Two-point ray tracing in dipping layered media with constant or linearly varying velocity function

Abstract

A stable and accurate computational method is introduced for two-point ray tracing in the dipping layered media with constant or linearly varying vertical velocity distributions. This method is similar to the method introduced by Kim and Baag (2002) in horizontally layered media except that the slowness of a ray through whole ray path does not conserve due to dipping layers. The take-off angle at the source can be determined by the two-point ray tracing in the dipping layered media and can be described with respect to the horizontal distance between source and receiver. An equation of the horizontal distance can be obtained from the equations of ray paths and of interfaces in a nonlinear form. This nonlinear equation is expanded in a Taylor series with terms up to the second order about initial take-off angle of the ray for two-point ray tracing. This expansion yields the quadratic equation with respect to correction angle, which is the angular difference between the true and calculated take-off angle at the source. In this study, the initial take-off angle is basically estimated by applying the method introduced by Kim and Baag (2002). The computational results show stable and accurate two-point ray tracing for several models which include low velocity layer and producing triplication (or more) zone. Therefore, the accuracy and convergence rate of this method are sufficient enough to apply the method to a wide varieties of seismic problems.