Reverse time adjoint migration

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. R401-R410
Author(s):  
Hongwei Liu ◽  
Almomin Ali ◽  
Yi Luo
Keyword(s):  
Wave Equations ◽  
Adjoint Operator ◽  
Velocity Model ◽  
Computer Algorithms ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
The Matrix ◽  
Time Marching ◽  
Backward Propagation

From a mathematical perspective, it is desirable to apply the adjoint operator for back propagating the receiver wavefield for migration of data residuals for inversion. For frequency-domain direct solvers, it is straightforward to apply the adjoint operator, whereas in most real applications of time-domain finite-difference (TDFD) stencils, the forward-propagation kernel function is reused for backward propagation for simplicity. However, when applying the exact adjoint operator, the migration result will be different, especially when strong variations exist in the velocity model. Actually, these three operators (forward, backward, and adjoint of the forward) can be expressed in matrix forms under the Born approximation for acoustic wave equations. These expressions linearly relate model perturbations to recorded seismic data. Every element in the matrices is well-defined, and all involved operations, such as the imaging condition and wavefield sampling, are included in the closed-form matrix expressions. These matrix expressions provide a platform for analyzing seismic modeling and inversion via mature linear algebra methodologies and provide clear strategies for developing computer algorithms. By analyzing the similarity of the matrix expressions, one can find that the time stepping approaches for all three operators are essentially the same. Based on this observation, a new time-marching stencil can be designed to realize the TDFD adjoint operator. Compared with traditional reverse time migration, the new method using the adjoint operator can provide better image quality, especially at sharp velocity boundaries.

Application of RTM 3D angle gathers to wide-azimuth data subsalt imaging

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB175-WB182 ◽  
Author(s):  
Yan Huang ◽  
Bing Bai ◽  
Haiyong Quan ◽  
Tony Huang ◽  
Sheng Xu ◽  
...  
Keyword(s):  
Model Updating ◽  
Velocity Model ◽  
Azimuth Angle ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Additional Information ◽  
Time Migration ◽  
Reflection Angle ◽  
Subsalt Imaging

The availability of wide-azimuth data and the use of reverse time migration (RTM) have dramatically increased the capabilities of imaging complex subsalt geology. With these improvements, the current obstacle for creating accurate subsalt images now lies in the velocity model. One of the challenges is to generate common image gathers that take full advantage of the additional information provided by wide-azimuth data and the additional accuracy provided by RTM for velocity model updating. A solution is to generate 3D angle domain common image gathers from RTM, which are indexed by subsurface reflection angle and subsurface azimuth angle. We apply these 3D angle gathers to subsalt tomography with the result that there were improvements in velocity updating with a wide-azimuth data set in the Gulf of Mexico.

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.

An exact adjoint operation pair in time extrapolation and its application in least-squares reverse-time migration

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. H27-H33 ◽  
Author(s):  
Jun Ji
Keyword(s):  
Least Squares ◽  
Adjoint Operator ◽  
Synthetic Data ◽  
Forward Modeling ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Product Test ◽  
Least Squares Migration ◽  
Time Extrapolation

To reduce the migration artifacts arising from incomplete data or inaccurate operators instead of migrating data with the adjoint of the forward-modeling operator, a least-squares migration often is considered. Least-squares migration requires a forward-modeling operator and its adjoint. In a derivation of the mathematically correct adjoint operator to a given forward-time-extrapolation modeling operator, the exact adjoint of the derived operator is obtained by formulating an explicit matrix equation for the forward operation and transposing it. The programs that implement the exact adjoint operator pair are verified by the dot-product test. The derived exact adjoint operator turns out to differ from the conventional reverse-time-migration (RTM) operator, an implementation of wavefield extrapolation backward in time. Examples with synthetic data show that migration using the exact adjoint operator gives similar results for a conventional RTM operator and that least-squares RTM is quite successful in reducing most migration artifacts. The least-squares solution using the exact adjoint pair produces a model that fits the data better than one using a conventional RTM operator pair.

Benefits of inserting salt stratification to detail velocity model prior to least-squares reverse-time migration

2021 ◽  
pp. 104469
Author(s):  
A. Maul ◽  
A. Bulcão ◽  
R.M. Dias ◽  
B. Pereira-Dias ◽  
L. Teixeira ◽  
...  
Keyword(s):  
Least Squares ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration

Improving input/output performance in 2D and 3D angle-domain common-image gathers from reverse time migration

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. S65-S77 ◽  
Author(s):  
Hu Jin ◽  
George A. McMechan ◽  
Bao Nguyen
Keyword(s):  
Velocity Model ◽  
Normal Direction ◽  
Propagation Direction ◽  
Input Output ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Step ◽  
Phase Gradient ◽  
Time Migration ◽  
2D And 3D

We have developed a new method of extracting angle-domain common-image gathers (ADCIGs) from prestack reverse time migration (RTM) that has minimal intermediate storage requirements. To include multipathing, we applied an imaging condition for prestack RTM that uses multiple excitation image times. Instead of saving the full-source snapshots at all time steps, we picked and saved only a few of the highest amplitude arrivals, and their corresponding excitation times, of the source wavefield at each grid point, and we crosscorrelated with the receiver wavefield. When extracting the ADCIGs from RTM, we calculated the source propagation direction from the gradient of the excitation times. The result was that the source time snapshots do not have to be saved or reconstructed during RTM or while extracting ADCIGs. We calculated the receiver propagation direction from Poynting vectors during the receiver extrapolation at each time step and the reflector normal direction by the phase-gradient method. With a new strategy that uses three direction vectors (the source and receiver propagation directions as well as the reflector normal direction), we provided more reliable ADCIGs that are free of low-wavenumber artifacts than any two of them do separately, when the migration velocity model was near to the correct velocity model. The 2D and 3D synthetic tests demonstrated the successful application of the new algorithms with acceptable accuracy, improved storage efficiency, and without an input/output bottleneck.

