Traveltime Computation and Migration in Anisotropic Media

Abstract

For seismic imaging of complex 3-D structures by e.g. prestack Kirchhoff depth migration large amounts of traveltime tables are required. This work provides a wavefront-oriented ray tracing technique for multi-valued traveltimes in smooth 3-D heterogeneous anisotropic media. In this method, wavefronts are propagated stepwise through the model and output quantities are interpolate (e.g., traveltimes, slowness) from rays to gridpoints. In contrast to isotropic media, where the input is a velocity model, the model for an anisotropic medium is defined by 21 elastic parameters at each gridpoint. To provide an efficient, accurate and fast algorithm for the interpolation of the elastic parameters to arbitrary points, the Cardinal Spline interpolation has been used, which produces an interpolated function that is continuous through the second derivative. The insertion of a new ray is performed by tracing it directly from the source. To calculate traveltimes at gridpoints a distance-weighted averaging method is used. To demonstrate the accuracy of the method the traveltimes computed for a homogeneous anisotropic model with elliptical symmetry are compared to exact traveltimes available for this medium. Since it exists no analytical solution for an inhomogeneous anisotropic model, I compare the results with an alternative method for traveltime computation, the FD perturbation method. To describe the subsurface models elastic parameters have been chosen that are related to real rocks. Kirchhoff migration is an inversion technique that images the structure of the subsurface from seismic reflection data. Even if newer migration methods exist that can in some cases provide better images, Kirchhoff migration is still a standard technique. However, to obtain a high quality image even illumination of the subsurface is essential. Conventional Kirchhoff migration, however, does not provide the desired angular coverage at the image point, especially when complex media are considered. In this work I suggest a new strategy for migration with angular parametrisation in anisotropic media. The method, which guarantees even illumination, combines the conventional ray shooting with a hyperbolic traveltime interpolation. This makes the technique very efficient. For the application to the migration in the angular domain the hyperbolic traveltime interpolation is extended to an irregular grid. To confirm the high potential of the new strategy, I present two synthetic data examples. First I apply the migration technique to a simple anisotropic model where elliptical symmetry is assumed. To show that the method can be applied to realistic data sets I also present a more complex isotropic model.