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.

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.

First-order particle velocity equations of decoupled P- and S-wavefields and their application in elastic reverse time migration

Geophysics ◽  
2021 ◽  
pp. 1-78
Author(s):  
Zhiyuan Li ◽  
Youshan Liu ◽  
Guanghe Liang ◽  
Guoqiang Xue ◽  
Runjie Wang
Keyword(s):  
Particle Velocity ◽  
Computational Cost ◽  
Staggered Grid ◽  
Additional Stress ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Computational Accuracy ◽  
First Order ◽  
Time Migration ◽  
Stress Variable

The separation of P- and S-wavefields is considered to be an effective approach for eliminating wave-mode cross-talk in elastic reverse-time migration. At present, the Helmholtz decomposition method is widely used for isotropic media. However, it tends to change the amplitudes and phases of the separated wavefields compared with the original wavefields. Other methods used to obtain pure P- and S-wavefields include the application of the elastic wave equations of the decoupled wavefields. To achieve a high computational accuracy, staggered-grid finite-difference (FD) schemes are usually used to numerically solve the equations by introducing an additional stress variable. However, the computational cost of this method is high because a conventional hybrid wavefield (P- and S-wavefields are mixed together) simulation must be created before the P- and S-wavefields can be calculated. We developed the first-order particle velocity equations to reduce the computational cost. The equations can describe four types of particle velocity wavefields: the vector P-wavefield, the scalar P-wavefield, the vector S-wavefield, and the vector S-wavefield rotated in the direction of the curl factor. Without introducing the stress variable, only the four types of particle velocity variables are used to construct the staggered-grid FD schemes, so the computational cost is reduced. We also present an algorithm to calculate the P and S propagation vectors using the four particle velocities, which is simpler than the Poynting vector. Finally, we applied the velocity equations and propagation vectors to elastic reverse-time migration and angle-domain common-image gather computations. These numerical examples illustrate the efficiency of the proposed methods.

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.

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.

Reducing artifacts of elastic reverse time migration by the deprimary technique

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S569-S577 ◽  
Author(s):  
Yang Zhao ◽  
Houzhu Zhang ◽  
Jidong Yang ◽  
Tong Fei
Keyword(s):  
Complex Function ◽  
Noise Removal ◽  
Pure Mode ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Imaging Condition ◽  
Velocity Models ◽  
Time Migration ◽  
Wavefield Decomposition

Using the two-way elastic-wave equation, elastic reverse time migration (ERTM) is superior to acoustic RTM because ERTM can handle mode conversions and S-wave propagations in complex realistic subsurface. However, ERTM results may not only contain classical backscattering noises, but they may also suffer from false images associated with primary P- and S-wave reflections along their nonphysical paths. These false images are produced by specific wave paths in migration velocity models in the presence of sharp interfaces or strong velocity contrasts. We have addressed these issues explicitly by introducing a primary noise removal strategy into ERTM, in which the up- and downgoing waves are efficiently separated from the pure-mode vector P- and S-wavefields during source- and receiver-side wavefield extrapolation. Specifically, we investigate a new method of vector wavefield decomposition, which allows us to produce the same phases and amplitudes for the separated P- and S-wavefields as those of the input elastic wavefields. A complex function involved with the Hilbert transform is used in up- and downgoing wavefield decomposition. Our approach is cost effective and avoids the large storage of wavefield snapshots that is required by the conventional wavefield separation technique. A modified dot-product imaging condition is proposed to produce multicomponent PP-, PS-, SP-, and SS-images. We apply our imaging condition to two synthetic models, and we demonstrate the improvement on the image quality of ERTM.

Imaging conditions for elastic reverse time migration

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. S95-S111 ◽  
Author(s):  
Wei Zhang ◽  
Ying Shi
Keyword(s):  
Decomposition Method ◽  
Inner Product ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Imaging Condition ◽  
Subsurface Structures ◽  
Time Migration ◽  
Imaging Conditions ◽  
Wave Modes

Elastic reverse time migration (RTM) has the ability to retrieve accurately migrated images of complex subsurface structures by imaging the multicomponent seismic data. However, the imaging condition applied in elastic RTM significantly influences the quality of the migrated images. We evaluated three kinds of imaging conditions in elastic RTM. The first kind of imaging condition involves the crosscorrelation between the Cartesian components of the particle-velocity wavefields to yield migrated images of subsurface structures. An alternative crosscorrelation imaging condition between the separated pure wave modes obtained by a Helmholtz-like decomposition method could produce reflectivity images with explicit physical meaning and fewer crosstalk artifacts. A drawback of this approach, though, was that the polarity reversal of the separated S-wave could cause destructive interference in the converted-wave image after stacking over multiple shots. Unlike the conventional decomposition method, the elastic wavefields can also be decomposed in the vector domain using the decoupled elastic wave equation, which preserves the amplitude and phase information of the original elastic wavefields. We have developed an inner-product imaging condition to match the vector-separated P- and S-wave modes to obtain scalar reflectivity images of the subsurface. Moreover, an auxiliary P-wave stress image can supplement the elastic imaging. Using synthetic examples with a layered model, the Marmousi 2 model, and a fault model, we determined that the inner-product imaging condition has prominent advantages over the other two imaging conditions and generates images with preserved amplitude and phase attributes.

scholarly journals Imaging of first-order surface-related multiples by reverse-time migration

2016 ◽  
Vol 208 (2) ◽  
pp. 1077-1087 ◽  
Author(s):  
Xuejian Liu ◽  
Yike Liu ◽  
Hao Hu ◽  
Peng Li ◽  
Majid Khan
Keyword(s):  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Time Migration ◽  
Order Surface

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.

Data-driven synthesis of primary plane-wave responses

2020 ◽  
Author(s):  
Giovanni Angelo Meles ◽  
Lele Zhang ◽  
Jan Thorbecke ◽  
Kees Wapenaar ◽  
Evert Slob
Keyword(s):  
Plane Wave ◽  
Point Sources ◽  
Data Driven ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wave Source ◽  
Time Migration ◽  
Source Data ◽  
Marine Data ◽  
Seismic Images

<p>Seismic images provided by standard Reverse Time Migration are usually contaminated by artefacts associated with the migration of multiples.</p><p>Multiples can corrupt seismic images by producing both false negatives, i.e. by destructively interfering with primaries, and false positives, i.e. by focusing energy at unphysical interfaces. Free-surface multiples particularly affect seismic images resulting from marine data, while internal multiples strongly contaminate both land and marine data. Multiple prediction / primary synthesis methods are usually designed to operate on point source gathers, and can therefore be computationally  demanding when large problems, involving hundreds of gathers, are considered.</p><p>In this contribution, a new scheme for fully data-driven retrieval of primary responses of plane-wave sources is presented. The proposed scheme, based on convolutions and cross-correlations of the reflection response with itself,  extends a recently devised Marchenko point-sources primary retrieval method for to plane-wave source data. As a result, the presented algorithm allows fully data-driven synthesis of primary reflections associated with plane-wave source data. Once primary plane-wave responses are estimated, they are used for multiple-free imaging via standard reverse time migration. Numerical tests of increasing complexity demonstrate the potential of the proposed algorithm to produce multiple-free images only involving the migration of few datasets.</p><p>The plane-wave source primary synthesis algorithm discussed in this contribution could then be used as an initial and unexpensive processing step, potentially guiding more expensive target imaging techniques. Moreover, the method could be applied to large 3D problems for which standard methods are prohibitively expensive from a computational point of view.</p>

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