Velocity rays for heterogeneous anisotropic media: Theory and implementation

Abstract

The surface of equal two-way time referred to as the isochron is a fundamental concept in seismic imaging. The shape of an isochron depends on the source and receiver locations, on the wave type, and on the parameters constituting the seismic velocity model. A perturbation of a parameter of the velocity model forces the isochron points to move along trajectories called velocity rays, with the selected model parameter as the variable along the rays. Based on earlier work describing first-order approximations to velocity rays, I develop a general theory for velocity rays valid for 3D heterogeneous and anisotropic velocity models. By this theory, velocity rays can be obtained in a way similar to the way conventional rays are computed by numeric integration of a system of ordinary differential equations (ODEs). The process is organized with ODE solvers on two levels, where the upper level is model independent. The lower level includes conventional one-way kinematic and dynamic tracing of source and receiver rays, as well as calculation of ray perturbation quantities. Accurate velocity rays are expected to be useful for perturbation of reflectors mapped from the time domain to the depth domain, for remigration of seismic images in the depth domain, and for velocity model updating.