Angle- and azimuth-domain common-image gathers by reverse time migration for 3D elastic isotropic media

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. S151-S167
Author(s):  
Zabihollah Khaksar ◽  
George A. McMechan
Keyword(s):  
Incident Angle ◽  
Migration Velocity ◽  
Spatial Gradient ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Disk Storage ◽  
Time Migration ◽  
Isotropic Media ◽  
The Hilbert Transform ◽  
Elastic Particle

A 2D algorithm for angle-domain common-image gather (CIG) calculation is extended and modified to produce 3D elastic angle and azimuth CIGs. The elastic seismic data are propagated with the elastic particle displacement wave equation, and then the PP-reflected and PS-converted waves are separated by divergence and curl calculations during application of the excitation-time imaging condition. The incident angles and azimuths are calculated using source propagation directions and the reflector normals. The source propagation direction vector is computed as the spatial gradient of the incident 3C P-wavefield. The vector normal to the reflector is calculated using the Hilbert transform. Ordering the migrated images with respect to incident angles for a fixed azimuth bin, or with respect to azimuths for a fixed incident angle bin, creates angle- or azimuth-domain CIGs, respectively. Sorting the azimuth gathers by the incident angle bins causes a shift to a greater depth for too-high migration velocity and to a smaller depth for too-low migration velocity. For the sorted incident angle gathers, the velocity-dependent depth moveout is within the angle gathers and across the azimuth gathers. This method is compared with three other 3D CIG algorithms with respect to the number of calculations and their disk storage and RAM requirements; it is three to six orders of magnitude faster and requires two to three orders of magnitude less disk space. The method is successfully tested with data for a modified part of the SEG/EAGE overthrust model.

Anisotropic migration velocity analysis using reverse-time migration

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. R13-R25 ◽  
Author(s):  
Wiktor Waldemar Weibull ◽  
Børge Arntsen
Keyword(s):  
Wave Equation ◽  
Seismic Anisotropy ◽  
Migration Velocity ◽  
Image Point ◽  
Velocity Analysis ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
Isotropic Media

Seismic anisotropy, if not accounted for, can cause significant mispositioning of the reflectors in depth-migrated images. Accounting for anisotropy in depth migration requires velocity analysis tools that can estimate the anisotropic background velocity field. We extended wave equation migration velocity analysis to deal with 2D tilted transverse isotropic media. The velocities were obtained automatically by nonlinear optimization of the focusing and stack power of common-image point gathers constructed using an extended imaging condition. We used the elastic two-way wave equation to reconstruct the wavefields needed for the image and gradient computations. This led to an anisotropic migration velocity analysis algorithm based on reverse-time migration. We illustrated the method with synthetic and field data examples based on marine surface seismic acquisition. The results showed that the method significantly improves the quality of the depth-migrated image. However, as is common in the case of velocity analysis using surface seismic data, the estimation of anisotropic parameters seems to be strongly nonunique.

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.

Angle-domain common-image gathers from plane-wave least-squares reverse time migration

Geophysics ◽  
2021 ◽  
pp. 1-60
Author(s):  
Chuang Li ◽  
Zhaoqi Gao ◽  
Jinghuai Gao ◽  
Feipeng Li ◽  
Tao Yang
Keyword(s):  
Inverse Problem ◽  
Plane Wave ◽  
Least Squares ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
Amplitude Versus

Angle-domain common-image gathers (ADCIGs) that can be used for migration velocity analysis and amplitude versus angle analysis are important for seismic exploration. However, because of limited acquisition geometry and seismic frequency band, the ADCIGs extracted by reverse time migration (RTM) suffer from illumination gaps, migration artifacts, and low resolution. We have developed a reflection angle-domain pseudo-extended plane-wave least-squares RTM method for obtaining high-quality ADCIGs. We build the mapping relations between the ADCIGs and the plane-wave sections using an angle-domain pseudo-extended Born modeling operator and an adjoint operator, based on which we formulate the extraction of ADCIGs as an inverse problem. The inverse problem is iteratively solved by a preconditioned stochastic conjugate gradient method, allowing for reduction in computational cost by migrating only a subset instead of the whole dataset and improving image quality thanks to preconditioners. Numerical tests on synthetic and field data verify that the proposed method can compensate for illumination gaps, suppress migration artifacts, and improve resolution of the ADCIGs and the stacked images. Therefore, compared with RTM, the proposed method provides a more reliable input for migration velocity analysis and amplitude versus angle analysis. Moreover, it also provides much better stacked images for seismic interpretation.

Direct vector-field method to obtain angle-domain common-image gathers from isotropic acoustic and elastic reverse time migration

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB135-WB149 ◽  
Author(s):  
Qunshan Zhang ◽  
George A. McMechan
Keyword(s):  
Direct Method ◽  
Incident Angle ◽  
Field Method ◽  
Propagation Direction ◽  
P Wave ◽  
Common Source ◽  
Spatial Gradient ◽  
Reverse Time ◽  
S Wave ◽  
Time Migration

