Elastic least-squares reverse time migration based on decoupled wave equations

Geophysics ◽  
2021 ◽  
pp. 1-72
Author(s):  
Yu Zhong ◽  
Hanming Gu ◽  
Yangting Liu ◽  
QingHui Mao
Keyword(s):  
Least Squares ◽  
Wave Equations ◽  
Wave Mode ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Waves ◽  
Limited Bandwidth ◽  
Time Migration ◽  
Adjoint State ◽  
Isotropic Media

Elastic reverse time migration (ERTM) is developed for better characterization of complex structures by imaging multicomponent seismic data. However, conventional ERTM is subject to limitations such as finite recording aperture, limited bandwidth, and imperfect illumination. Elastic least-squares reverse time migration (ELSRTM) can improve imaging accuracy gradually with iterations by minimizing the residuals between observed and calculated multicomponent data. Conventional ELSRTM suffers from crosstalk artifacts caused by coupled elastic wavefields with different wave modes. Decomposing the coupled elastic wavefields into pure P- and S-waves is an effective method to suppress these crosstalk artifacts. Considering the trade-off between calculation accuracy and efficiency, we have developed a new ELSRTM scheme for isotropic media based on decoupled wave equations to suppress these wave mode-related crosstalk artifacts in the images of conventional ELSRTM. Pure wavefields are obtained by solving the decoupled wave equations using the finite-difference (FD) method in our new ELSRTM method. We also derive new decoupled adjoint-state wave equations, which are suitable for the elastic velocity-stress equations in isotropic media. We further propose the gradient equations based on pure wavefields to update the reflectivity images. Synthetic examples demonstrate that our new ELSRTM method can generate images that better represent the subsurface when compared with conventional ERTM and conventional ELSRTM.

Elastic least-squares reverse time migration using the energy norm

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S237-S248 ◽  
Author(s):  
Daniel Rocha ◽  
Paul Sava
Keyword(s):  
Least Squares ◽  
Normal Incidence ◽  
Wave Mode ◽  
Energy Norm ◽  
Earth Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Mode Decomposition ◽  
High Convergence Rate

Incorporating anisotropy and elasticity into least-squares migration is an important step toward recovering accurate amplitudes in seismic imaging. An efficient way to extract reflectivity information from anisotropic elastic wavefields exploits properties of the energy norm. We derive linearized modeling and migration operators based on the energy norm to perform anisotropic least-squares reverse time migration (LSRTM) describing subsurface reflectivity and correctly predicting observed data without costly decomposition of wave modes. Imaging operators based on the energy norm have no polarity reversal at normal incidence and remove backscattering artifacts caused by sharp interfaces in the earth model, thus accelerating convergence and generating images of higher quality when compared with images produced by conventional methods. With synthetic and field data experiments, we find that our elastic LSRTM method generates high-quality images that predict the data for arbitrary anisotropy, without the complexity of wave-mode decomposition and with a high convergence rate.

scholarly journals Attenuation compensation for least-squares reverse time migration using the viscoacoustic-wave equation

Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. S251-S262 ◽  
Author(s):  
Gaurav Dutta ◽  
Gerard T. Schuster
Keyword(s):  
Least Squares ◽  
Seismic Waves ◽  
Adjoint Equations ◽  
Inversion Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Adjoint State ◽  
Attenuation Models ◽  
Adjoint State Method

Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. Conventional acoustic reverse time migration (RTM) and least-squares reverse time migration (LSRTM) do not account for this distortion, which can lead to defocusing of migration images in highly attenuative geologic environments. To correct for this distortion, we used a linearized inversion method, denoted as [Formula: see text]-LSRTM. During the least-squares iterations, we used a linearized viscoacoustic modeling operator for forward modeling. The adjoint equations were derived using the adjoint-state method for back propagating the residual wavefields. The merit of this approach compared with conventional RTM and LSRTM was that [Formula: see text]-LSRTM compensated for the amplitude loss due to attenuation and could produce images with better balanced amplitudes and more resolution below highly attenuative layers. Numerical tests on synthetic and field data illustrated the advantages of [Formula: see text]-LSRTM over RTM and LSRTM when the recorded data had strong attenuation effects. Similar to standard LSRTM, the sensitivity tests for background velocity and [Formula: see text] errors revealed that the liability of this method is the requirement for smooth and accurate migration velocity and attenuation models.

Multidirectional-vector-based elastic reverse time migration and angle-domain common-image gathers with approximate wavefield decomposition of P- and S-waves

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. S57-S79 ◽  
Author(s):  
Chen Tang ◽  
George A. McMechan
Keyword(s):  
Wave Mode ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
S Waves ◽  
Time Migration ◽  
Mode Separation ◽  
Reflection Image ◽  
Wavefield Decomposition ◽  
Imaging Conditions

