Traveltimes for tilted TI media

Abstract

For many years, both the isotropic model and the transverse isotropic model with a vertical symmetry axis (VTI) were the standard in seismic modeling. These models are used to describe massive homogeneous sediments such as a thick sandstone body (isotropic model) or horizontally layered sediment (VTI model). The modern seismic often deals with complex geological objects with a complicated structure and intrusions. For seismic modeling and inversion, we need to use more advanced models that can accurately describe such a complex geology. The transverse isotropic model with the tilted axis of symmetry (TTI) is a good compromise between the complexity of the model and a realistic approximation. The TTI model is used to describe geological formations such as sediment near the flanks of salt domes, fold-and-thrust belts and rotated blocks due to tectonic processes, or with stress-induced anisotropy due to the anomalous stresses around the salt bodies.

The traveltime computation is an important tool in seismic data processing applied for velocity analysis, migration and rock physics analysis, with traveltime parameters defined by the coefficients of the Taylor series for traveltime or traveltime squared as a function of offset. These parameters provide an efficient tool for analyzing the effect of the medium parameters on a short- and long-offset moveout. The traveltime parameters can also be used for a Dix-type inversion into the interval parameters.

The aim of this thesis is to derive the traveltime parameters for TTI media, as well to show their applicability for seismic data processing and inversion.

The thesis consists of three main papers and three supplementary papers given in the Appendices. In order to best analyze the effect of the tilt angle, I will first consider the elliptical tilted TI (ETI) model as the natural extension of the elliptical isotropic model. Next, the results will be extended for a non-elliptical case given by a TTI model, and both ETI and TTI models are defined for vertically heterogeneous scenarios. Lastly, the special type of TTI medium, when the symmetry axis is normal to the reflector (DTI medium), is studied. The approximated double-square-root (DSR) operator for DTI was derived and applied for phase-shift prestack depth migration, while some supplementary projects related to the VTI moveout approximations, reflection coefficients and rock physics modeling are described in the Appendices.