Math Formulation for Ray Trace from Hypocenter Scan, Directed by Geodesic Paths on Spheroid (In Routine “VXplane transformWX [GZ3D(…)].h”)

Abstract

This paper concerns a method for performing a very rapid scan for the localization of the foci of Earthquakes (Hypocenters) while taking the Earth spheroidal geometry directly into account. This scanning process is divided into two parts: firstly the geodesic pathways are laid down on the spheroidal surface between the known epicenter and each of the active sensors (sensors for which a substantial number of P-wave onsets are known) and then secondly, the scan can take place using these pathways as guides for the P2P ray tracing necessary to form the scan itself.