Depth migration by the Gaussian beam summation method

Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. S81-S93 ◽  
Author(s):  
Mikhail M. Popov ◽  
Nikolay M. Semtchenok ◽  
Peter M. Popov ◽  
Arie R. Verdel
Keyword(s):  
Wave Equation ◽  
Model Building ◽  
Velocity Structure ◽  
Velocity Model ◽  
Summation Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Depth Migration ◽  
Time Migration ◽  
Ray Methods

Seismic depth migration aims to produce an image of seismic reflection interfaces. Ray methods are suitable for subsurface target-oriented imaging and are less costly compared to two-way wave-equation-based migration, but break down in cases when a complex velocity structure gives rise to the appearance of caustics. Ray methods also have difficulties in correctly handling the different branches of the wavefront that result from wave propagation through a caustic. On the other hand, migration methods based on the two-way wave equation, referred to as reverse-time migration, are known to be capable of dealing with these problems. However, they are very expensive, especially in the 3D case. It can be prohibitive if many iterations are needed, such as for velocity-model building. Our method relies on the calculation of the Green functions for the classical wave equation by per-forming a summation of Gaussian beams for the direct and back-propagated wavefields. The subsurface image is obtained by cal-culating the coherence between the direct and backpropagated wavefields. To a large extent, our method combines the advantages of the high computational speed of ray-based migration with the high accuracy of reverse-time wave-equation migration because it can overcome problems with caustics, handle all arrivals, yield good images of steep flanks, and is readily extendible to target-oriented implementation. We have demonstrated the quality of our method with several state-of-the-art benchmark subsurface models, which have velocity variations up to a high degree of complexity. Our algorithm is especially suited for efficient imaging of selected subsurface subdomains, which is a large advantage particularly for 3D imaging and velocity-model refinement applications such as subsalt velocity-model improvement. Because our method is also capable of providing highly accurate migration results in structurally complex subsurface settings, we have also included the concept of true-amplitude imaging in our migration technique.

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.

scholarly journals Reconstructing the primary reflections in seismic data by Marchenko redatuming and convolutional interferometry

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. Q15-Q26 ◽  
Author(s):  
Giovanni Angelo Meles ◽  
Kees Wapenaar ◽  
Andrew Curtis
Keyword(s):  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Surface Reflection ◽  
Reflection Data ◽  
Reference Velocity ◽  
Time Migration ◽  
Recorded Data

State-of-the-art methods to image the earth’s subsurface using active-source seismic reflection data involve reverse time migration. This and other standard seismic processing methods such as velocity analysis provide best results only when all waves in the data set are primaries (waves reflected only once). A variety of methods are therefore deployed as processing to predict and remove multiples (waves reflected several times); however, accurate removal of those predicted multiples from the recorded data using adaptive subtraction techniques proves challenging, even in cases in which they can be predicted with reasonable accuracy. We present a new, alternative strategy to construct a parallel data set consisting only of primaries, which is calculated directly from recorded data. This obviates the need for multiple prediction and removal methods. Primaries are constructed by using convolutional interferometry to combine the first-arriving events of upgoing and direct-wave downgoing Green’s functions to virtual receivers in the subsurface. The required upgoing wavefields to virtual receivers are constructed by Marchenko redatuming. Crucially, this is possible without detailed models of the earth’s subsurface reflectivity structure: Similar to the most migration techniques, the method only requires surface reflection data and estimates of direct (nonreflected) arrivals between the virtual subsurface sources and the acquisition surface. We evaluate the method on a stratified synclinal model. It is shown to be particularly robust against errors in the reference velocity model used and to improve the migrated images substantially.

Elastic reverse time migration using acoustic propagators

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. S399-S408 ◽  
Author(s):  
Yunyue Elita Li ◽  
Yue Du ◽  
Jizhong Yang ◽  
Arthur Cheng ◽  
Xinding Fang
Keyword(s):  
Wave Equations ◽  
Mode Conversion ◽  
Computational Cost ◽  
Body Waves ◽  
Constant Density ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Isotropic Constant ◽  
Time Migration

Elastic wave imaging has been a significant challenge in the exploration industry due to the complexities in wave physics and numerical implementation. We have separated the governing equations for P- and S-wave propagation without the assumptions of homogeneous Lamé parameters to capture the mode conversion between the two body waves in an isotropic, constant-density medium. The resulting set of two coupled second-order equations for P- and S-potentials clearly demonstrates that mode conversion only occurs at the discontinuities of the shear modulus. Applying the Born approximation to the new equations, we derive the PP, PS, SP, and SS imaging conditions from the first gradients of waveform matching objective functions. The resulting images are consistent with the physical perturbations of the elastic parameters, and, hence, they are automatically free of the polarity reversal artifacts in the converted images. When implementing elastic reverse time migration (RTM), we find that scalar wave equations can be used to back propagate the recorded P-potential, as well as individual components in the vector field of the S-potential. Compared with conventional elastic RTM, the proposed elastic RTM implementation using acoustic propagators not only simplifies the imaging condition, it but also reduces the computational cost and the artifacts in the images. We have determined the accuracy of our method using 2D and 3D numerical examples.

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