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.

Depth-Recursive Tomography of the Bohemian Massif at the CEL09 Transect—Part A: Resolution Estimates and Deblurring Aspects

“…The idea that the regularized input data can stabilize the ray tomographic inversion is not new (e.g., Zhang et al 1998). They inverted the regularized travel-time curves rather than the single uncorrelated travel times in order to obtain a stable solution for the joint refraction and reflection inversion.…”

“…3c-4 in Flecha et al (2004) or Zhang et al (1998) for synthetic tests. Novotný et al (2009) succeeded in delineating a regional LVZ bound to the root of the Franconian fault that was hit by the KTB superdeep well at a depth of 7-8 km.…”

Near-surface seismic refraction applied to exploring subsurface clay layer at a new mining area in southeast Cairo, Egypt

“…These techniques can broadly be grouped into the following four categories: (1) intercept−time method (Adachi 1954;Barton and Barker 2003;Hales 1958;Hagedoorn 1959), (2) reciprocal or delay-time method (Leung 1995(Leung , 1997(Leung , 2003Palmer 1980;Wyrobek 1956;Sjogren 2000) and (3) ray-tracing method (Jones and Jovanovich 1985;Whiteley 2002Whiteley , 2004, (4) inversion and tomography method (Boschetti et al 1996;Hecht 2003;Hofmann and Schrott 2003;Roach 2003;Schuster and Quintus-Bosz 1993;Sheehan et al 2005;Watanabe et al 1999;Wright 2006;Zhang and Toksöz 1998). Intercept−time methods can be done with a pencil and calculator or, at most, a spread sheet program.…”

Applications of engineering seismology for site characterization

“…By applying a nonlinear traveltime tomography (Zhang and Toksoz, 1997) to the first-arrival times picked from the three shot records (Fig. 4), we estimated a near-surface P-wave velocity-depth model along the receiver spread at each of the 20 locations.…”