Viscoacoustic reverse time migration using a time-domain complex-valued wave equation

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S505-S519 ◽  
Author(s):  
Jidong Yang ◽  
Hejun Zhu
Keyword(s):  
Wave Equation ◽  
Time Domain ◽  
Wave Equations ◽  
Seismic Wave Propagation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Reverse Wave ◽  
Time Migration ◽  
Complex Valued ◽  
Dispersion Term

During seismic wave propagation, intrinsic attenuation inside the earth gives rise to amplitude loss and phase dispersion. Without appropriate correction strategies in migration, these effects degrade the amplitudes and resolution of migrated images. Based on a new time-domain viscoacoustic wave equation, we have developed a viscoacoustic reverse time migration (RTM) approach to correct attenuation-associated dispersion and dissipation effects. A time-reverse wave equation is derived to extrapolate the receiver wavefields, in which the sign of the dissipation term is reversed, whereas the dispersion term remains unchanged. The difference between the forward and time-reverse wave equations is consistent with the physical insights of attenuation compensation during wavefield backpropagation. Due to the introduction of an imaginary unit in the dispersion term, the forward and time-reverse wave equations are complex valued. They are similar to the time-dependent Schrödinger equation, whose real and imaginary parts are coupled during wavefield extrapolation. The analytic property of the extrapolated source and receiver wavefields allows us to explicitly separate up- and downgoing waves. A causal imaging condition is implemented by crosscorrelating downgoing source and upgoing receiver wavefields to remove low-wavenumber artifacts in migrated images. Numerical examples demonstrate that our viscoacoustic RTM approach is capable of producing subsurface reflectivity images with correct spatial locations as well as amplitudes.

Viscoacoustic least-squares reverse time migration using a time-domain complex-valued wave equation

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. S479-S499 ◽  
Author(s):  
Jidong Yang ◽  
Hejun Zhu
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Time Domain ◽  
Inverse Operator ◽  
Total Variation Regularization ◽  
Imaging Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Complex Valued

With limited recording apertures, finite-frequency source functions, and irregular subsurface illuminations, traditional imaging methods have been insufficient to produce satisfactory reflectivity images with high resolution and amplitude fidelity. This is because most traditional imaging approaches are commonly formulated as the adjoint instead of the inverse operator with respect to the forward-modeling operator. In addition, intrinsic attenuation introduces amplitude loss and phase dispersion during wave propagation. Without considering these effects, migrated images might be kinematically and dynamically incorrect. We have developed a viscoacoustic least-squares reverse time migration (LSRTM) method based on a time-domain complex-valued wave equation. According to the Born approximation, we first linearized the viscoacoustic wave equation and derived a demigration operator. Then, using the complex-valued Lagrange multiplier method, we derived the adjoint viscoacoustic wave equation and corresponding sensitivity kernel. With the forward and adjoint operators, a linear inverse problem is formulated to estimate the subsurface reflectivity model. A total-variation regularization scheme is introduced to enhance the robustness of our viscoacoustic LSRTM, and a diagonal Hessian is used as the preconditioner to accelerate the convergence. Three synthetic examples are used to demonstrate that our approach enables us to compensate attenuation effects, improve imaging resolution, and enhance amplitude fidelity in comparison with the adjoint imaging method.

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.

An approach for attenuation-compensating multidimensional constant-Q viscoacoustic reverse time migration

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. S33-S46
Author(s):  
Ali Fathalian ◽  
Daniel O. Trad ◽  
Kristopher A. Innanen
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Velocity Model ◽  
Seismic Wave Propagation ◽  
Image Resolution ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Phase Dispersion ◽  
Time Migration ◽  
Amplitude Attenuation

Simulation of wave propagation in a constant-[Formula: see text] viscoacoustic medium is an important problem, for instance, within [Formula: see text]-compensated reverse time migration (RTM). Processes of attenuation and dispersion influence all aspects of seismic wave propagation, degrading the resolution of migrated images. To improve the image resolution, we have developed a new approach for the numerical solution of the viscoacoustic wave equation in the time domain and we developed an associated viscoacoustic RTM ([Formula: see text]-RTM) method. The main feature of the [Formula: see text]-RTM approach is compensation of attenuation effects in seismic images during migration by separation of amplitude attenuation and phase dispersion terms. Because of this separation, we are able to compensate the amplitude loss effect in isolation, the phase dispersion effect in isolation, or both effects concurrently. In the [Formula: see text]-RTM implementation, an attenuation-compensated operator is constructed by reversing the sign of the amplitude attenuation and a regularized viscoacoustic wave equation is invoked to eliminate high-frequency instabilities. The scheme is tested on a layered model and a modified acoustic Marmousi velocity model. We validate and examine the response of this approach by using it within an RTM scheme adjusted to compensate for attenuation. The amplitude loss in the wavefield at the source and receivers due to attenuation can be recovered by applying compensation operators on the measured receiver wavefield. Our 2D and 3D numerical tests focus on the amplitude recovery and resolution of the [Formula: see text]-RTM images as well as the interface locations. Improvements in all three of these features beneath highly attenuative layers are evident.

