Scalar and Vector Invariants of Rays and Wave Fronts in the Three-Dimensional Inhomogeneous Anisotropic Media

Local geometric and kinematic characteristics of body waves are considered for a general case of 3-D inhomogeneous arbitrary anisotropic media. Equations written in a matrix form are obtained for continuation of the wave front fundamental tensors along the ray. As against earlier works, coefficients in the equations involve phase velocities only, alongside with unit normal vectors and main directions at the wave front surface. A new equation of geometrical spreading is derived and presented in a simple form. Relations for a set of second derivatives of the eikonal are deduced using metric properties of unique coordinate systems (ray and ray-centered). Curvature and torsion formulas are written in a compact form, invariant with respect to coordinate system and anisotropy type options.