Group velocity along general direction in a general anisotropic medium

An attempt has been made to study the three-dimensional wave propagation in a general anisotropic medium. A procedure is presented to solve the inverse problem of finding the group velocity in a given direction of ray travel, without using numerical differentiation. The phase direction, derived from the given ray direction, is used to calculate phase velocity. Then, such a phase velocity and phase direction are used to calculate group velocity. Analytical expressions are derived for the directional derivatives of phase velocity which are used to calculate group velocity. Algebraic expressions are derived in a computation convenient manner. Newton’s method (without numerical differentiation) for solving a system of two non-linear simultaneous equations is the only numerical method used. The ray directions along which a wave (or energy) can travel with more than one group velocity may be difficult to treat. Variations of phase velocity and group velocity with ray direction in three dimensions are plotted for a hypothetical model of general anisotropic medium