Tracing of rays through heterogeneous media: An accurate and efficient procedure

Abstract

We present an accurate and computationally efficient method for tracing rays through a medium of heterogeneous velocity. Efficiency is obtained through approximations, while accuracy is maintained by using higher‐order terms in the approximations when necessary. The method was developed as part of a general seismic inversion technique for traveltime information where the medium is discretized into rectangular cells, each of which is characterized by a velocity gradient. However, as a stand‐alone tool for forward modeling this method may be applied to other cell geometries and the velocity field need not be a linear function of position in each cell. We use path length as the independent variable rather than position or orientation. The position, orientation, and traveltime of the ray are algebraic expressions of path length, so that trigonometric functions are avoided. If either position or orientation is used as the independent variable, trigonometric expressions invariably arise in evaluating the dependent variables. Such transcendental functions are computationally inefficient in large problems.