Azimuth-preserved local angle-domain prestack time migration in isotropic, vertical transversely isotropic and azimuthally anisotropic media

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. S51-S64 ◽  
Author(s):  
Jiubing Cheng ◽  
Tengfei Wang ◽  
Chenlong Wang ◽  
Jianhua Geng

Conventional prestack migration does not preserve local directional information of the seismic waves at the image points. New attempts such as sectored migration of azimuth-limited or common-offset-vector data only concern source-receiver azimuth and offset on the surface, which can be poor representation of subsurface wavepath direction. Moreover, they could result in inaccurate imaging because they do not account for the energy propagation between azimuths or offset-vectors. In the past decade, local angle-domain seismic imaging has been highly advocated to avoid migration artifacts and to improve velocity estimation in complex media. Considering prestack time migration (PSTM) is still widely used in seismic imaging and seismic data preconditioning for amplitude variations with offset or incident-angle (AVO/AVA) analysis, fracture detection, and reservoir characterization, we present an azimuth-preserved local angle-domain Kirchhoff PSTM approach for such purposes. We apply a seismic imaging condition in 3D local angle domain and use extended superposition of impulse responses retaining subsurface angular attributes, which are evaluated through the incident and scattering phase slowness vectors using classical-diffraction moveout equations in isotropic, vertical transversely isotropic (VTI) and azimuthally anisotropic media. Two-dimensional synthetic examples demonstrate what the migrated results look like in local angle domain. A wide-azimuth synthetic example with horizontal transversely isotropy (HTI) proves the necessity of azimuthal migration for reliable imaging and azimuthal analysis when azimuthal anisotropy exists in the overburden. Real data examples show the advantages of imaging in subsurface angle domain for properly focusing and revealing azimuth- and angle-dependent variations of residual moveout and migrated amplitudes.

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. S199-S216
Author(s):  
Xinru Mu ◽  
Jianping Huang ◽  
Jidong Yang ◽  
Xu Guo ◽  
Yundong Guo

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.


Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA65-WCA73 ◽  
Author(s):  
Dennis Cooke ◽  
Andrej Bóna ◽  
Benn Hansen

Starting with the double-square-root equation we derive expressions for a velocity-independent prestack time migration and for the associated migration velocity. We then use that velocity to identify multiples and suppress them as part of the imaging step. To describe our algorithm, workflow, and products, we use the terms velocity-independent and oriented. While velocity-independent imaging does not require an input migration velocity, it does require input [Formula: see text]-values (also called local event slopes) measured in both the shot and receiver domains. There are many possible methods of calculating these required input [Formula: see text]-values, perhaps the simplest is to compute the ratio of instantaneous spatial frequency to instantaneous temporal frequency. Using a synthetic data set rich in multiples, we test the oriented algorithm and generate migrated prestack gathers, the oriented migration velocity field, and stacked migrations. We use oriented migration velocities for prestack multiple suppression. Without this multiple suppression step, the velocity-independent migration is inferior to a conventional Kirchhoff migration because the oriented migration will flatten primaries and multiples alike in the common image domain. With this multiple suppression step, the velocity-independent are very similar to a Kirchhoff migration generated using the known migration velocity of this test data set.


Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. S15-S27 ◽  
Author(s):  
Jiubing Cheng ◽  
Jianhua Geng ◽  
Huazhong Wang ◽  
Zaitian Ma

