Vertical seismic profile synthetics by dynamic ray tracing in laterally varying layered anisotropic structures

Abstract

Dynamic ray tracing (DRT) is important in evaluating high‐frequency seismic wave fields in complicated structures. Two formulations of the DRT equations for inhomogeneous anisotropic media are presented. One of them is represented by the classical DRT system, suggested by Červený 15 years ago. Both systems are specified in Cartesian coordinates. The DRT equations are supplemented with formulae for the transformation of DRT across a smoothly curved interface between two inhomogeneous anisotropic media. Červený's formulation of the DRT is applied to the computation of vertical seismic profile (VSP) synthetics. The results of DRT are used for the evaluation of the geometrical spreading and of the coefficients of the paraxial ray approximation for travel times and ray amplitudes. In addition, the DRT is also used in the interval ray tracing procedure, a procedure searching for rays starling from the source and terminating in a specified interval on a profile. Results of numerical modeling of VSP measurements in a three‐dimensional laterally varying structure consisting of Isotropic and anisotropic layers separated by curved interfaces are presented. Ray diagrams of selected elementary waves, time‐distance curves, and multisource three‐component VSP synthetics generated for two different source locations calculated for the anisotropic model are compared with the results determined for a reference Isotropic model. The latter is obtained by averaging phase velocities of the anisotropic model. This comparison clearly shows the effects of anisotropy and the lateral variation of the model on seismic wave fields. The reliability of the ray synthetics is briefly discussed.