Nonlinear tomographic inversion by using Wentzel-Kramers-Brillouin modal condition

In the horizontal refraction tomography (HRT) scheme [A. G. Voronovich and E. C. Shang, J. Acoust. Sec. Am. 98, 2708-2716 (1995)], the 3-D tomographic inversion is performed in two stages: (1) retrieving the modal wave numbers k(m)(x,y) in the horizontal plane, and (2) reconstructing the vertical sound-speed profile (SSP) at each node of the horizontal plane based on a set of retrieved modal wave numbers k(m)(x,y). Usually, a nonlinear approach must be considered for the 1-D vertical inversion of the second stage. In this paper, a nonlinear inversion method based on the WKB modal condition is proposed. Using the WKB modal condition has the following advantages: (a) it is efficient because the data k(m)(x,y) can be matched directly to the SSP without a model-based replica calculation; (b) it works even when just a few modes are available; and (c) the error of the inversion can be estimated analytically. Some results of the simulation to verify the concept are presented. (C) 1997 Acoustical Society of America. [S0001-4966(97)04512-8].