Traveltime calculation and prestack depth migration in tilted transversely isotropic media

The principal objective of our work is to develop a technique for prestack depth migration in tilted transversely isotropic (TTI) media in which the axis of symmetry is not vertical and may be spatially varying. Such models are required to image seismic data in geologically complex regions such as the Canadian Foothills. We have developed a 2D Kirchhoff integral-based migration algorithm in which the traveltime computation comprises the major task. Among the existing traveltime computation algorithms such as ray tracing with interpolation, ray bending, and eikonal solvers, a direct or a brute force approach of traveltime computation is generally highly robust. We have modified a direct method of first-arrival P-wave traveltime computation in 2D media that accounts for TTI. The algorithm requires that the group velocity be computed at each gridpoint, using either an analytic solution or by an approximate Fourier series expansion. The P-wave traveltime contours computed for complex geologic models show the pronounced effects from TTI media. Our results, using laboratory P-wave data collected over a physical model of an anisotropic thrust sheet, reveal that a 2D Kirchhoff migration based on our traveltime algorithm (TTI model) images the structure beneath the thrust sheet very well. ne vertical transversely isotropic (assuming a vertical axis of symmetry) or isotropic imaging introduces false anticlinal structures. We compare our results with those obtained by a recursive-extrapolation method and find that our approach images the underside of one of the thrust sheets better.