Analytic description of P-wave ray direction and polarization in orthorhombic media

Modeling and inversion of seismic signatures in azimuthally anisotropic media is of primary importance in seismic characterization of fracture networks. The formalism developed here provides a convenient way for studying the behavior of group (ray) velocity and polarization in models with orthorhombic symmetry. The expressions for the group-velocity and polarization vectors become particularly simple in the coordinate system associated with the vertical plane that contains the phase-velocity vector. For example, the two "in-plane" components of the exact group-velocity vector can be obtained from phase velocity using the well-known equations for transversely isotropic media with a vertical symmetry axis (VTI). Due to the presence of azimuthal velocity variation, the group-velocity vector acquires an "out-of-plane" component that also has a concise analytic representation. To understand the influence of the anisotropy parameters on the orientation of the group-velocity and polarization vectors, we derive linearized weak-anisotropy approximations based on Tsvankin's notation for orthorhombic media. Despite the influence of azimuthal anisotropy, the relationship between the P-wave group-velocity and polarization directions in orthorhombic media is similar to that in TI media. The group-velocity and polarization vectors deviate from the slowness vector in the same direction (both in the vertical plane and azimuthally) and usually are close to each other; in this sense, P-wave polarization in orthorhombic media of geologic significance is almost "isotropic." This conclusion is in agreement with existing numerical results and is further verified h ere by modeling for orthorhombic media with substantial anisotropy.