Straightforward derivation of Hubral’s wavefront curvature differential equation in inhomogeneous isotropic media

Abstract

“Wavefront curvatures in three‐dimensional laterally inhomogeneous media with curved interfaces” (Hubral, 1980, this issue) shows a differential equation [formula (4.1)] which describes the alteration of the wavefront curvature matrix along a raypath in the case of an isotropic velocity v which is an arbitrary function of the locus in the three‐dimensional space. Hubral derives his equation by referring to papers of Popov and Pšenčik (1976, 1978) and Hubral (1979).