BENT-RAY TRAVELTIME TOMOGRAPHY AND MIGRATION WITHOUT RAY TRACING

Abstract

We present a new method of traveltime tomography. In this method, the traveltime between source and receiver is described by an analytical function, which consists of a series expansion of geometrical coordinates of the source and receiver locations. As the traveltime is derived from the eikonal equation, the analytical function must also satisfy the eikonal equation. This condition imposes a strong constraint on the uniqueness of the analytical function. The coefficients of the series expansion are estimated by minimizing the misfit between the observed and the analytical time function in a least-squares sense. Once the coefficients of the series expansion are known, the eikonal equation, which turns out to also be in the form of a series expansion, provides the velocity in the medium. Thus there are two analytical functions, one defining the traveltime and the other defining the slowness, and they can be used for pre-stack depth migration and velocity model definition. The feasibility of this approach is first tested on a synthetic data set and then applied to a real data set. This new method of tomography and pre-stack migration provides a significant gain in computation time compared with ray-tracing techniques. The method can easily be extended to incorporate reflection data and has potential for solving 3-D seismic reflection and global seismology inverse problems.