scholarly journals Reducing Residual Moveout Seismic Anisotropy Model Using Three-Ray GMA (General Moveout Approximation)

2020 ◽  
Vol 43 (3) ◽  
pp. 125-133
Author(s):  
Egie Wijaksono ◽  
Humbang Purba
Keyword(s):  
Seismic Anisotropy ◽  
Seismic Imaging ◽  
Comparative Method ◽  
Synthetic Data ◽  
Single Layer ◽  
Transversely Isotropic ◽  
Vertical Axis ◽  
Hockey Stick ◽  
Anisotropy Model ◽  
Marine Seismic

A “ hockey stick” phenomenon is one of anisotropic effects that should be eliminated in marine seismic data. It can increase residual moveout at the far offsets and impact to the distortion of refl ection event amplitude, eventually, reduce the seismic imaging quality. Conventional hyperbolic moveout approximation, an algorithm isotropic model commonly used for seismic processing, has a drawback in supressing such phenomenon. It is also not reliable for medium anisotropy model and long offset data. Many researchers formulated nonhyperbolic moveout approimations but it has limitation analysis for inteval offset-depth ratio (ODR) more than four. We present three-ray generalized moveout approximation (three-ray GMA) for transversely isotropic medium with vertical axis of symmetry (VTI), which is a modifi ed non-hyperbolic moveout approximation from original GMA, to cover up of the weakness of the hyperbolic approximation. The objective of this study is to eliminate “ hockey stick” effect and minimize the residual moveout much smaller at once at the far offsets (offsetdepth ratio 4). In this study, we used synthetic data for single layer model in VTI medium to calculate relative traveltime error for each recent method over a range of offsets (0 ≤ ODR ≤ 6) and anisotropic parameters (0 ≤  ≤ 0.5). We also make comparative method for multi layer and implement it in a velocity analysis and residual moveout calculation. The three-ray GMA shows a better capability than comparative method to reduce residual moveout for larger offset. This result is important for enhancing seismic imaging.

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.

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.

Extraction of P‐ and S‐waves from the vertical component of the particle velocity at the sea floor

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 231-240 ◽  
Author(s):  
Lasse Amundsen ◽  
Arne Reitan
Keyword(s):  
Particle Velocity ◽  
Synthetic Data ◽  
Vertical Component ◽  
Transversely Isotropic ◽  
Vertical Axis ◽  
Elastic Stiffness ◽  
P Wave ◽  
S Wave ◽  
Sea Floor ◽  
S Waves

At the boundary between two solid media in welded contact, all three components of particle velocity and vertical traction are continuous through the boundary. Across the boundary between a fluid and a solid, however, only the vertical component of particle velocity is continuous while the horizontal components can be discontinuous. Furthermore, the pressure in the fluid is the negative of the vertical component of traction in the solid, while the horizontal components of traction vanish at the interface. Taking advantage of this latter fact, we show that total P‐ and S‐waves can be computed from the vertical component of the particle velocity recorded by single component geophones planted on the sea floor. In the case when the sea floor is transversely isotropic with a vertical axis of symmetry, the computation requires the five independent elastic stiffness components and the density. However, when the sea floor material is fully isotropic, the only material parameter needed is the local shear wave velocity. The analysis of the extraction problem is done in the slowness domain. We show, however, that the S‐wave section can be obtained by a filtering operation in the space‐frequency domain. The P‐wave section is then the difference between the vertical component of the particle velocity and the S‐wave component. A synthetic data example demonstrates the performance of the algorithm.

Estimation of interval anisotropy parameters using velocity-independent layer stripping

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. WB117-WB127 ◽  
Author(s):  
Xiaoxiang Wang ◽  
Ilya Tsvankin
Keyword(s):  
Symmetry Plane ◽  
Synthetic Data ◽  
Single Layer ◽  
Transversely Isotropic ◽  
P Wave ◽  
Correlated Noise ◽  
Fractured Reservoir ◽  
Processing Parameter ◽  
Reflection Data ◽  
Error Amplification

