A 3D reflection ray-tracing method based on linear traveltime perturbation interpolation

Abstract

The linear traveltime interpolation (LTI) method, one of the common methods to calculate the wavefront traveltimes and the raypaths in complex media, is based on the assumption that the traveltime varies linearly along each cell boundary of a discrete model. The linear assumption may result in large calculation errors when the cell size is large. To solve this problem, we have adopted a linear traveltime perturbation interpolation (LTPI) method. In LTPI, the original traveltime is decomposed into two parts: a reference traveltime and a traveltime perturbation. The reference traveltime, being one propagating in the equivalent homogeneous medium, varies nonlinearly. The traveltime perturbation, defined as the difference between the original and reference traveltimes, is assumed to be linear along each cell boundary. The traveltime perturbation is much less than the reference traveltime; therefore, the original traveltime keeps its nonlinearity. We modify LTPI to suit to irregular hexahedral cells for simulating the undulating interfaces more precisely. By combining the modified LTPI with the wavefront group-marching method, we have developed a reflection ray-tracing method in 3D complex media. Numerical experiments indicate that the modified LTPI is more accurate than LTI in computing wavefront traveltimes and raypaths. Besides, the modified LTPI performs more consistently than LTI in different grid spacing. Therefore, under a certain accuracy requirement, the modified LTPI is more efficient than LTI.