Q-compensated reverse-time migration

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. S77-S87 ◽  
Author(s):  
Tieyuan Zhu ◽  
Jerry M. Harris ◽  
Biondo Biondi
Keyword(s):  
Image Resolution ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Pass Filter ◽  
Low Pass Filter ◽  
High Attenuation ◽  
Phase Dispersion ◽  
Time Migration ◽  
Amplitude Attenuation ◽  
Attenuation And Dispersion

Reduced amplitude and distorted dispersion of seismic waves caused by attenuation, especially strong attenuation, always degrades the resolution of migrated images. To improve image resolution, we evaluated a methodology of compensating for attenuation ([Formula: see text]) effects in reverse-time migration ([Formula: see text]-RTM). The [Formula: see text]-RTM approach worked by mitigating the amplitude attenuation and phase dispersion effects in source and receiver wavefields. Source and receiver wavefields were extrapolated using a previously published time-domain viscoacoustic wave equation that offered separated amplitude attenuation and phase dispersion operators. In our [Formula: see text]-RTM implementation, therefore, attenuation- and dispersion-compensated operators were constructed by reversing the sign of attenuation operator and leaving the sign of dispersion operator unchanged, respectively. Further, we designed a low-pass filter for attenuation and dispersion operators to stabilize the compensating procedure. Finally, we tested the [Formula: see text]-RTM approach on a simple layer model and the more realistic BP gas chimney model. Numerical results demonstrated that the [Formula: see text]-RTM approach produced higher resolution images with improved amplitude and phase compared to the noncompensated RTM, particularly beneath high-attenuation zones.

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.

An efficient local operator-based Q-compensated reverse time migration algorithm with multistage optimization

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S249-S259 ◽  
Author(s):  
Tong Zhou ◽  
Wenyi Hu ◽  
Jieyuan Ning
Keyword(s):  
Seismic Attenuation ◽  
Depth Information ◽  
Frequency Noise ◽  
Processing Unit ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Time Migration ◽  
Imaging Results

Most existing [Formula: see text]-compensated reverse time migration ([Formula: see text]-RTM) algorithms are based on pseudospectral methods. Because of the global nature of pseudospectral operators, these methods are not ideal for efficient parallelization, implying that they may suffer from high computational cost and inefficient memory usage for large-scale industrial problems. In this work, we reported a novel [Formula: see text]-RTM algorithm — the multistage optimized [Formula: see text]-RTM method. This [Formula: see text]-RTM algorithm uses a finite-difference method to compensate the amplitude and the phase simultaneously by uniquely combining two techniques: (1) a negative [Formula: see text] method for amplitude compensation and (2) a multistage dispersion optimization technique for phase correction. To prevent high-frequency noise from growing exponentially and ruining the imaging results, we apply a finite impulse response low-pass filter using the Kaiser window. The theoretical analyses and numerical experiments demonstrate that this [Formula: see text]-RTM algorithm precisely recovers the decayed amplitude and corrects the distorted phase caused by seismic attenuation effects, and hence produces higher resolution subsurface images with the correct structural depth information. This new method performs best in the frequency range of 10–70 Hz. Compared with pseudospectral [Formula: see text]-RTM methods, this [Formula: see text]-RTM approach offers nearly identical imaging quality. Based on local numerical differential operators, this [Formula: see text]-RTM method is very suitable for parallel computing and graphic processing unit implementation, an important feature for large 3D seismic surveys.

Effective Q-compensated reverse time migration using new decoupled fractional Laplacian viscoacoustic wave equation

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. S57-S69 ◽  
Author(s):  
Qingqing Li ◽  
Li-Yun Fu ◽  
Hui Zhou ◽  
Wei Wei ◽  
Wanting Hou
Keyword(s):  
Wave Equation ◽  
Fractional Laplacian ◽  
Seismic Waves ◽  
Laplacian Operator ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Phase Dispersion ◽  
Time Migration ◽  
Dispersion Effects ◽  
Amplitude Attenuation

