Anisotropic elastic wavefield imaging using the energy norm

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. S225-S234 ◽  
Author(s):  
Daniel Rocha ◽  
Nicolay Tanushev ◽  
Paul Sava
Keyword(s):  
Transverse Isotropy ◽  
Wave Mode ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Migration ◽  
Mode Decomposition ◽  
Anisotropic Energy ◽  
Anisotropic Elastic ◽  
Arbitrary Anisotropy

Based on the energy conservation principle, we derive a scalar imaging condition for anisotropic elastic wavefield migration. Compared with conventional imaging conditions that correlate displacement components or potentials from source and receiver wavefields, the proposed imaging condition does not suffer from polarity reversal, which degrades the image quality after stacking over shots. Our imaging condition also accounts for the directionality of the wavefields in space and time, leading to the attenuation of backscattering artifacts, which commonly appear in elastic reverse time migration images in the presence of strong model contrasts. In addition, our new imaging condition does not require wave-mode decomposition, which demands significant additional cost for elastic wavefields in anisotropic media. To properly image structures, we rely on the anisotropy parameters used in migration, as one would do for any other imaging condition. Our imaging condition is suitable for arbitrary anisotropy. We show the successful application of the anisotropic energy imaging condition by performing numerical experiments on simple and complex geologic models. We compare its quality with conventional counterparts by simulating complex geologic settings with vertical or tilted transverse isotropy.

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.

Tilted transverse isotropic reverse time migration with angle gathers: Implementation and efficiency

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. S419-S432 ◽  
Author(s):  
Sean J. Delaney ◽  
Gareth S. O’Brien ◽  
Ruairi Short ◽  
Gilles Civario
Keyword(s):  
Transverse Isotropy ◽  
Dispersion Analysis ◽  
Staggered Grid ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Migration ◽  
Concurrent Communication ◽  
Software Implementations ◽  
Transverse Isotropic

We have developed a 3D reverse time migration (RTM) implementation, with an extended imaging condition, in the presence of tilted transverse isotropy (TTI), using finite-difference time-domain solvers on the rotated staggered grid (RSG) and the Lebedev grid. We have evaluated dispersion analysis of both schemes for a sample TTI medium. Using synthetic and real seismic data in realistic execution configurations, we found surprising inconsistency with quantitative cost estimates in the literature. For fixed accuracy, the RSG scheme proved most efficient in our tests, and not two to three times less efficient, as had been posited. Of course, variability may arise with particular medium properties, computer architectures, or software implementations. Having analyzed wavefield modeling performance in detail, we then quantified the realistic costs associated with the imaging condition in RTM, especially extended imaging conditions. For large extensions of the imaging condition, the associated cost dominates the total execution time and adds very significantly to the total cost of the migration. Our implementation targets both shared and distributed memory parallelism, making it suitable for general CPU clusters, nonuniform memory access architectures, and Intel Xeon-Phi. We have also discussed other aspects of our implementation in detail. In particular, we have explored an alternative method to achieve concurrent communication and computation in RTM.

Use of RTM full 3D subsurface angle gathers for subsalt velocity update and image optimization: Case study at Shenzi field

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB27-WB39 ◽  
Author(s):  
Zheng-Zheng Zhou ◽  
Michael Howard ◽  
Cheryl Mifflin
Keyword(s):  
Model Building ◽  
Transverse Isotropy ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Edge Diffraction ◽  
Time Migration ◽  
Image Optimization ◽  
Free Generation

Various reverse time migration (RTM) angle gather generation techniques have been developed to address poor subsalt data quality and multiarrival induced problems in gathers from Kirchhoff migration. But these techniques introduce new problems, such as inaccuracies in 2D subsurface angle gathers and edge diffraction artifacts in 3D subsurface angle gathers. The unique rich-azimuth data set acquired over the Shenzi field in the Gulf of Mexico enabled the generally artifact-free generation of 3D subsurface angle gathers. Using this data set, we carried out suprasalt tomography and salt model building steps and then produced 3D angle gathers to update the subsalt velocity. We used tilted transverse isotropy RTM with extended image condition to generate full 3D subsurface offset domain common image gathers, which were subsequently converted to 3D angle gathers. The angle gathers were substacked along the subsurface azimuth axis into azimuth sectors. Residual moveout analysis was carried out, and ray-based tomography was used to update velocities. The updated velocity model resulted in improved imaging of the subsalt section. We also applied residual moveout and selective stacking to 3D angle gathers from the final migration to produce an optimized stack image.

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.

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.

3D passive wavefield imaging using the energy norm

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. KS13-KS27 ◽  
Author(s):  
Daniel Rocha ◽  
Paul Sava ◽  
Jeffrey Shragge ◽  
Ben Witten
Keyword(s):  
Wave Mode ◽  
Source Location ◽  
Time Step ◽  
Elastic Wave Equation ◽  
Imaging Condition ◽  
Mode Decomposition ◽  
Passive Seismic ◽  
Anisotropic Elastic ◽  
Wavefield Extrapolation ◽  
Multicomponent Data

In passive seismic monitoring of microseismicity, full-wavefield imaging offers a robust approach for the estimation of source location and mechanism. With multicomponent data and the full 3D anisotropic elastic wave equation, the coexistence of P- and S-modes at the source location in time-reversal wavefield extrapolation allows the development of imaging conditions that identify the source position and radiation pattern. We have developed an imaging condition for passive wavefield imaging that is based on energy conservation and is related to the source mechanism. Similar to the correlation between the decomposed P- and S-wavefields — the most common imaging condition used in passive elastic wavefield imaging — our proposed imaging condition compares the different modes present in the displacement field producing a strong and focused correlation at the source location without costly wave-mode decomposition at each time step. Numerical experiments demonstrate the advantages of the proposed imaging condition (compared to PS correlation with decomposed wave modes), its sensitivity with respect to velocity inaccuracy, and its quality and efficacy in estimating the source location.

scholarly journals Application of the continuous wavelet transform in the extraction of directional data on RTM imaging condition wavefields

2018 ◽  
Vol 8 (2) ◽  
Author(s):  
Juan Guillermo Paniagua Castrillón ◽  
Olga Lucía Quintero- Montoya
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Low Frequency ◽  
Continuous Wavelet ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Model Quality ◽  
Directional Information ◽  
Imaging Condition ◽  
Time Migration

Low-frequency artifacts in reverse time migration result from unwanted cross-correlation of the source and receiver wavefields at non-reflecting points along ray-paths. These artifacts can hide important details in migrated models and increase poor interpretation risk. Some methods have been proposed to avoid or reduce the number of these artifacts, preserving reflections, and improving model quality, implementing other strategies such as modification of the wave equation, proposing other imaging conditions, and using image filtering techniques. One of these methods uses wavefield decomposition, correlating components of the wavefields that propagate in opposite directions. We propose a method for extracting directional information from the RTM imaging condition wavefields to obtain characteristics allowing for better, more refined imaging. The method works by separating directional information about the wavefields based on the continuous wavelet transform (CWT), and the analysis of the main changes on the frequency content revealed within the scalogram obtained by a Gaussian wavelet family. Through numerical applications, we demonstrate that this method can effectively remove undesired artifacts in migrated images. In addition, we use the Laguerre-Gauss filtering to improve the results obtained with the proposed method.

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