Decoupling of the vector wave equation of elasticity for radially heterogeneous media

Abstract

The potential representation of the vector fields is employed to effect the decoupling of the vector wave equation of elasticity for radially heterogeneous isotropic media. Two types of decoupling are considered: decoupling for all values of the frequency and decoupling for high frequencies, which is useful in the ray-theory treatment. In the case of decoupling for all frequencies, the three constitutive parameters of the medium should satisfy a pair of nonlinear differential equations. For high-frequency decoupling, one of these equations becomes unnecessary. A few useful examples of the media that satisfy the conditions of decoupling are given.