Acoustic wave propagation in orthorhombic media: Phase velocity, group velocity, and moveout approximations

Abstract

An approximation is of practical interest whenever an exact approach is not available or is too complicated to be used. Kinematic properties of wave propagation in orthorhombic media are generally more complicated than in transversely isotropic media — an issue that emphasizes the necessity of proper approximate equations that keep a balance between accuracy and simplicity. Exact phase velocity equation in orthorhombic media is algebraically too complicated for some practical purposes, even after acoustic assumption. Although the exact phase velocity equation is readily calculated, there is not an explicit equation for the exact group velocity as a function of group angle nor for the traveltime as a function of offset. Accordingly, we have developed new approximate phase velocity, group velocity, and moveout equations for acoustic orthorhombic media in a simple and uniform functional form. They fit to their corresponding exact kinematic properties, within and outside the orthorhombic symmetry planes. We find a higher accuracy of our approximations compared with other existing approximations in a variety of orthorhombic models. As an example, we convert our phase velocity approximation to a dispersion relation in the frequency domain and use it for wavefield modeling in a heterogeneous orthorhombic model. Our dispersion relation is simpler and more accurate than the original equation being in use in the wave extrapolation modeling by low-rank approximation.