An acoustic wave equation for orthorhombic anisotropy

Tariq Alkhalifah

tariq@sep.stanford.edu

ABSTRACT

Using a dispersion relation derived under the acoustic medium assumption for P-waves in orthorhombic anisotropic media, I obtain an acoustic wave equation valid under the same assumption. Although this assumption is physically impossible for anisotropic media, it results in wave equations that are kinematically and dynamically accurate for elastic media. The orthorhombic acoustic wave equation, unlike the transversely isotropic (TI) one, is a six-order equation with three sets of complex conjugate solutions. Only one set of these solutions are perturbations of the familiar acoustic wavefield solution in isotropic media for in-coming and out-going P-waves, and thus, are of interest here. The other two sets of solutions are simplify the result of this artificially derived sixth order equation, and thus, represent unwanted artifacts. Like in the TI case, these artifacts can be eliminated by placing the source in an isotropic layer, where such artifacts do not exist.