Implementation of prestack reverse time migration using frequency-domain extrapolation

Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. S61-S72 ◽  
Author(s):  
Kun Xu ◽  
Bing Zhou ◽  
George A. McMechan
Keyword(s):  
Frequency Domain ◽  
Synthetic Data ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Disk Storage ◽  
Time Migration ◽  
Seismic Experiment ◽  
Excitation Time ◽  
Parallel Iterative ◽  
Wavefield Extrapolation

We implement prestack reverse time migration (RTM) using frequency-domain extrapolation. We assume the observed data are the scattered field from the seismic experiment; then we time reverse them and derive the corresponding multipoint virtual sources to place along the receiver line rather than treat them as boundary conditions, which are common in time-domain reverse time migration (TRTM). Because the number of virtual sources is equal to the number of independent true sources in prestack frequency-domain reverse-time migration (FRTM), wavefield extrapolation is efficient in the frequency domain using a direct lower/upper (LU) triangular solver for 2D solutions and is still feasible using a parallel iterative or hybrid direct/iterative solver for 3D solutions. Each frequency implicitly contains information for all times, so we can implement the excitation-time and crosscorrelation imaging conditions straightforwardly without disk storage or input/output (I/O). Comparing costs, prestack shot-record FRTM is competitive with prestack shot-record TRTM. In our tests, prestack acoustic-wave FRTM accurately recovers the correct images of subsurface reflectors using 2D synthetic data.

An implicit stabilization strategy for Q-compensated reverse time migration

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. S169-S183
Author(s):  
Hanming Chen ◽  
Hui Zhou ◽  
Ying Rao
Keyword(s):  
Robust Stabilization ◽  
Synthetic Data ◽  
Frequency Noise ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Time Migration ◽  
Wavefield Extrapolation ◽  
Amplitude Compensation ◽  
Seismic Images

Reverse time migration with [Formula: see text] compensation ([Formula: see text]-RTM) is an effective approach to enhance the resolution of seismic images because it retrieves the amplitude loss and phase distortion induced by the viscosity of media. According to the crosscorrelation imaging condition, [Formula: see text]-RTM requires compensation for the amplitude loss in the propagation paths of source and receiver wavefields, which can be realized by solving an amplitude-boosted wave equation. However, the amplitude-boosted simulations suffer from numerical instability due to the amplification of high-frequency noise. We have developed a robust stabilization strategy for [Formula: see text]-RTM by incorporating a time-variant filter into the amplitude-boosted wavefield extrapolation step. We modify the Fourier spectrum of the operator that controls the amplitude compensation to be time variant, and we add to the spectrum a stabilization factor. Doing so, we integrate the time-variant filter into the viscoacoustic wave propagator implicitly, and we avoid any explicit filtering operation in [Formula: see text]-RTM. We verify the robustness of this stabilized [Formula: see text]-RTM with two synthetic data examples. We also apply this technique to a field data set to demonstrate the imaging improvements compared to an acoustic RTM and a more traditional [Formula: see text]-RTM method.

Reverse time migration in tilted transversely isotropic media

2020 ◽  
Vol 38 (2) ◽  
Author(s):  
Razec Cezar Sampaio Pinto da Silva Torres ◽  
Leandro Di Bartolo
Keyword(s):  
Seismic Anisotropy ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Computer Clusters ◽  
Time Migration ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Tti Media

ABSTRACT. Reverse time migration (RTM) is one of the most powerful methods used to generate images of the subsurface. The RTM was proposed in the early 1980s, but only recently it has been routinely used in exploratory projects involving complex geology – Brazilian pre-salt, for example. Because the method uses the two-way wave equation, RTM is able to correctly image any kind of geological environment (simple or complex), including those with anisotropy. On the other hand, RTM is computationally expensive and requires the use of computer clusters. This paper proposes to investigate the influence of anisotropy on seismic imaging through the application of RTM for tilted transversely isotropic (TTI) media in pre-stack synthetic data. This work presents in detail how to implement RTM for TTI media, addressing the main issues and specific details, e.g., the computational resources required. A couple of simple models results are presented, including the application to a BP TTI 2007 benchmark model.Keywords: finite differences, wave numerical modeling, seismic anisotropy. Migração reversa no tempo em meios transversalmente isotrópicos inclinadosRESUMO. A migração reversa no tempo (RTM) é um dos mais poderosos métodos utilizados para gerar imagens da subsuperfície. A RTM foi proposta no início da década de 80, mas apenas recentemente tem sido rotineiramente utilizada em projetos exploratórios envolvendo geologia complexa, em especial no pré-sal brasileiro. Por ser um método que utiliza a equação completa da onda, qualquer configuração do meio geológico pode ser corretamente tratada, em especial na presença de anisotropia. Por outro lado, a RTM é dispendiosa computacionalmente e requer o uso de clusters de computadores por parte da indústria. Este artigo apresenta em detalhes uma implementação da RTM para meios transversalmente isotrópicos inclinados (TTI), abordando as principais dificuldades na sua implementação, além dos recursos computacionais exigidos. O algoritmo desenvolvido é aplicado a casos simples e a um benchmark padrão, conhecido como BP TTI 2007.Palavras-chave: diferenças finitas, modelagem numérica de ondas, anisotropia sísmica.

