OrthoAcoustic

Numerical analysis of the acoustic wave equation for orthorhombic anisotropy

Orthorhombic anisotropy allows us to add azimiuthul variations, caused primarely by vertical fractures, to the widely recognized and used transversely isotropic with vertical symmetry (VTI) model. In this case, an additional three parameters are needed to describe the medium in the acousitc approximation. As a result, the acoustic orthorhombic anisotropic wave equation is a sixth-order linear partial differential equation with three sets of possible solutions corresponding to the ingoing and outgoing $P$-wave, as well as four other solutons steming from the two-shear wave components, both ingoing and outgoing. Analytical analysis of the solutions of this new equation in a homogeneous medium show that stability of the solutions occur

only when

Similar to the transversely isotropic case, these additional solutions can be lation 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.