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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.
Tariq Alkhalifah (Wed,) studied this question.