Moveout analysis of long-spread P-wave data is widely used to estimate the key time-processing parameter [Formula: see text] in layered transversely isotropic media with a vertical symmetry axis (VTI). Inversion for interval [Formula: see text] values, however, suffers from instability caused by the trade-off between the effective moveout parameters and by subsequent error amplification during Dix-type layer stripping. We propose an alternative approach to nonhyperbolic moveout inversion based on the velocity-independent layer-stripping (VILS) method of Dewangan and Tsvankin. Also, we develop the 3D version of VILS and apply it to interval parameter estimation in orthorhombic media using wide-azimuth, long-spread data. If the overburden is laterally homogeneous and has a horizontal symmetry plane, VILS produces the exact interval traveltime-offset function in the target layer without knowledgeof the velocity field. Hence, Dix-type differentiation of moveout parameters used in existing techniques is replaced by the much more stable layer stripping of reflection traveltimes. The interval traveltimes are then inverted for the moveout parameters using the single-layer nonhyperbolic moveout equation. The superior accuracy and stability of the algorithm are illustrated on ray-traced synthetic data for typical VTI and orthorhombic models. Even small correlated noise in reflection traveltimes causes substantial distortions in the interval [Formula: see text] values computed by conventional Dix-type differentiation. In contrast, the output of VILS is insensitive to mild correlated traveltime errors. The algorithm is also tested on wide-azimuth P-wave reflection data recorded above a fractured reservoir at Rulison field in Colorado. The interval moveout parameters estimated by VILS in the shale layer above the reservoir are more plausible and less influenced by noise than those obtained by the Dix-type method.

Seismic anisotropy in the upper 500 m of the Southern Sydney Basin

Geophysics ◽  
1999 ◽  
Vol 64 (6) ◽  
pp. 1901-1911 ◽  
Author(s):  
Milovan Urosević ◽  
Christopher Juhlin
Keyword(s):  
Elastic Constants ◽  
Seismic Anisotropy ◽  
Full Range ◽  
Transversely Isotropic ◽  
Real Data ◽  
Vertical Axis ◽  
P Wave ◽  
Small Range ◽  
P Waves ◽  
Vsp Data

An analysis of seismic anisotropy at a BHP mining site in the Southern Sydney Basin by combined use of crosshole and vertical seismic profiling (VSP) data is presented. The upper 250 m in this area is highly heterogeneous and has a major impact on the analysis of P-wave traveltimes. It is shown that using P-wave information solely would not, at least in this case, lead to any reasonable estimate of the elastic constants, in particular C13, even if the measurements contained a full range of incident angles. However, if the measurements of SV-waves are available, even over a small range of incident angles, then C13 is determined more accurately. P-wave velocities measured in the vertical and horizontal directions show that anisotropy is present in the area. Additional measurements, along different incident angles, indicate that the rock down to 500 m depth is predominantly transversely isotropic (TI) with a vertical axis of symmetry. The P-wave anisotropy can be approximated as elliptical. Using the elastic constants estimated from the data analyses, synthetic seismograms for heterogeneous TI media were generated. Comparison of the seismic modeling with real crosshole data shows that it is necessary to include both fault zones and gas accumulations in the model to qualitatively match the real data. By using SV-waves in the multioffset VSP data, reflectors are mapped more accurately than by using P-waves, even under the assumption of isotropy and in the presence of heterogeneity. Mapping of converted P-SV waves by a straight ray approach also produced better results than the corresponding isotropic P-wave mapping. Inclusion of elliptical anisotropy into Kirchhoff migration resulted in better P-wave images than using an isotopic migration code. We conclude that both P-wave VSP multioffset mapping and tomographic inversion methods need to account for anisotropy to be accurate in this area, while SV-waves may be handled using isotropic codes. The same is true for crosshole and surface seismic data.

Do dipole sonic logs measure group or phase velocity (revisited)?

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. C311-C322
Author(s):  
Stephen Horne ◽  
Richard T. Coates ◽  
Alexei Bolshakov
Keyword(s):  
Symmetry Axis ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Vertical Axis ◽  
Flexural Waves ◽  
S Wave ◽  
Slowness Surface ◽  
Phase Velocities ◽  
Group And Phase Velocities ◽  
Sonic Logs

We have revisited the debate about whether flexural waves from dipole sonic tools and standard processing algorithms measure group or phase velocities in anisotropic formations. We observe that much of the confusion arises from a failure to understand the different meanings of group and phase velocities. Using a transversely isotropic medium with a vertical axis of symmetry that exhibits a triplication in its S-wave group slowness surface, we generate synthetic flexural sonic waveforms corresponding to boreholes at angles of 0°–90° with respect to the anisotropy symmetry axis in 1° increments. We processed these synthetic data using standard time- and frequency-domain semblance methods. The results conclusively demonstrate that dipole sonic logs measure the group slowness for the group angle corresponding to the angle between the borehole and the anisotropic symmetry axis. In addition, data that we have evaluated suggest that current tool geometries and semblance processing may not always be sensitive enough to resolve all branches of the group slowness triplication surface.

