3-D prestack migration in anisotropic media

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 79-90 ◽  
Author(s):  
Zhengxin Dong ◽  
George A. McMechan
Keyword(s):  
A Priori ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Anisotropic Media ◽  
P Wave ◽  
Common Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Prestack Migration ◽  
Time Migration

A three‐dimensional (3-D) prestack reverse‐time migration algorithm for common‐source P‐wave data from anisotropic media is developed and illustrated by application to synthetic data. Both extrapolation of the data and computation of the excitation‐time imaging condition are implemented using a second‐order finite‐ difference solution of the 3-D anisotropic scalar‐wave equation. Poorly focused, distorted images are obtained if data from anisotropic media are migrated using isotropic extrapolation; well focused, clear images are obtained using anisotropic extrapolation. A priori estimation of the 3-D anisotropic velocity distribution is required. Zones of anomalous, directionally dependent reflectivity associated with anisotropic fracture zones are detectable in both the 3-D common‐ source data and the corresponding migrated images.

Acoustic prestack migration of cross‐hole data

Geophysics ◽  
1988 ◽  
Vol 53 (8) ◽  
pp. 1015-1023 ◽  
Author(s):  
Liang‐Zie Hu ◽  
George A. McMechan ◽  
Jerry M. Harris
Keyword(s):  
Synthetic Data ◽  
Field Application ◽  
Scale Model ◽  
Common Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Prestack Migration ◽  
Time Migration ◽  
Time Space ◽  
Low Pass

Subsurface imaging with common‐source cross‐hole data can be achieved using prestack reverse‐time migration. The algorithm consists of extrapolation of the recorded wave field, application of the excitation‐time imaging condition, and postprocessing of the resulting image with a low‐pass wavenumber filter. The wavenumber filter removes the artifact associated with the direct arrival; this artifact is not separable from the scattered data before migration because, in the cross‐hole geometry, they significantly overlap in time, space, and wavenumber. Migration of synthetic data produces the best possible results, but images produced by migration of scale‐model data are not greatly inferior. Apparently, acceptable images can be obtained from a surprisingly few sources, if these sources are located sufficiently far apart to give independent information and the recording aperture is sufficiently wide.

True-amplitude prestack depth migration

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. S155-S166 ◽  
Author(s):  
Feng Deng ◽  
George A. McMechan
Keyword(s):  
Velocity Ratio ◽  
Synthetic Data ◽  
Transmission Losses ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Prestack Migration ◽  
Time Migration ◽  
Geometric Spreading

Most current true-amplitude migrations correct only for geometric spreading. We present a new prestack depth-migration method that uses the framework of reverse-time migration to compensate for geometric spreading, intrinsic [Formula: see text] losses, and transmission losses. Geometric spreading is implicitly compensated by full two-way wave propagation. Intrinsic [Formula: see text] losses are handled by including a [Formula: see text]-dependent term in the wave equation. Transmission losses are compensated based on an estimation of angle-dependent reflectivity using a two-pass recursive reverse-time prestack migration. The image condition used is the ratio of receiver/source wavefield amplitudes. Two-dimensional tests using synthetic data for a dipping-layer model and a salt model show that loss-compensating prestack depth migration can produce reliable angle-dependent reflection coefficients at the target. The reflection coefficient curves are fitted to give least-squares estimates of the velocity ratio at the target. The main new result is a procedure for transmission compensation when extrapolating the receiver wavefield. There are still a number of limitations (e.g., we use only scalar extrapolation for illustration), but these limitations are now better defined.

Elastic least-squares reverse time migration with hybrid l1/l2 misfit function

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. S271-S291 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Peng Yang ◽  
Wencai Xu ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Adjoint Equations ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Wave Image

We have developed the theory and synthetic tests of elastic least-squares reverse time migration (ELSRTM). In this method, a least-squares reverse time migration algorithm is used to image multicomponent seismic data based on the first-order elastic velocity-stress wave equation, in which the linearized elastic modeling equations are used for forward modeling and its adjoint equations are derived based on the adjoint-state method for back propagating the data residuals. Also, we have developed another ELSRTM scheme based on the wavefield separation technique, in which the P-wave image is obtained using P-wave forward and adjoint wavefields and the S-wave image is obtained using P-wave forward and S-wave adjoint wavefields. In this way, the crosstalk artifacts can be minimized to a significant extent. In general, seismic data inevitably contain noise. We apply the hybrid [Formula: see text] misfit function to the ELSRTM algorithm to improve the robustness of our ELSRTM to noise. Numerical tests on synthetic data reveal that our ELSRTM, when compared with elastic reverse time migration, can produce images with higher spatial resolution, more-balanced amplitudes, and fewer artifacts. Moreover, the hybrid [Formula: see text] misfit function makes the ELSRTM more robust than the [Formula: see text] misfit function in the presence of noise.

