Geometrical-spreading and ray-caustic decomposition of elementary seismic waves

The computation of the geometrical-spreading factor and the number of caustics is often considered to be the most fundamental step in computing zero-order ray solutions for elementary-wave Green's functions along a ray that originates at a point source and passes through a 3-D laterally inhomogeneous isotropic medium. Here, a new factorization method is described that establishes both quantities recursively along the ray segments into which the total ray can be subdivided. As a consequence of the proposed method, the point-source geometrical-spreading factor and the number of ray caustics along the total ray can be decomposed into (1) point-source spreading factors of the ray segments and (2) certain Fresnel zone contributions at the ray-segment connection points. In a so-called '3-D simple medium,' by which any 3-D laterally inhomogeneous medium can be approximated, the new factorization approach permits a simple computation of both quantities. It thus simplifies and provides new insights into the computation of ray-theoretical Green's functions.