Stacking-velocity tomography for tilted orthorhombic media

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. C171-C180 ◽  
Author(s):  
Qifan Liu ◽  
Ilya Tsvankin
Keyword(s):  
Parameter Estimation ◽  
Subsurface Layer ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
P Waves ◽  
Additional Information ◽  
Reflection Data ◽  
Anisotropic Layers ◽  
Zero Offset ◽  
Velocity Tomography

Tilted orthorhombic (TOR) models are typical for dipping anisotropic layers, such as fractured shales, and can also be due to nonhydrostatic stress fields. Velocity analysis for TOR media, however, is complicated by the large number of independent parameters. Using multicomponent wide-azimuth reflection data, we develop stacking-velocity tomography to estimate the interval parameters of TOR media composed of homogeneous layers separated by plane dipping interfaces. The normal-moveout (NMO) ellipses, zero-offset traveltimes, and reflection time slopes of P-waves and split S-waves ([Formula: see text] and [Formula: see text]) are used to invert for the interval TOR parameters including the orientation of the symmetry planes. We show that the inversion can be facilitated by assuming that the reflector coincides with one of the symmetry planes, which is a common geologic constraint often employed for tilted transversely isotropic media. This constraint makes the inversion for a single TOR layer feasible even when the initial model is purely isotropic. If the dip plane is also aligned with one of the symmetry planes, we show that the inverse problem for [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-waves can be solved analytically. When only [Formula: see text]-wave data are available, parameter estimation requires combining NMO ellipses from a horizontal and dipping interface. Because of the increase in the number of independent measurements for layered TOR media, constraining the reflector orientation is required only for the subsurface layer. However, the inversion results generally deteriorate with depth because of error accumulation. Using tests on synthetic data, we demonstrate that additional information such as knowledge of the vertical velocities (which may be available from check shots or well logs) and the constraint on the reflector orientation can significantly improve the accuracy and stability of interval parameter estimation.

On the reconstruction of the shape of a seismic streamer

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. H1-H6
Author(s):  
Bruno Goutorbe ◽  
Violaine Combier
Keyword(s):  
A Priori ◽  
Synthetic Data ◽  
Seismic Survey ◽  
Random Errors ◽  
Generalized Inversion ◽  
Reconstruction Methods ◽  
Seismic Acquisition ◽  
Marine Seismic ◽  
Gps Devices ◽  
Vessel Reconstruction

In the frame of 3D seismic acquisition, reconstructing the shape of the streamer(s) for each shot is an essential step prior to data processing. Depending on the survey, several kinds of constraints help achieve this purpose: local azimuths given by compasses, absolute positions recorded by global positioning system (GPS) devices, and distances calculated between pairs of acoustic ranging devices. Most reconstruction methods are restricted to work on a particular type of constraint and do not estimate the final uncertainties. The generalized inversion formalism using the least-squares criterion can provide a robust framework to solve such a problem — handling several kinds of constraints together, not requiring an a priori parameterization of the streamer shape, naturally extending to any configuration of streamer(s), and giving rigorous uncertainties. We explicitly derive the equations governing the algorithm corresponding to a marine seismic survey using a single streamer with compasses distributed all along it and GPS devices located on the tail buoy and on the vessel. Reconstruction tests conducted on several synthetic examples show that the algorithm performs well, with a mean error of a few meters in realistic cases. The accuracy logically degrades if higher random errors are added to the synthetic data or if deformations of the streamer occur at a short length scale.

Seismic Anisotropy in Salt Bodies - Implications for Seismic Imaging

2000 ◽  
Author(s):  
D.G. Raymer ◽  
J.-M. Kendall ◽  
D. Pedlar ◽  
R.R. Kendall ◽  
M.C. Mueller
Keyword(s):  
Seismic Anisotropy ◽  
Seismic Imaging
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