Conventional offset domain prestack migration tends to bring ambiguity and migration artifacts because it smears energy from different angles at the image point. To avoid this, prestack depth migration implementations in angle domain have been investigated in the past decades. As an efficient imaging tool, angle domain Kirchhoff prestack time migration is still useful and was proposed recently. However, existing algorithms cannot handle ray bending and anisotropy correctly. Practically, azimuth analysis for fractured reservoirs should be carried out after migration for most geological settings. Unfortunately, the existing migration algorithm implicitly involves some kind of binning to source-receiver azimuth, which may not be the real wave-pathazimuth, especially for side-scattering or out-of-plane waves. In this paper, we present an algorithm for 3D Kirchhoff prestack time migration in average illumination azimuth and incident angle domain, which matches true wave path naturally and more accurately. To handle ray bending and vertical transversely isotropy, we propose several approaches to estimate two-way traveltime and the corresponding angular attributes through extended offset-to-angle mapping. Based upon these approaches, our 3D prestack time migration can provide high-quality common-image gathers for amplitude variation with incident angle and/or amplitude variation with offset and azimuth analyses, even in media with slight to moderate lateral heterogeneity. The 2D and 3D synthetic examples prove the validity of our methods.


Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. C37-C47 ◽  
Author(s):  
Xuekai Sun ◽  
Sam Zandong Sun

Considering that geologic structures disturb prestack amplitude relationships, anisotropic migration is thus advocated not only for extracting azimuth-preserved common image gathers (CIGs), but also for preserving fracture-induced amplitude responses. However, most conventional anisotropic migration methods are hindered by their inefficiency in either modeling azimuthal traveltime variations at large offsets or characterizing subsurface reflections. Given that prestack time migration is widely applied for most practical purposes, we began with reformulations on a quartic traveltime formula, through which a new set of anisotropic parameters was developed. Then, an anisotropic migration method was established in the local-angle domain (LAD) for more reasonable uses of subsurface wavefield information. We also used a traveltime inversion scheme to estimate those anisotropic parameters required by anisotropic migration. Using this methodology on a physical model with a fracture medium, we derived better focused CIGs by thoroughly correcting the anisotropic effects of overburden. As a result, predicted properties of the fracture medium showed fewer interventions of geologic impacts. In a field example, a comprehensive study was performed on a deep carbonate reservoir to examine influences of different anisotropic migration algorithms on ultimate fracture prediction. Comparisons of the signal-to-noise ratio and agreements with formation microimage information reconfirmed the superiority of LAD anisotropic migration in recovering true properties of subsurface fractures, relative to routine methods (i.e., azimuth-sectored migration and anisotropic migration in the surface-offset domain).


Geophysics ◽  
2005 ◽  
Vol 70 (5) ◽  
pp. D43-D53 ◽  
Author(s):  
Xiaoxia Xu ◽  
Ilya Tsvankin ◽  
Andrés Pech

For processing and inverting reflection data, it is convenient to represent geometrical spreading through the reflection traveltime measured at the earth's surface. Such expressions are particularly important for azimuthally anisotropic models in which variations of geometrical spreading with both offset and azimuth can significantly distort the results of wide-azimuth amplitude-variation-with-offset (AVO) analysis. Here, we present an equation for relative geometrical spreading in laterally homogeneous, arbitrarily anisotropic media as a simple function of the spatial derivatives of reflection traveltimes. By employing the Tsvankin-Thomsen nonhyperbolic moveout equation, the spreading is represented through the moveout coefficients, which can be estimated from surface seismic data. This formulation is then applied to P-wave reflections in an orthorhombic layer to evaluate the distortions of the geometrical spreading caused by both polar and azimuthal anisotropy. The relative geometrical spreading of P-waves in homogeneous orthorhombic media is controlled by five parameters that are also responsible for time processing. The weak-anisotropy approximation, verified by numerical tests, shows that azimuthal velocity variations contribute significantly to geometrical spreading, and the existing equations for transversely isotropic media with a vertical symmetry axis (VTI) cannot be applied even in the vertical symmetry planes. The shape of the azimuthally varying spreading factor is close to an ellipse for offsets smaller than the reflector depth but becomes more complicated for larger offset-to-depth ratios. The overall magnitude of the azimuthal variation of the geometrical spreading for the moderately anisotropic model used in the tests exceeds 25% for a wide range of offsets. While the methodology developed here is helpful in modeling and analyzing anisotropic geometrical spreading, its main practical application is in correcting the wide-azimuth AVO signature for the influence of the anisotropic overburden.


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