We have developed an alternative (new) method to produce common-image gathers in the incident-angle domain by calculating wavenumbers directly from the P-wave polarization rather than using the dominant wavenumber as the normal to the source wavefront. In isotropic acoustic media, the wave propagation direction can be directly calculated as the spatial gradient direction of the acoustic wavefield, which is parallel to the wavenumber direction (the normal to the wavefront). Instantaneous wavenumber, obtained via a novel Hilbert transform approach, is used to calculate the local normal to the reflectors in the migrated image. The local incident angle is produced as the difference between the propagation direction and the normal to the reflector. By reordering the migrated images (over all common-source gathers) with incident angle, common-image gathers are produced in the incident-angle domain. Instantaneous wavenumber takes the place of the normal to the reflector in the migrated image. P- and S-wave separations allow both PP and PS common-image gathers to be calculated in the angle domain. Unlike the space-shift image condition for calculating the common-image gather in angle domain, we use the crosscorrelation image condition, which is substantially more efficient. This is a direct method, and is less dependent on the data quality than the space-shift method. The concepts were successfully implemented and tested with 2D synthetic acoustic and elastic examples, including a complicated (Marmousi2) model that illustrates effects of multipathing in angle-domain common-image gathers.

Separating quasi-P-wave in transversely isotropic media with a vertical symmetry axis by synthesized pressure applied to ocean-bottom seismic data elastic reverse time migration

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. C295-C307 ◽  
Author(s):  
Pengfei Yu ◽  
Jianhua Geng ◽  
Chenlong Wang
Keyword(s):  
Transversely Isotropic ◽  
P Wave ◽  
Ocean Bottom ◽  
Receiver Side ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Isotropic Media ◽  
Wave Imaging ◽  
Obs Data

Quasi-P (qP)-wavefield separation is a crucial step for elastic P-wave imaging in anisotropic media. It is, however, notoriously challenging to quickly and accurately obtain separated qP-wavefields. Based on the concepts of the trace of the stress tensor and the pressure fields defined in isotropic media, we have developed a new method to rapidly separate the qP-wave in a transversely isotropic medium with a vertical symmetry axis (VTI) by synthesized pressure from ocean-bottom seismic (OBS) data as a preprocessing step for elastic reverse time migration (ERTM). Another key aspect of OBS data elastic wave imaging is receiver-side 4C records back extrapolation. Recent studies have revealed that receiver-side tensorial extrapolation in isotropic media with ocean-bottom 4C records can sufficiently suppress nonphysical waves produced during receiver-side reverse time wavefield extrapolation. Similarly, the receiver-side 4C records tensorial extrapolation was extended to ERTM in VTI media in our studies. Combining a separated qP-wave by synthesizing pressure and receiver-side wavefield reverse time tensorial extrapolation with the crosscorrelation imaging condition, we have developed a robust, fast, flexible, and elastic imaging quality improved method in VTI media for OBS data.

Least-squares reverse time migration in the presence of velocity errors

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S567-S580 ◽  
Author(s):  
Jizhong Yang ◽  
Yunyue Elita Li ◽  
Arthur Cheng ◽  
Yuzhu Liu ◽  
Liangguo Dong
Keyword(s):  
Least Squares ◽  
Velocity Model ◽  
Migration Velocity ◽  
Resolution Limit ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Large Velocity ◽  
Iterative Inversion ◽  
Inversion Procedure

Least-squares reverse time migration (LSRTM), which aims to match the modeled data with the observed data in an iterative inversion procedure, is very sensitive to the accuracy of the migration velocity model. If the migration velocity model contains errors, the final migration image may be defocused and incoherent. We have used an LSRTM scheme based on the subsurface offset extended imaging condition, least-squares extended reverse time migration (LSERTM), to provide a better solution when large velocity errors exist. By introducing an extra dimension in the image space, LSERTM can fit the observed data even when significant errors are present in the migration velocity model. We further investigate this property and find that after stacking the extended migration images along the subsurface offset axis within the theoretical lateral resolution limit, we can obtain an image with better coherency and fewer migration artifacts. Using multiple numerical examples, we demonstrate that our method provides superior inversion results compared to conventional LSRTM when the bulk velocity errors are as large as 10%.

Q-compensated reverse time migration in tilted transversely isotropic media

Geophysics ◽  
2020 ◽  
pp. 1-79
Author(s):  
Ali Fathalian ◽  
Daniel O. Trad ◽  
Kristopher A. Innanen
Keyword(s):  
Time Domain ◽  
Transversely Isotropic ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Modeling And Analysis ◽  
Seismic Amplitude ◽  
Time Migration ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
The Time Domain

Anisotropy and absorption are critical to the modeling and analysis of seismic amplitude,phase, and traveltime data. To neglect any of these phenomena, which are often bothoperating simultaneously, degrades the resolution and interpretability of migrated images.However, a full accounting of anisotropy and anelasticity is computationally complex andexpensive. One strategy for accommodating these aspects of wave propagation, while keepingcost and complexity under control, is to do so within an acoustic approximation. Weset up a procedure for solving the time-domain viscoacoustic wave equation for tilted transverselyisotropic (TTI) media, based on a standard linear solid model and, from this, developa viscoacoustic reverse time migration (Q-RTM) algorithm. In this approach, amplitudecompensation occurs within the migration process through a manipulation of attenuationand phase dispersion terms in the time domain differential equations. Specifically, theback-propagation operator is constructed by reversing the sign only of the amplitude lossoperators, but not the dispersion-related operators, a step made possible by reformulatingthe absorptive TTI equations such that the loss and dispersion operators appear separately.The scheme is tested on synthetic examples to examine the capacity of viscoacoustic RTM to correct for attenuation, and the overall stability of the procedure.

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