Reverse time migration

Geophysics ◽  
1983 ◽  
Vol 48 (11) ◽  
pp. 1514-1524 ◽  
Author(s):  
Edip Baysal ◽  
Dan D. Kosloff ◽  
John W. C. Sherwood
Keyword(s):  
Wave Amplitude ◽  
Synthetic Data ◽  
Data Sets ◽  
Field Observations ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Method ◽  
Zero Offset ◽  
Time Extrapolation

Migration of stacked or zero‐offset sections is based on deriving the wave amplitude in space from wave field observations at the surface. Conventionally this calculation has been carried out through a depth extrapolation. We examine the alternative of carrying out the migration through a reverse time extrapolation. This approach may offer improvements over existing migration methods, especially in cases of steeply dipping structures with strong velocity contrasts. This migration method is tested using appropriate synthetic data sets.

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.

Least-squares reverse time migration via linearized waveform inversion using a Wasserstein metric

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. S411-S423
Author(s):  
Peng Yong ◽  
Jianping Huang ◽  
Zhenchun Li ◽  
Wenyuan Liao ◽  
Luping Qu
Keyword(s):  
Least Squares ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Gradient Algorithm ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wasserstein Metric ◽  
Time Migration ◽  
Imaging Results ◽  
Primal Dual

Least-squares reverse time migration (LSRTM), an effective tool for imaging the structures of the earth from seismograms, can be characterized as a linearized waveform inversion problem. We have investigated the performance of three minimization functionals as the [Formula: see text] norm, the hybrid [Formula: see text] norm, and the Wasserstein metric ([Formula: see text] metric) for LSRTM. The [Formula: see text] metric used in this study is based on the dynamic formulation of transport problems, and a primal-dual hybrid gradient algorithm is introduced to efficiently compute the [Formula: see text] metric between two seismograms. One-dimensional signal analysis has demonstrated that the [Formula: see text] metric behaves like the [Formula: see text] norm for two amplitude-varied signals. Unlike the [Formula: see text] norm, the [Formula: see text] metric does not suffer from the differentiability issue for null residuals. Numerical examples of the application of three misfit functions to LSRTM on synthetic data have demonstrated that, compared to the [Formula: see text] norm, the hybrid [Formula: see text] norm and [Formula: see text] metric can accelerate LSRTM and are less sensitive to non-Gaussian noise. For the field data application, the [Formula: see text] metric produces the most reliable imaging results. The hybrid [Formula: see text] norm requires tedious trial-and-error tests for the judicious threshold parameter selection. Hence, the more automatic [Formula: see text] metric is recommended as a robust alternative to the customary [Formula: see text] norm for time-domain LSRTM.

An efficient vector elastic reverse time migration method in the hybrid time and frequency domain for anisotropic media

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S511-S522 ◽  
Author(s):  
Kai Gao ◽  
Lianjie Huang
Keyword(s):  
Frequency Domain ◽  
Anisotropic Media ◽  
Reverse Time ◽  
Computationally Efficient ◽  
Reverse Time Migration ◽  
Computational Costs ◽  
Time Migration ◽  
Migration Imaging ◽  
Efficient Vector ◽  
Wave Migration

Vector elastic reverse time migration (ERTM) produces subsurface elastic images with correct polarities using multicomponent seismic data. However, the decomposition of elastic wavefields into vector P- and S-wavefields is computationally expensive, particularly in heterogeneous and complex anisotropic media. We have developed a computationally efficient vector ERTM method in the hybrid time and frequency domain by combining three existing techniques. Rather than decomposing elastic wavefields into vector qP- and qS-wavefields during time-domain wavefield propagation, we conduct the wavefield decomposition in the frequency domain for several selected frequencies. In general, the number of selected frequencies needed for migration imaging is much smaller than the number of time steps during forward and backward wavefield propagation, leading to greatly reduced computational costs associated with the qP-/qS-wavefield vector separation in complex heterogeneous anisotropic media. We further combine an implicit directional wavefield separation into the vector ERTM to enhance the image quality. The numerical results demonstrate that our method produces high-quality elastic-wave migration images with notably reduced computational costs compared to the conventional vector ERTM method.

Acoustic and elastic numerical wave simulations by recursive spatial derivative operators

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. T167-T174 ◽  
Author(s):  
Dan Kosloff ◽  
Reynam C. Pestana ◽  
Hillel Tal-Ezer
Keyword(s):  
Synthetic Data ◽  
Analytic Solutions ◽  
Numerical Dispersion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Lamb’S Problem ◽  
Dynamic Elasticity ◽  
Time Migration ◽  
Recursive Operators

A new scheme for the calculation of spatial derivatives has been developed. The technique is based on recursive derivative operators that are generated by an [Formula: see text] fit in the spectral domain. The use of recursive operators enables us to extend acoustic and elastic wave simulations to shorter wavelengths. The method is applied to the numerical solution of the 2D acoustic wave equation and to the solution of the equations of 2D dynamic elasticity in an isotropic medium. An example of reverse-time migration of a synthetic data set shows that the numerical dispersion can be significantly reduced with respect to schemes that are based on finite differences. The method is tested for the solutions of the equations of dynamic elasticity by comparing numerical and analytic solutions to Lamb’s problem.

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