Elastic reverse time migration (E-RTM) has limitations when the migration velocities contain strong contrasts. First, the traditional scheme of P/S-wave mode separation is based on Helmholtz’s equations, which ignore the conversion between P- and S-waves at the current separation time. Thus, it contains an implicit assumption of the constant shear modulus and requires smoothing the heterogeneous model to approximately satisfy a locally constant condition. Second, the vector-based imaging condition needs to use the reflection-image normal, and it also cannot give the correct polarity of the PP image in all possible conditions. Third, the angle-domain common-image gathers (ADCIGs) calculated using the Poynting vectors (PVs) do not consider the wave interferences that happen at each reflector. Therefore, smooth models are often used for E-RTM. We relax this condition by proposing an improved data flow that involves three new contributions. The first contribution is an improved system of P/S-wave mode separation that considers the converted wave generated at the current time, and thus it does not require the constant-shear-modulus assumption. The second contribution is the new elastic imaging conditions based on multidirectional vectors; they can give the correct image polarity in all possible conditions without knowledge of the reflection-image normal. The third contribution is two methods to calculate multidirectional propagation vectors (PRVs) for RTM images and ADCIGs: One is the elastic multidirectional PV, and the other uses the sign of wavenumber-over-frequency ([Formula: see text]) ratio obtained from an amplitude-preserved approximate-propagation-angle-based wavefield decomposition to convert the particle velocities into multidirectional PRVs. The robustness of the improved data flow is determined by several 2D numerical examples. Extension of the schemes into 3D and amplitude-preserved imaging conditions is also possible.

Elastic least-squares reverse time migration in vertical transverse isotropic media

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S539-S553 ◽  
Author(s):  
Jidong Yang ◽  
Hejun Zhu ◽  
George McMechan ◽  
Houzhu Zhang ◽  
Yang Zhao
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Transversely Isotropic ◽  
Image Resolution ◽  
Total Variation Regularization ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Isotropic Media ◽  
Band Limited

Using adjoint-based elastic reverse time migration, it is difficult to produce high-quality reflectivity images due to the limited acquisition apertures, band-limited source time function, and irregular subsurface illumination. Through iteratively computing the Hessian inverse, least-squares migration enables us to reduce the point-spread-function effects and improve the image resolution and amplitude fidelity. By incorporating anisotropy in the 2D elastic wave equation, we have developed an elastic least-squares reverse time migration (LSRTM) method for multicomponent data from the vertically transversely isotropic (VTI) media. Using the perturbed stiffness parameters [Formula: see text] and [Formula: see text] as PP and PS reflectivities, we linearize the elastic VTI wave equation and obtain a Born modeling (demigration) operator. Then, we use the Lagrange multiplier method to derive the corresponding adjoint wave equation and reflectivity kernels. With linearized forward modeling and adjoint migration operators, we solve a linear inverse problem to estimate the subsurface reflectivity models for [Formula: see text] and [Formula: see text]. To reduce the artifacts caused by data over-fitting, we introduce total-variation regularization into the reflectivity inversion, which promotes a sparse solution in terms of the model derivatives. To accelerate the convergence of LSRTM, we use source illumination to approximate the diagonal Hessian and use it as a preconditioner for the misfit gradient. Numerical examples help us determine that our elastic VTI LSRTM method can improve the spatial resolution and amplitude fidelity in comparison to adjoint migration.

Pure qP-wave least-squares reverse time migration in vertically transverse isotropic media and its application to field data

2020 ◽  
Vol 17 (2) ◽  
pp. 208-220
Author(s):  
Jian-Ping Huang ◽  
Xin-Ru Mu ◽  
Zhen-Chun Li ◽  
Qing-Yang Li ◽  
Shuang-Qi Yuan ◽  
...  
Keyword(s):  
Least Squares ◽  
Field Data ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Isotropic Media ◽  
Transverse Isotropic

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 Reverse-Time Migration with Complex Topography

Energies ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7837
Author(s):  
Yu Zhong ◽  
Hanming Gu ◽  
Yangting Liu ◽  
Qinghui Mao
Keyword(s):  
Surface Topography ◽  
Seismic Data ◽  
Wave Equations ◽  
Oil And Gas ◽  
Complex Topography ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Waves ◽  
Time Migration ◽  
Multicomponent Seismic

Migration is an important step in seismic data processing for oil and gas exploration. The accuracy of migration directly affects the accuracy of subsequent oil and gas reservoir characterization. Reverse-time migration is one of the most accurate migration methods at present. Multi-wave and multicomponent seismic data contain more P- and S-wave information. Making full use of multi-wave and multicomponent seismic data can offer more information about underground structure and lithology, as well as improve the accuracy of seismic exploration. Elastic reverse-time migration (ERTM) has no dip restriction and can be applied to image multi-wave and multicomponent seismic data in complex structural areas and some special lithology structures. However, the surface topography of complex regions has an influence on wavefield and seriously degrades the quality of ERTM’s migration results. We developed a new ERTM method to migrate multi-wave and multicomponent seismic data in the region with complex surface topography. We first fill the layers between the highest and lowest undulating surface with near-surface elastic parameters in a complex topography model to obtain a new model with a horizontal surface. This allows the finite difference (FD) method based on the regular rectangular grid to be used to numerically solve elastic wave equations in the model with complex topography. The decoupled wave equations are used to generate source P- and S-waves and receiver P- and S-waves to reduce crosstalk artefacts in ERTM. A topography-related filter is further used to remove the influence of surface topography on migration results. The scalar imaging condition is also applied to generate PP and PS migration images. Some numerical examples with different complex topographies demonstrate that our proposed ERTM method can remove the influence of complex topography on ERTM’s images and effectively generate high-quality ERTM images.

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