serve as an alternative to the common-shot ADCIGs. We have developed a theoretical kinematic framework between these two domains, and we determined that the common SOG gives an alternative measurement of kinematic correctness in the presence of incorrect velocity. Specifically, we exploit analytical expressions for the image misposition between these two domains, with respect to the traveltime perturbation caused by velocity errors. Four formulations of the PP and PS residual moveout functions are derived and provide insightful information of the velocity error, angle, and PS velocity ratio contained in ERTM gathers. The analytical solutions are validated with homogeneous examples with a series of varied parameters. We found that the SOGs may perform in the way of simplicity and linearity as an alternative to the common-shot migration. To make a full comparison with ADCIGs, we have developed a cost-effective workflow of ERTM SOGs. A fast vector P- and S-wave decomposition can be obtained via spatial gradients at selected time steps. A selected ERTM imaging condition is then modified in which the migration is done by offset groups between each source and receiver pair for each P- and S-wave decomposition. Two synthetic (marine and land) examples are used to demonstrate the feasibility of our methods.

True-amplitude linearized waveform inversion with the quasi-elastic wave equation

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R827-R844 ◽  
Author(s):  
Zongcai Feng ◽  
Gerard Schuster
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Wave Equations ◽  
Waveform Inversion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Elastic Wave Equation ◽  
P Waves ◽  
Time Migration

We present a quasi-elastic wave equation as a function of the pressure variable, which can accurately model PP reflections with elastic amplitude variation with offset effects under the first-order Born approximation. The kinematic part of the quasi-elastic wave equation accurately models the propagation of P waves, whereas the virtual-source part, which models the amplitudes of reflections, is a function of the perturbations of density and Lamé parameters [Formula: see text] and [Formula: see text]. The quasi-elastic wave equation generates a scattering radiation pattern that is exactly the same as that for the elastic wave equation, and only requires the solution of two acoustic wave equations for each shot gather. This means that the quasi-elastic wave equation can be used for true-amplitude linearized waveform inversion (also known as least-squares reverse time migration) of elastic PP reflections, in which the corresponding misfit gradients are with respect to the perturbations of density and the P- and S-wave impedances. The perturbations of elastic parameters are iteratively updated by minimizing the [Formula: see text]-norm of the difference between the recorded PP reflections and the predicted pressure data modeled from the quasi-elastic wave equation. Numerical tests on synthetic and field data indicate that true-amplitude linearized waveform inversion using the quasi-elastic wave equation can account for the elastic PP amplitudes and provide a robust estimate of the perturbations of P- and S-wave impedances and, in some cases, the density. In addition, true-amplitude linearized waveform inversion provides images with a wider bandwidth and fewer artifacts because the PP amplitudes are accurately explained. We also determine the 2D scalar quasi-elastic wave equation for P-SV reflections and the 3D vector equation for PS reflections.

High-order finite-difference approximations to solve pseudoacoustic equations in 3D VTI media

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. T225-T235 ◽  
Author(s):  
Leandro Di Bartolo ◽  
Leandro Lopes ◽  
Luis Juracy Rangel Lemos
Keyword(s):  
Finite Difference ◽  
Wave Equations ◽  
Computational Cost ◽  
Transversely Isotropic ◽  
High Order ◽  
Staggered Grid ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Grid Scheme

Pseudoacoustic algorithms are very fast in comparison with full elastic ones for vertical transversely isotropic (VTI) modeling, so they are suitable for many applications, especially reverse time migration. Finite differences using simple grids are commonly used to solve pseudoacoustic equations. We have developed and implemented general high-order 3D pseudoacoustic transversely isotropic formulations. The focus is the development of staggered-grid finite-difference algorithms, known for their superior numerical properties. The staggered-grid schemes based on first-order velocity-stress wave equations are developed in detail as well as schemes based on direct application to second-order stress equations. This last case uses the recently presented equivalent staggered-grid theory, resulting in a staggered-grid scheme that overcomes the problem of large memory requirement. Two examples are presented: a 3D simulation and a prestack reverse time migration application, and we perform a numerical analysis regarding computational cost and precision. The errors of the new schemes are smaller than the existing nonstaggered-grid schemes. In comparison with existing staggered-grid schemes, they require 25% less memory and only have slightly greater computational cost.