Implicit static corrections in prestack migration of common‐source data

Geophysics ◽  
1990 ◽  
Vol 55 (6) ◽  
pp. 757-760 ◽  
Author(s):  
G. A. McMechan ◽  
H. W. Chen
Keyword(s):  
Surface Velocity ◽  
Common Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Near Surface ◽  
Prestack Migration ◽  
Time Migration ◽  
Excitation Time ◽  
Source Data ◽  
Static Corrections

Static effects due to surface topography and near‐surface velocity variations may be accurately compensated for, in an implicit way, during prestack reverse‐time migration of common‐source gathers, obviating the need for explicit static corrections. Receiver statics are incorporated by extrapolating the observed data from the actual recorder positions; source statics are incorporated by computing the excitation‐time imaging conditions from the actual source positions.

Polarization-based wave-equation migration velocity analysis in acoustic media

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. U77-U88 ◽  
Author(s):  
Qunshan Zhang ◽  
George A. McMechan
Keyword(s):  
Wave Equation ◽  
Velocity Ratio ◽  
Empirical Relation ◽  
Synthetic Data ◽  
P Wave ◽  
Reverse Time ◽  
Seismic Reflection Data ◽  
Prestack Migration ◽  
Time Migration ◽  
Acoustic Media

The source extrapolation step in wave-equation prestack reverse-time migration gives wavefield polarization information, which can be used to generate angle-domain common-image gathers (ADCIGs) from seismic reflection data from acoustic media. Concatenation of P-wave polarization segments gives wavefield propagation paths (“wavepaths”), which are similar to the raypaths in ray-based velocity tomography. The ADCIGs provide residual depth moveout (RMO) information, from which a system of linear equations is constructed for tomography to solve for the velocity ratio used for velocity updating. An empirical relation between the RMO data and the velocity ratio updates reduces the amount of computation, and is stabilized by the feedback provided by the iterative loop through prestack migration, to RMO, to velocity update, to prestack migration. Correcting the RMOs to flatten the ADGIGs is the convergence condition. Synthetic data for a layered model with a fault successfully illustrates the method.

A wavefield-separation-based elastic least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S279-S297 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Synthetic Data ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
S Waves ◽  
Numerical Tests ◽  
Time Migration

Elastic least-squares reverse time migration (ELSRTM) has the potential to provide improved subsurface reflectivity estimation. Compared with elastic RTM (ERTM), ELSRTM can produce images with higher spatial resolution, more balanced amplitudes, and fewer artifacts. However, the crosstalk between P- and S-waves can significantly degrade the imaging quality of ELSRTM. We have developed an ELSRTM method to suppress the crosstalk artifacts. This method includes three crucial points. The first is that the forward and backward wavefields are extrapolated based on the separated elastic velocity-stress equation of P- and S-waves. The second is that the separated vector P- and S-wave residuals are migrated to form reflectivity images of Lamé constants [Formula: see text] and [Formula: see text] independently. The third is that the reflectivity images of [Formula: see text] and [Formula: see text] are obtained by the vector P-wave wavefields achieved in the backward extrapolation of the separated vector P-wave residuals and the vector S-wave wavefields achieved in the backward extrapolation of the separated vector S-wave residuals, respectively. Numerical tests with synthetic data demonstrate that our ELSRTM method can produce images free of crosstalk artifacts. Compared with ELSRTM based on the coupled wavefields, our ELSRTM method has better convergence and higher accuracy.

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.

3-D elastic prestack, reverse‐time depth migration

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 597-609 ◽  
Author(s):  
Wen‐Fong Chang ◽  
George A. McMechan
Keyword(s):  
Finite Differences ◽  
Synthetic Data ◽  
P Wave ◽  
Common Source ◽  
Reverse Time ◽  
Depth Migration ◽  
Full Wave ◽  
Source Data ◽  
Recorded Data ◽  
Time Extrapolation

By combining and extending previous algorithms for 2-D prestack elastic migration and 3-D prestack acoustic migration, a full 3-D elastic prestack depth migration algorithm is developed. Reverse‐time extrapolation of the recorded data is by 3-D elastic finite differences; computation of the image time for each point in the 3-D volume is by 3-D acoustic finite differences. The algorithm operates on three‐component, vector‐wavefield common‐source data and produces three‐component vector reflectivity distributions. Converted P‐to‐S reflections are automatically imaged with the primary P‐wave reflections. There are no dip restrictions as the full wave equation is used. The algorithm is illustrated by application to synthetic data from three models; a flat reflector, a dipping truncated wedge overlying a flat reflector, and the classical French double dome and fault model.

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.

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