An Elasticity Theorem for Heterogeneous Media, with an Example of Body Wave Dispersion in the Earth

An explicit surface integral expression is derived, for the divergence (div u) of elastic displacement in an inhomogeneous anisotropic medium. In isotropic media, simple ray theory methods permit approximate evaluation of the integral; and (to the same order) an approximate relation is found between div u and the irrotational component of u. The resulting formula for P-wave displacement is expected to find application in the study of seismic sources: it is used here to evaluate the frequencydependent interference properties of P-waves, near the shadow boundary of the Earth's core.