abstract
The determination of local earthquake hypocenters and orgin times from first-P-arrival times by Geiger's method requires a technique for finding the minimum travel time (and derivatives) between the source and the station. Sophisticated ray tracing techniques have been developed for this purpose for use in complex velocity structures. Unfortunately, the two common techniques, shooting and bending, are generally prohibitively expensive for routine use in data analysis. The bending method is also particularly vulnerable to the problem of local minima in travel time. A method has been developed known as the ray initializer, which can be used to circumvent these problems in many cases. First, the technique can find a reasonable estimate of the minimum-time ray path in a quick and efficient manner. The velocity in a region local to the source and receiver is laterally averaged to yield an approximate layered velocity model. One-dimensional ray tracing techniques are used to find the minimum-time path for this layered structure. The ray path estimate can then be used as the starting path in a bending routine, a procedure resulting in more rapid convergence and the avoidance of local minima. Second, the travel time found by numerical integration along the estimated ray path is an excellent approximation to the actual travel time. Thus, in many cases, the ray initializer can be substituted for a three-dimensional ray tracing routine with a tremendous increase in efficiency and only a small loss in accuracy. It is found that the location of an explosion, derived using the ray initializer, is nearly identical to a complete ray tracing solution, even for a highly complex velocity structure.
Simple and Exact Closed-Form Expression for Determination of a Penetrated Ray Path in a Ray Tracing