Nonlinear Refraction Traveltime Tomography

Abstract

We identify a few unique issues that are important for performing a nonlinear refraction traveltime tomography effectively. These include accuracy of traveltime and raypath calculation for a turning ray and physical information in a refraction traveltime curve. Consequently, we develop a shortest path raytracing method with an optimized node distribution that can accurately calculate refraction traveltimes and raypaths in any velocity model. We find that minimizing misfit of refraction traveltimes with the least-squares criterion does not account for the whole physical meaning of a refraction traveltime curve. We therefore pose a different nonlinear inverse problem that explicitly minimizes misfits of both traveltimes (integrated slownesses) and traveltime gradients (apparent slownesses). As a result, we enhance the resolution of the tomographic inversion as well as the convergence speed. We regularize our inverse problem with the Tikhonov method as opposed to applying ad hoc smoothing to keep the inversion stable. The use of the Tikhonov regularization avoids solving an ill-posed problem and allows us to invert an infinite number of unknowns. We apply this tomographic technique to image the shallow velocity structure at a coastal site near Boston, Massachusetts. The results are consistent with a local boring survey.