Ray tracing for qP rays in a linearized general (21 parameter) anisotropic medium is investigated. A smoothly varying inhomogeneous medium is initially assumed and the axes of anisotropy within the layers are allowed to be oriented at arbitrary angles with respect to the model coordinates. As in almost all applications of ray tracing the two point problem is the most useful. That is given a source and receiver location within a anisotropic medium, determine the ray path(s) between the two points. This introduces two coupled nonlinear equations which must be solved. Initially, the medium will be chosen to be a smoothly varying inhomogeneous anisotropic medium with no rotations of the axes. These assumptions may appear to be quite restrictive; however, it would seem to be a reasonable foundation upon which to advance to more complicated media types within the context of qP ray propagation in an orthorhombic anisotropic structure. The density normalized anisotropic parameters used to describe an orthorhombic media, 2 which have the dimensions of ( velocity ) , will be in Voigt notation, Aij , as this notation is familiar. One of the applications of this ray tracing method is for Born-Kirchoff migration, so that some attention will be afforded that topic.
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