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 comput ing zero-order ray solutions for elementary-wave Green's functions alo ng a ray that originates at a point source and passes through a 3-D la terally inhomogeneous isotropic medium. Here, a new factorization meth od is described that establishes both quantities recursively along the ray segments into which the total ray can be subdivided;As a conseque nce of the proposed method, the point-source geometrical-spreading fac tor and the number of ray caustics along the total ray can be decompos ed into (1) point-source spreading factors of the ray segments and (2) certain Fresnel zone contributions at the ray-segment connection poin ts. In a so-called ''3-D simple medium,'' by which any 3-D laterally i nhomogeneous medium can be approximated, the new factorization approac h permits a simple computation of both quantities. It thus simplifies and provides new insights into the computation of ray-theoretical Gree n's functions.