Seismic waves are attenuated and distorted during propagation because of the conversion of acoustic energy to heat energy. We focus on intrinsic attenuation, which is caused by [Formula: see text], which is the portion of energy lost during each cycle or wavelength. Amplitude attenuation can decrease the energy of the wavefields, and dispersion effects distort the phase of seismic waves. Attenuation and dispersion effects can reduce the resolution of image, and they can especially distort the real position of interfaces. On the basis of the viscoacoustic wave equation consisting of a single standard linear solid, we have derived a new viscoacoustic wave equation with decoupled amplitude attenuation and phase dispersion. Subsequently, we adopt a theoretical framework of viscoacoustic reverse time migration that can compensate the amplitude loss and the phase dispersion. Compared with the other variable fractional Laplacian viscoacoustic wave equations with decoupled amplitude attenuation and phase dispersion terms, the order of the Laplacian operator in our equation is a constant. The amplitude attenuation term is solved by pseudospectral method, and only one fast Fourier transform is required in each time step. The phase dispersion term can be computed using a finite-difference method. Numerical examples prove that our equation can accurately simulate the attenuation effects very well. Simulation of the new viscoacoustic equation indicates high efficiency because only one constant fractional Laplacian operator exists in this new viscoacoustic wave equation, which can reduce the number of inverse Fourier transforms to improve the computation efficiency of forward modeling and [Formula: see text]-compensated reverse time migration ([Formula: see text]-RTM). We tested the [Formula: see text]-RTM by using Marmousi and BP gas models and compared the [Formula: see text]-RTM images with those without compensation and attenuation (the reference image). [Formula: see text]-RTM results match well with the reference images. We also compared the field data migration images with and without compensation. Results demonstrate the accuracy and efficiency of the presented new viscoacoustic wave equation.

Improved seismic image by Q-compensated reverse time migration: Application to crosswell field data, west Texas

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. B61-B67 ◽  
Author(s):  
Tieyuan Zhu ◽  
Jerry M. Harris
Keyword(s):  
Image Resolution ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
High Frequencies ◽  
Time Migration ◽  
West Texas ◽  
Final Formula ◽  
Seismic Image ◽  
Internal Structures ◽  
Sonic Logs

To test the effectiveness of the [Formula: see text]-compensated reverse time migration ([Formula: see text]-RTM) method, we applied it to crosswell seismic data from western Texas. This crosswell field survey was aimed at determining the boundaries and even the internal features of the reservoir. In this area, the reservoir geologic body exhibits strong attenuation that reduces high frequencies more rapidly. Thus, conventional acoustic RTM produces a dimmed image (reduced amplitude and low resolution) of the reservoir area and structures underneath. In contrast, [Formula: see text]-RTM is able to compensate for the attenuation effects during imaging. The [Formula: see text] and [Formula: see text] profiles needed for [Formula: see text]-RTM were produced by joint traveltime and frequency shift tomography. Preprocessing of the data was carried out to reduce noise, remove tube waves, and to separate up- and downgoing wavefields. Along with recovered high wavenumbers, the final [Formula: see text]-RTM image provided many details about geologic layers and structures. The lateral and vertical extent and internal structures within the reservoir unit were clearly determined. These geologic features were also correlated to the velocity profile and sonic logs. We concluded that [Formula: see text]-RTM imaging practically improved the image resolution in attenuating geologic media.

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.

Reverse time migration via frequency-adaptive multiscale spatial grids

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. S41-S55 ◽  
Author(s):  
Yongchae Cho ◽  
Richard L. Gibson, Jr.
Keyword(s):  
Coarse Grid ◽  
Image Resolution ◽  
Imaging Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Fine Grid ◽  
Wave Modeling ◽  
Time Migration ◽  
Wave Solutions ◽  
Spatial Grid

Reverse time migration (RTM) is widely used because of its ability to recover complex geologic structures. However, RTM also has a drawback in that it requires significant computational cost. In RTM, wave modeling accounts for the largest part of the computing cost for calculating forward- and backward-propagated wavefields before applying an imaging condition. For this reason, we have applied a frequency-adaptive multiscale spatial grid to enhance the efficiency of the wave simulations. To implement wave modeling for different values of the spatial grid interval, we apply a model reduction technique, the generalized multiscale finite-element method (GMsFEM), which solves local spectral problems on a fine grid to simulate wave propagation on a coarser grid. We can enhance the speed of computation without sacrificing accuracy by using coarser grids for lower frequency waves, while applying a finer grid for higher frequency waves. In the proposed method, we can control the size of the coarse grid and level of heterogeneity of the wave solutions to tune the trade-off between speedup and accuracy. As we increase the expected level of complexity of the wave solutions, the GMsFEM wave modeling can capture more detailed features of waves. After computing the forward and backward wavefield on the coarse grid, we reproject the coarse wave solutions to the fine grid to construct the RTM gradient image. Although wave solutions are computed on a coarse grid, we still obtain the RTM images without reducing the image resolution by projecting coarse wave solutions to the fine grid. We determine the efficiency of the proposed imaging method using the Marmousi-2 model. We compare the RTM images using GMsFEM with a fixed coarse mesh and a multiple frequency-adaptive coarse meshes to indicate the image quality and computational speed of the new approach.

