TTI Anisotropic Depth Migration - Which Tilt Estimate Should We Use?

Reflection tomography in the migrated domain can help reconstruct heterogeneous, anisotropic velocity fields needed for accurate depth imaging of complex geologic structures. The presence of anisotropy, however, increases the uncertainty in velocity analysis and typically requires a priori constraints on the model parameters. Here, we develop a 2D P-wave tomographic algorithm for heterogeneous transversely isotropic media with a tilted symmetry axis (TTI) and investigate the conditions necessary for stable estimation of the symmetry-direction velocity V P0 and the anisotropy parameters ε and δ. The model is divided into rectangular cells, and the parameters V P0 , ε, δ, and the tilt ν of the symmetry axis are defined at the grid points. To increase the stability of the inversion, the symmetry axis is set orthogonal to the imaged reflectors, with the tilt interpolated inside each layer. The iterative migration velocity analysis involves efficient linearized parameter updating designed to minimize the residual moveout in image gathers for all available reflection events. The moveout equation in the depth-migrated domain includes a nonhyperbolic term that describes long-offset data, which are particularly sensitive to ε. Synthetic tests for models with a "quasi-factorized" TTI syncline (i.e., ε and δ are constant inside the anisotropic layer) and a TTI thrust sheet demonstrate that stable parameter estimation requires either strong smoothness constraints or additional information from walkaway VSP (vertical seismic profiling) traveltimes. If the model is quasifactorized with a linear spatial variation of V P0 , it may be possible to obtain the interval TTI parameters just from long-spread reflection data.

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confidence: 99%

Ray-based gridded tomography for tilted transversely isotropic media

Wang

Tsvankin

2013

“…On real data imaging examples, TTI RTM has given the best images in a complex Gulf of Mexico wide-azimuth survey (Huang et al, 2009), although the velocity models for TTI migration were simplified as structurally conformable transverse isotropy (STI), which requires the symmetry axis to be consistent with the normal vectors of reflectors (Audebert et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

3D angle gathers from reverse time migration

Xu¹,

Zhang²,

Tang³

2011

226

Common-image gathers are an important output of prestack depth migration. They provide information needed for velocity model building and amplitude and phase information for subsurface attribute interpretation. Conventionally, common-image gathers are computed using Kirchhoff migration on commonoffset/azimuth data volumes. When geologic structures are complex and strong contrasts exist in the velocity model, the complicated wave behaviors will create migration artifacts in the image gathers. As long as the gather output traces are indexed by any surface attribute, such as source location, receiver location, or surface plane-wave direction, they suffer from the migration artifacts caused by multiple raypaths. These problems have been addressed in a significant amount of work, resulting in common-image gathers computed in the reflection angle domain, whose traces are indexed by the subsurface reflection angle and/or the subsurface azimuth angle.Most of these efforts have concentrated on Kirchhoff and oneway wave-equation migration methods. For reverse time migration, subsurface angle gathers can be produced using the same approach as that used for one-way wave-equation migration. However, these approaches need to be revisited when producing high-quality subsurface angle gathers in three dimensions (reflection angle/azimuth angle), especially for wide-azimuth data. We have developed a method for obtaining 3D subsurface reflection angle/azimuth angle common-image gathers specifically for the amplitude-preserved reverse time migration. The method builds image gathers with a highdimensional convolution of wavefields in the wavenumber domain. We have found a windowed antileakage Fourier transform method that leads to an efficient and practical implementation. This approach has generated high-resolution angle-domain gathers on synthetic 2.5D data and 3D wideazimuth real data.

“…Specifically, since the layering has a general preferred direction, we find that the transversely isotropic (TI) assumption to be the most practical type of anisotropy to represent big parts of the subsurface. The tilt in this case is naturally set in the direction normal to the layering (Alkhalifah and Bednar, 2000;Audebert et al, 2006;Behera and Tsvankin, 2009;Alkhalifah and Sava, 2010). Thus, this type of model approximates a big portion of the anisotropy resulting from the thin layering.…”

Section: Introductionmentioning

confidence: 99%

Traveltime approximations for transversely isotropic media with an inhomogeneous background

Alkhalifah

2011

A transversely isotropic model with a tilted symmetry axis (TI) is regarded as one of the most effective approximations to the Earth subsurface, especially for imaging purposes. However, we commonly utilize this model by setting the axis of symmetry normal to the reflector. This assumption may be accurate in many places, but deviations from this assumption will cause errors in the wavefield description. Using perturbation theory and Taylor's series, I expand the solutions of the eikonal equation for 2D transversely isotropic media with respect to the independent parameter θ, the angle the tilt of the axis of symmetry makes with the vertical, in a generally inhomogeneous TI background with a vertical axis of symmetry (VTI). I do an additional expansion in terms of the independent (anellipticity) parameter η in a generally inhomogeneous elliptically anisotropic background medium. These new TI traveltime solutions are given by expansions in η and θ with coefficients extracted from solving linear firstorder partial differential equations. Pade approximations are used to enhance the accuracy of the representation by predicting the behavior of the higher-order terms of the expansion. A simplification of the expansion for homogenous media provides nonhyperbolic moveout descriptions of the traveltime for TI models that are more accurate than other recently derived approximations. In addition, for 3D media, I develop traveltime approximations using Taylor's series type of expansions in the azimuth of the axis of symmetry. The coefficients of all these expansions can also provide us with the medium sensitivity gradients (Jacobian) for nonlinear tomographic-based inversion for the tilt in the symmetry axis.