On Seismic Imaging: Geodesics, Isochrons, and Fermat's Principle

Abstract

Analytic expressions are derived for the isochrons in an inhomogeneous medium characterized by a linear velocity gradient and for an anisotropic medium characterized by an elliptical velocity dependence. The results were generated for a single surface source and five wellbore receivers over a dipping interface. The traveltime and reflection-point results appear to be sensitive to a given assumption of the velocity field. In complex geological areas the location of the planar reflector is tangent to the convex hull of isochrons and might not correspond to their intersection points since the two concepts need to coincide.