An acoustic wave equation for orthorhombic anisotropy

Abstract

Using a dispersion relation derived under the acoustic medium assumption, I obtain an acoustic wave equation for orthorhombic media. Although an acoustic wave equation does not strictly describe a wave in anisotropic media, it accurately describes the kinematics of P‐waves. The orthorhombic acoustic wave equation, unlike the transversely isotropic one, is a sixth‐order equation with three sets of complex conjugate solutions. Only one set of these solutions are perturbations of the familiar acoustic wavefield solution for isotropic media for incoming and outgoing P‐waves and, thus, are of interest here. The other two sets of solutions are simply the result of this artificially derived sixth‐order equation.