Topography-Dependent Eikonal Traveltime Tomography for Upper Crustal Structure Beneath an Irregular Surface

Abstract

Seismic modeling of the crust with nonflat topography can be made by first-arrival traveltime tomography, which faces the challenge of an irregular free surface. A feasible way to deal with this problem consists of expanding the physical space by overlapping a low velocity layer above the irregular surface in order to have a flat topography, besides using the classical eikonal equation solver for traveltime computation. However, the undesirable consequences of this method include seismic ray deviations due to the transition from an irregular surface that is the free boundary to an inner discontinuity lying in the expanded computational space. An alternative solution, called irregular surface flattening, which involves the transformation between curvilinear and Cartesian coordinate systems, has been recently proposed through the formulation of the topography-dependent eikonal equation (TDEE) and a new solver for forward modeling of traveltimes. Based on the solution of this equation, we present topography-dependent eikonal traveltime tomography (hereafter TDETT) for seismic modeling of the upper crust. First-arrival traveltimes are calculated using the TDEE solver and the raypaths with the minimum traveltime that can be found by following the steepest traveltime gradient from the receiver to the source. By solving an algebraic equation system that connects the slowness perturbations with the already determined traveltimes, these variables can be obtained making use of the back-projection algorithm. This working scheme is evaluated through three numerical examples with different topographic complexities that are conducted from synthetic data and a fourth example with somewhat more complicated topography and real data acquired in northeastern Tibet. The comparison of the results obtained by both methods, i.e., physical space expansion above the irregular surface and irregular surface flattening, fully validates the tomography scheme that is proposed to construct seismic velocity models with nonflat topography.