SS: The Future of Seismic Imaging; Reverse Time Migration an Full Wavefield Inversion - Wave equation based model building and imaging in complex settings

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.

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Least-squares reverse time migration in TTI media using a pure qP-wave equation

Geophysics ◽

10.1190/geo2019-0320.1 ◽

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.

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3D angle gathers from reverse time migration

Geophysics ◽

10.1190/1.3536527 ◽

2011 ◽

Vol 76 (2) ◽

pp. S77-S92 ◽

Cited By ~ 175

Author(s):

Sheng Xu ◽

Yu Zhang ◽

Bing Tang

Keyword(s):

Wave Equation ◽

Model Building ◽

Velocity Model ◽

Azimuth Angle ◽

Three Dimensions ◽

Practical Implementation ◽

Reverse Time ◽

Reverse Time Migration ◽

Time Migration ◽

Reflection Angle

Common-image gathers are an important output of prestack depth migration. They provide information needed for velocity model building and amplitude and phase information for subsurface attribute interpretation. Conventionally, common-image gathers are computed using Kirchhoff migration on common-offset/azimuth data volumes. When geologic structures are complex and strong contrasts exist in the velocity model, the complicated wave behaviors will create migration artifacts in the image gathers. As long as the gather output traces are indexed by any surface attribute, such as source location, receiver location, or surface plane-wave direction, they suffer from the migration artifacts caused by multiple raypaths. These problems have been addressed in a significant amount of work, resulting in common-image gathers computed in the reflection angle domain, whose traces are indexed by the subsurface reflection angle and/or the subsurface azimuth angle. Most of these efforts have concentrated on Kirchhoff and one-way wave-equation migration methods. For reverse time migration, subsurface angle gathers can be produced using the same approach as that used for one-way wave-equation migration. However, these approaches need to be revisited when producing high-quality subsurface angle gathers in three dimensions (reflection angle/azimuth angle), especially for wide-azimuth data. We have developed a method for obtaining 3D subsurface reflection angle/azimuth angle common-image gathers specifically for the amplitude-preserved reverse time migration. The method builds image gathers with a high-dimensional convolution of wavefields in the wavenumber domain. We have found a windowed antileakage Fourier transform method that leads to an efficient and practical implementation. This approach has generated high-resolution angle-domain gathers on synthetic 2.5D data and 3D wide-azimuth real data.

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Seismic wave-equation demigration/migration

Geophysics ◽

10.1190/1.3380705 ◽

2010 ◽

Vol 75 (3) ◽

pp. S111-S119 ◽

Cited By ~ 4

Author(s):

Hervé Chauris ◽

Mondher Benjemaa

Keyword(s):

Wave Equation ◽

Source Term ◽

Model Building ◽

Synthetic Data ◽

Velocity Model ◽

Single Scattering ◽

Reverse Time ◽

Reverse Time Migration ◽

Velocity Models ◽

Time Migration

Reverse-time migration is a well-known method based on a single-scattering approximation; it is designed to obtain seismic images in the case of a complex subsurface. It can, however, be a very time-consuming task because the number of computations is directly proportional to the number of processed sources. In the context of velocity model-building, iterative approaches require that one derives a series of migrated sections for different velocity models. We propose to replace the summation over sources by a summation over depth offsets or time delays defined in the subsurface. For that, we have developed a new relationship between two migrated sections obtained for two different velocity models. Starting from one of the two images, we obtain a second section correctly and efficiently. For each time delay, we compute a generalized source term by extending the concept of exploding reflector to nonzero offset. We obtain the final migrated section by solving the same wave equation in the perturbed model with the modified source term. Our work included testing the methodology on 2D synthetic data sets, particularly when the initial and perturbed velocity models differ greatly.

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Numerical simulation of the acoustic wave equation by the method of reverse time migration

International Journal of Advanced Trends in Computer Science and Engineering ◽

10.30534/ijatcse/2020/189952020 ◽

2020 ◽

Vol 9 (5) ◽

pp. 8223-8227

Keyword(s):

Numerical Simulation ◽

Wave Equation ◽

Acoustic Wave ◽

Acoustic Wave Equation ◽

Reverse Time ◽

Reverse Time Migration ◽

Time Migration

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Depth-Extrapolation-Based True-Amplitude Full-Wave-Equation Migration from Topography

Applied Sciences ◽

10.3390/app11073010 ◽

2021 ◽

Vol 11 (7) ◽

pp. 3010

Author(s):

Hao Liu ◽

Xuewei Liu

Keyword(s):

Wave Equation ◽

Partial Derivative ◽

Model Experiment ◽

Surface Velocity ◽

Seismic Exploration ◽

Initial Condition ◽

Reverse Time ◽

Reverse Time Migration ◽

Full Wave ◽

Time Migration

The lack of an initial condition is one of the major challenges in full-wave-equation depth extrapolation. This initial condition is the vertical partial derivative of the surface wavefield and cannot be provided by the conventional seismic acquisition system. The traditional solution is to use the wavefield value of the surface to calculate the vertical partial derivative by assuming that the surface velocity is constant. However, for seismic exploration on land, the surface velocity is often not uniform. To solve this problem, we propose a new method for calculating the vertical partial derivative from the surface wavefield without making any assumptions about the surface conditions. Based on the calculated derivative, we implemented a depth-extrapolation-based full-wave-equation migration from topography using the direct downward continuation. We tested the imaging performance of our proposed method with several experiments. The results of the Marmousi model experiment show that our proposed method is superior to the conventional reverse time migration (RTM) algorithm in terms of imaging accuracy and amplitude-preserving performance at medium and deep depths. In the Canadian Foothills model experiment, we proved that our method can still accurately image complex structures and maintain amplitude under topographic scenario.

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