Circular Wavefront Assumptions for Gridded Traveltime Computations

John C. Bancroft

Traveltime computations are an integral part of modelling and imaging seismic data by providing efficient kinematic information on the location of propagated energy. The traveltimes may be computed analytically using simplifying assumptions, or may be estimated on a complex geological structure using raytracing or gridded traveltimes. A basic requirement for the propagation of gridded traveltimes is the estimation of one point on a corner of a square, given the traveltimes on the other three corners. A number of solutions are available to solve for the unknown time and are based on either a planewave assumption, a finite difference solution to the Eikonal equation, or an assumption that the wavefront at the square is curved. A solution for a curved wavefront assumption requires estimating the center of curvature, and requires solving a quartic equation. An alternate method is presented to estimate the center of curvature for a curved wavefront that uses an iterative procedure and does not require solving the quartic equation.