An eikonal-based formulation for traveltime perturbation with respect to the source location

Abstract

Traveltime calculations amount to solving the nonlinear eikonal equation for a given source location. The relationship between the eikonal solution and its perturbations is analyzed with respect to the source location and a partial differential equation is developed that relates the traveltime field for one source location to that for a nearby source. This linear first-order equation in one form depends on lateral changes in velocity and in another form is independent of the velocity field and relies on second-order derivatives of the original traveltime field. For stable finite-difference calculations, this requires the velocity field to be smooth in a sense similar to ray-tracing requirements. Our formulation for traveltime perturbation has several potential applications, such that as traveltime calculation by source-location perturbation, velocity-independent interpolation including datuming, and velocity estimation. Additionally, higher-order expansions provide parameters necessary for Gaussian-beam computations.