Nonlinear refraction traveltime tomography

Abstract A few important issues for performing nonlinear refraction traveltime tomography have been identified. They include the accuracy of the traveltime and raypath calculations for refraction, the physical information in the refraction traveltime curves, and the characteristics of the refraction traveltime errors. Consequently, we develop a shortest path ray-tracing method with an optimized node distribution that can calculate refraction traveltimes and raypaths accurately in any velocity model. We find that structure ambiguity caused by short and long rays in the seismic refraction method may influence the inversion solution significantly. Therefore, we pose a nonlinear inverse problem that explicitly minimizes the misfits of the average slownesses (ratios of traveltimes to the corresponding ray lengths) and the apparent slownesses (derivatives of traveltimes with respect to distance). As a result, we enhance the resolution as well as the convergence speed. To regularize our inverse problem, we use the Tikhonov method to avoid solving an ill-posed inverse problem. Errors in refraction traveltimes are characterized in terms of a common-shot error, a constant deviation for recordings from the same shot, and a relative traveltime-gradient error with zero mean with respect to the true gradient of the traveltime curve. Therefore, we measure the uncertainty of our tomography solution using a nonlinear Monte Carlo approach and compute the posterior model covariance associated with two different types of random data vectors and one random model vector. The nonlinear uncertainty analysis indicates that the resolution of a tomography solution may not correspond to the ray coverage. We apply this tomography technique to image the shallow velocity structure at a coastal site near Boston, Massachusetts. The results are consistent with a subsequent drilling survey.