Potentials for Elastic Displacement in Spherically Symmetric Media

The choice of P and S designations is somewhat arbitrary in heterogeneous elastic media, but becomes precise in the high-frequency limit of ray theory. This fact is used in a radially heterogeneous isotropic medium to establish three potentials (P,S,T) with the following properties: (1) every displacement solution is represented by some (P,S,T); (2) T(r,t) is decoupled from P and S, is a potential for SH motion, and satisfies second-order wave equation; and (3) the coupling of P and SV is represented by coupled equations in potentials P and S. At high frequencies these equations decouple (for an important class of sources) into separate second-order wave equations for P and S. An important role, in this decoupled case, is played by the variable density. Several possibilities suggested by the general P and SV equations are also outlined.