Viscoelastic reverse time migration with attenuation compensation

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. S61-S73 ◽  
Author(s):  
Tieyuan Zhu ◽  
Junzhe Sun
Keyword(s):  
Wave Propagation ◽  
Wave Attenuation ◽  
Time Derivative ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
High Attenuation ◽  
First Order ◽  
Time Migration ◽  
Seismic Images

We have developed a theory of viscoelastic reverse time migration (RTM). The main feature of viscoelastic RTM is a compensation for P- and S-wave attenuation effects in seismic images during migration. The forward modeling engine is based on a viscoelastic wave equation involving fractional Laplacians. Because of the decoupled attenuation property, wave propagation can be simulated in three scenarios, i.e., only the amplitude loss effect, only the phase dispersion effect, or both effects simultaneously. This separation brings practical flexibility to studying attenuation effects on wave propagation and imaging. The backward modeling operator is constructed by reversing the sign of first-order time derivative amplitude loss operators. Synthetic examples determine the ability of viscoelastic RTM to illuminate degraded areas and shadow zones caused by attenuation. Numerical experiments also reveal that [Formula: see text]-compensated imaging is noticeably more accurate in kinematics and dynamics than elastic imaging in the presence of high attenuation. Results from a synthetic 3D model determine the superiority of viscoelastic RTM over elastic RTM in imaging salt flanks and delineation of salt boundaries, which are dimmed in elastic images.

scholarly journals Least-squares reverse-time migration with sparsity constraints

2021 ◽  
Vol 18 (2) ◽  
pp. 304-316
Author(s):  
Di Wu ◽  
Yanghua Wang ◽  
Jingjie Cao ◽  
Nuno V da Silva ◽  
Gang Yao
Keyword(s):  
Side Effects ◽  
Least Squares ◽  
Synthetic Data ◽  
Image Resolution ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
L1 Norm ◽  
Constrained Least Squares ◽  
Time Migration ◽  
Sparsity Constraints

Abstract Least-squares reverse-time migration (RTM) works with an inverse operation, rather than an adjoint operation in a conventional RTM, and thus produces an image with a higher resolution and more balanced amplitude than the conventional RTM image. However, least-squares RTM introduces two side effects: sidelobes around reflectors and high-wavenumber migration artifacts. These side effects are caused mainly by the limited bandwidth of seismic data, the limited coverage of receiver arrays and the inaccuracy of the modeling kernel. To mitigate these side effects and to further boost resolution, we employed two sparsity constraints in the least-squares inversion operation, namely the Cauchy and L1-norm constraints. For solving the Cauchy-constrained least-squares RTM, we used a preconditioned nonlinear conjugate-gradient method. For solving the L1-norm constrained least-squares RTM, we modified the iterative soft thresholding method. While adopting these two solution methods, the Cauchy-constrained least-squares RTM converged faster than the L1-norm constrained least-squares RTM. Application examples with synthetic data and laboratory modeling data demonstrated that the constrained least-squares RTM methods can mitigate the side effects and promote image resolution.

Least-squares reverse time migration with an angle-dependent weighting factor

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S299-S310 ◽  
Author(s):  
Kai Yang ◽  
Jianfeng Zhang
Keyword(s):  
Least Squares ◽  
Step Length ◽  
Weighting Factor ◽  
Deep Part ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Pass Filter ◽  
Time Migration ◽  
L2 Norm ◽  
The Right

Least-squares reverse time migration (LSRTM) produces higher quality images than conventional RTM. However, directly using the standard gradient formula, the inverted images suffer from low-wavenumber noise. Using a simple high-pass filter on the gradient can alleviate the effect of the low-wavenumber noise. But, owing to the illumination issue, the amplitudes are not balanced and in the deep part they are often weak. These two issues can be mitigated by the iterative approach, but it needs more iterations. We introduced an angle-dependent weighting factor to weight the gradient of LSRTM to suppress the low-wavenumber noise and also to emphasize the gradient in the deep part. An optimal step length for the L2-norm objective function is also presented to scale the gradient to the right order. Two numerical examples performed with the data synthesized on the Sigsbee2A and Marmousi models indicate that when using this weighted gradient combined with the preconditioned [Formula: see text]-BFGS algorithm with the optimal step length, only a few iterations can achieve satisfying results.

scholarly journals One-step data-domain least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. R361-R368 ◽  
Author(s):  
Qiancheng Liu ◽  
Daniel Peter
Keyword(s):  
Least Squares ◽  
Wiener Filter ◽  
Real Data ◽  
Image Resolution ◽  
Inversion Algorithm ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Iterative Inversion ◽  
One Step

Least-squares reverse time migration (LSRTM) is an iterative inversion algorithm for estimating the broadband-wavenumber reflectivity model. Although it produces superior results compared with conventional reverse time migration (RTM), LSRTM is computationally expensive. We have developed a one-step LSRTM method by considering the demigrated and observed data to design a deblurring preconditioner in the data domain using the Wiener filter. For the Wiener filtering, we further use a stabilized division algorithm via the Taylor expansion. The preconditioned observed data are then remigrated to obtain a deblurred image. The total cost of this method is about two RTMs. Through synthetic and real data experiments, we see that one-step LSRTM is able to enhance image resolution and balance source illumination at low computational costs.

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