Scalar and vector imaging based on wave mode decoupling for elastic reverse time migration in isotropic and transversely isotropic media

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. S383-S398 ◽  
Author(s):  
Chenlong Wang ◽  
Jiubing Cheng ◽  
Børge Arntsen
Keyword(s):  
Computational Cost ◽  
Transversely Isotropic ◽  
Polarity Reversal ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Wave Modes

Recording P- and S-wave modes acquires more information related to rock properties of the earth’s interior. Elastic migration, as a part of multicomponent seismic data processing, potentially offers a great improvement over conventional acoustic migration to create a spatial image of some medium properties. In the framework of elastic reverse time migration, we have developed new scalar and vector imaging conditions assisted by efficient polarization-based mode decoupling to avoid crosstalk among the different wave modes for isotropic and transversely isotropic media. For the scalar imaging, we corrected polarity reversal of zero-lag PS images using the local angular attributes on the fly of angle-domain imaging. For the vector imaging, we naturally used the polarization information in the decoupled single-mode vector fields to automatically avoid the polarity reversal and to estimate the local angular attributes for angle-domain imaging. Examples of increasing complexity in 2D and 3D cases found that the proposed approaches can be used to obtain a physically interpretable image and angle-domain common-image gather at an acceptable computational cost. Decoupling and imaging the 3D S-waves involves some complexity, which has not been addressed in the literature. For this reason, we also attempted at illustrating the physical contents of the two separated S-wave modes and their contribution to seismic full-wave imaging.

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.

scholarly journals An alternative formula for approximate extended Born inversion

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. S1-S8 ◽  
Author(s):  
Jie Hou ◽  
William W. Symes
Keyword(s):  
Computational Cost ◽  
Constant Density ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Approximate Inverse ◽  
Generalized Radon Transform ◽  
Time Migration ◽  
Alternative Formula ◽  
Approximate Inverses ◽  
Asymptotic Accuracy

Various modifications of reverse time migration (RTM) provide asymptotic inverses to the subsurface offset extended Born modeling operator for constant-density acoustics. These approximate inverses have the same quality (asymptotic accuracy) as do generalized Radon transform pseudoinverses, but they can be computed without any ray tracing whatsoever. We have developed an approximate inverse of this type whose additional computational cost, above that of subsurface offset extended RTM, is negligible.

Source-free converted-wave reverse time migration: Formulation and limitations

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. S17-S27 ◽  
Author(s):  
Yue Du ◽  
Yunyue Elita Li ◽  
Jizhong Yang ◽  
Arthur Cheng ◽  
Xinding Fang
Keyword(s):  
Wave Equations ◽  
Mode Conversion ◽  
Objective Functions ◽  
Source Information ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Converted Wave ◽  
Imaging Condition ◽  
Time Migration ◽  
Elastic Wave Equations

The source-free converted-wave (SFCW) reverse time migration is an alternative way to image the subsurface when the source information is missing or the overburden velocities are complex. However, it is challenging due to the lack of source-wavefield constraints. We have derived the SFCW imaging condition from the first gradients of waveform matching objective functions using a set of coupled P- and S-potential equations and small-perturbation approximations. We found that the images obtained from this SFCW imaging condition are second-order approximations to the shear-modulus perturbations. The images produced by the proposed imaging condition are free of the polarity reversal effects and have clear physical meanings. We also find that the acoustic wave equations can be used to back propagate the recorded P- and S-potentials, and the resulting images have the same kinematic accuracy and fewer unphysical mode-conversion artifacts than the SFCW images obtained by the elastic wave equations. Using multiple numerical examples, we determine the accuracy of our formulations, analyze the resolution and artifacts on the resulting images, and develop the limitations of the proposed method.

Vector-based elastic reverse time migration based on scalar imaging condition

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. S111-S127 ◽  
Author(s):  
Qizhen Du ◽  
ChengFeng Guo ◽  
Qiang Zhao ◽  
Xufei Gong ◽  
Chengxiang Wang ◽  
...  
Keyword(s):  
Alternative Methods ◽  
Polarity Reversal ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Converted Wave ◽  
Imaging Condition ◽  
Time Migration ◽  
Wavefield Separation ◽  
Wave Modes

The scalar images (PP, PS, SP, and SS) of elastic reverse time migration (ERTM) can be generated by applying an imaging condition as crosscorrelation of pure wave modes. In conventional ERTM, Helmholtz decomposition is commonly applied in wavefield separation, which leads to a polarity reversal problem in converted-wave images because of the opposite polarity distributions of the S-wavefields. Polarity reversal of the converted-wave image will cause destructive interference when stacking over multiple shots. Besides, in the 3D case, the curl calculation generates a vector S-wave, which makes it impossible to produce scalar PS, SP, and SS images with the crosscorrelation imaging condition. We evaluate a vector-based ERTM (VB-ERTM) method to address these problems. In VB-ERTM, an amplitude-preserved wavefield separation method based on decoupled elastic wave equation is exploited to obtain the pure wave modes. The output separated wavefields are both vectorial. To obtain the scalar images, the scalar imaging condition in which the scalar product of two vector wavefields with source-normalized illumination is exploited to produce scalar images instead of correlating Cartesian components or magnitude of the vector P- and S-wave modes. Compared with alternative methods for correcting the polarity reversal of PS and SP images, our ERTM solution is more stable and simple. Besides these four scalar images, the VB-ERTM method generates another PP-mode image by using the auxiliary stress wavefields. Several 2D and 3D numerical examples are evaluated to demonstrate the potential of our ERTM method.

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