Azimuthally dependent kinematic properties of orthorhombic media

An orthorhombic velocity model covers anisotropy and vertical/horizontal heterogeneity in the uniform 3D framework. It is important to define the azimuthal dependence of kinematic parameters of this model in the phase and group domains. I have derived equations for azimuthal dependent anellipticity in orthorhombic media and a simple equation to link the group and phase azimuths at zero horizontal slowness projection (zero offset). I found that the orthorhombic media cannot be treated as azimuthally dependent transversely isotropic media. To define the effective kinematic properties from a multilayered orthorhombic medium is a nontrivial task, and I have developed an approximate least-squares solution for that problem. Numerical examples with the orthorhombic model and its special cases (a transversely isotropic model with vertical and horizontal symmetry axes and an elliptical isotropic model) were used to illustrate the effect of the individual orientation of symmetry planes on the effective kinematic properties.