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Scanning anisotropy parameters
Parameter estimation in an inhomogeneous anisotropic medium offers many challenges, chief among them is the trade off between inhomogeneity and anisotropy. It is especially hard to estimate the anisotropy parameter η in complex media. Using perturbation theory and Taylor’s series, I expand the solutions of the anisotropic eikonal equation for transversely isotropic (TI) media with vertical symmetry axis (VTI) in terms of the independent parameter η in a generally inhomogeneous elliptically anisotropic medium background. This new VTI traveltime solution is based on a set of precomputed traveltimes extracted from solving linear partial differential equations. The traveltimes obtained from these equations serve as the coefficients of a Taylor-type expansion of the total traveltime in terms of η. Shanks transform is used to predict the transient behavior of the expansion and improve its accuracy using fewer terms. A homogeneous medium simplification of the expansion provides classical nonhyperbolic moveout descriptions of the traveltime that are more accurate than other recently driven approximations. In addition, this formula provides a tool to scan for anisotropic parameters in a general inhomogeneous medium background. A Marmousi test demonstrates the accuracy of this approximation. For titled axis of symmetry, the equations are still applicable with a slightly more complicated framework as the vertical velocity and NMO velocity are not readily available from the data.
Department of Physical Science and Engineering 4700 King Abdullah University of Science and Technology
Thuwal 23955-6900 Saudi Arabia
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