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.

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.

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.

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.

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.

Diffraction imaging for fault-karst structure by least-squares reverse time migration

2020 ◽  
pp. 1-40
Author(s):  
Xinru Mu ◽  
Jianping Huang ◽  
Liyun Fu ◽  
Shikai Jian ◽  
Bing Hu ◽  
...  
Keyword(s):  
Least Squares ◽  
Western China ◽  
Small Scale ◽  
Imaging Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Imaging Results ◽  
Heterogeneous Structures ◽  
Karst Reservoir

The fault-karst reservoir, which evolved from the deformation and karstification of carbonate rock, is one of the most important reservoir types in western China. Along the deep-seated fault zones, there are a lot widely spread and densely distributed fractures and vugs. The energy of the diffractions generated by heterogeneous structures, such as faults, fractures and vugs, are much weaker than that of the reflections produced by continuous formation interface. When using conventional full wavefield imaging method, the imaging results of continuous layers usually cover small-scale heterogeneities. Given that, we use plane-wave destruction (PWD) filter to separate the diffractions from the full data and image the separated diffractions using least-squares reverse time migration (LSRTM) method. We use several numerical examples to demonstrate that the newly developed diffractions LSRTM (D-LSRTM) can improve the definition of the heterogeneous structures, characterize the configuration and internal structure of the fault-karst structure well and enhance the interpretation accuracy for fault-karst reservoir.

Reverse Time Migration Using the Pseudospectral Time-Domain Algorithm

2016 ◽  
Vol 24 (02) ◽  
pp. 1650005 ◽  
Author(s):  
Jiangang Xie ◽  
Zichao Guo ◽  
Hai Liu ◽  
Qing Huo Liu
Keyword(s):  
Time Domain ◽  
Acoustic Waves ◽  
Fdtd Method ◽  
Pseudospectral Method ◽  
Imaging Method ◽  
Processing Unit ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Eighth Order ◽  
Time Migration

We propose a pre-stack reverse time migration (RTM) seismic imaging method using the pseudospectral time-domain (PSTD) algorithm. Traditional pseudospectral method uses the fast Fourier transform (FFT) algorithm to calculate the spatial derivatives, but is limited by the wraparound effect due to the periodicity assumed in the FFT. The PSTD algorithm combines the pseudospectral method with a perfectly matched layer (PML) for acoustic waves. PML is a highly effective absorbing boundary condition that can eliminate the wraparound effect. It enables a wide application of the pseudospectral method to complex models. RTM based on the PSTD algorithm has advantages in the computational efficiency compared to traditional methods such as the second-order and high order finite difference time-domain (FDTD) methods. In this work, we implement the PSTD algorithm for acoustic wave equation based RTM. By applying the PSTD-RTM method to various seismic models and comparing it with RTM based on the eighth-order FDTD method, we find that PSTD-RTM method has better performance and saves more than 50% memory. The method is suitable for parallel computation, and has been accelerated by general purpose graphics processing unit.

Sign in / Sign up

Export Citation Format

Share Document