Attenuation compensation in anisotropic least-squares reverse time migration

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. S411-S423 ◽  
Author(s):  
Yingming Qu ◽  
Jianping Huang ◽  
Zhenchun Li ◽  
Zhe Guan ◽  
Jinli Li
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Homogeneous Model ◽  
Seismic Wave Propagation ◽  
Negative Influence ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wavenumber Domain ◽  
Time Migration ◽  
Numerical Noise

Anisotropic and attenuating properties of subsurface media cause amplitude loss and waveform distortion in seismic wave propagation, resulting in negative influence on seismic imaging. To correct the anisotropy effect and compensate amplitude attenuation, a compensated-amplitude vertical transverse isotropic (VTI) least-squares reverse time migration (LSRTM) method is adopted. In this method, the attenuation term of an attenuated acoustic wave equation is extended to a VTI quasi-differential wave equation, which takes care of effects from anisotropy and attenuation. The finite-difference method is used to solve the equation, in which attenuation terms are solved in the wavenumber domain, and other terms are solved in the space or wavenumber domain. Stable regularization operators are derived and introduced to the equations to eliminate severe numerical noise in high-frequency components during backward propagation. Meanwhile, a demigration operator, migration operator, and gradient formula for attenuated VTI media are derived to implement the amplitude-compensated VTI LSRTM. Test of a homogeneous model proves the accuracy of the attenuated VTI quasi-differential equations and the effectiveness of the regularization operators. A numerical example for a modified Marmousi model verifies the accuracy and superiority to the amplitude-compensated VTI LSRTM. Our results show that the sensitivity to anisotropic parameters is much higher than that to the [Formula: see text] parameters.

scholarly journals Depth-Extrapolation-Based True-Amplitude Full-Wave-Equation Migration from Topography

2021 ◽  
Vol 11 (7) ◽  
pp. 3010
Author(s):  
Hao Liu ◽  
Xuewei Liu
Keyword(s):  
Wave Equation ◽  
Partial Derivative ◽  
Model Experiment ◽  
Surface Velocity ◽  
Seismic Exploration ◽  
Initial Condition ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Full Wave ◽  
Time Migration

The lack of an initial condition is one of the major challenges in full-wave-equation depth extrapolation. This initial condition is the vertical partial derivative of the surface wavefield and cannot be provided by the conventional seismic acquisition system. The traditional solution is to use the wavefield value of the surface to calculate the vertical partial derivative by assuming that the surface velocity is constant. However, for seismic exploration on land, the surface velocity is often not uniform. To solve this problem, we propose a new method for calculating the vertical partial derivative from the surface wavefield without making any assumptions about the surface conditions. Based on the calculated derivative, we implemented a depth-extrapolation-based full-wave-equation migration from topography using the direct downward continuation. We tested the imaging performance of our proposed method with several experiments. The results of the Marmousi model experiment show that our proposed method is superior to the conventional reverse time migration (RTM) algorithm in terms of imaging accuracy and amplitude-preserving performance at medium and deep depths. In the Canadian Foothills model experiment, we proved that our method can still accurately image complex structures and maintain amplitude under topographic scenario.

Q least-squares reverse time migration based on the first-order viscoacoustic quasidifferential equations

Geophysics ◽  
2021 ◽  
pp. 1-65
Author(s):  
Yingming Qu ◽  
Yixin Wang ◽  
Zhenchun Li ◽  
Chang Liu
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Surface Topography ◽  
Density Perturbation ◽  
Second Order ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Time Migration ◽  
Grid Scheme

Seismic wave attenuation caused by subsurface viscoelasticity reduces the quality of migration and the reliability of interpretation. A variety of Q-compensated migration methods have been developed based on the second-order viscoacoustic quasidifferential equations. However, these second-order wave-equation-based methods are difficult to handle with density perturbation and surface topography. In addition, the staggered grid scheme, which has an advantage over the collocated grid scheme because of its reduced numerical dispersion and enhanced stability, works in first-order wave-equation-based methods. We have developed a Q least-squares reverse time migration method based on the first-order viscoacoustic quasidifferential equations by deriving Q-compensated forward-propagated operators, Q-compensated adjoint operators, and Q-attenuated Born modeling operators. Besides, our method using curvilinear grids is available even when the attenuating medium has surface topography and can conduct Q-compensated migration with density perturbation. The results of numerical tests on two synthetic and a field data sets indicate that our method improves the imaging quality with iterations and produces better imaging results with clearer structures, higher signal-to-noise ratio, higher resolution, and more balanced amplitude by correcting the energy loss and phase distortion caused by Q attenuation. It also suppresses the scattering and diffracted noise caused by the surface topography.

Fast plane-wave reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S549-S556 ◽  
Author(s):  
Xiongwen Wang ◽  
Xu Ji ◽  
Hongwei Liu ◽  
Yi Luo
Keyword(s):  
Time Delay ◽  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Time Domain ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wave Source ◽  
Computation Cost ◽  
Time Migration

Plane-wave reverse time migration (RTM) could potentially provide quick subsurface images by migrating fewer plane-wave gathers than shot gathers. However, the time delay between the first and the last excitation sources in the plane-wave source largely increases the computation cost and decreases the practical value of this method. Although the time delay problem is easily overcome by periodical phase shifting in the frequency domain for one-way wave-equation migration, it remains a challenge for time-domain RTM. We have developed a novel method, referred as to fast plane-wave RTM (FP-RTM), to eliminate unnecessary computation burden and significantly reduce the computational cost. In the proposed FP-RTM, we assume that the Green’s function has finite-length support; thus, the plane-wave source function and its responding data can be wrapped periodically in the time domain. The wrapping length is the assumed total duration length of Green’s function. We also determine that only two period plane-wave source and data after the wrapping process are required for generating the outcome with adequate accuracy. Although the computation time for one plane-wave gather is twice as long as a normal shot gather migration, a large amount of computation cost is saved because the total number of plane-wave gathers to be migrated is usually much less than the total number of shot gathers. Our FP-RTM can be used to rapidly generate RTM images and plane-wave domain common-image gathers for velocity model building. The synthetic and field data examples are evaluated to validate the efficiency and accuracy of our method.

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