Linearization of the matched field processing approach to acoustic tomography

Abstract

This paper continues the approach presented in Tolstoy et al. [J. Acoust. Soc. Am. 89, 1119–1127 (1991)] but offers a much improved inversion technique, i.e., a linearization of the problem which reformats the computations in terms of a simple nonsquare matrix inversion for an overdetermined system. This work was motivated by the desire to improve upon the speed and accuracy of the original algorithm that had a tendency to stall unpredictably [Tolstoy and Frazer, in Computational Acoustics, edited by D. Lee, A. Cakmak, and R. Vichnevetsky (North-Holland, Amsterdam, 1991)]. This work has the additional bonus that sound-speed accuracies are now an order of magnitude better than the earlier technique. In addition, calculations confirm that for simulations with white, Gaussian, uncorrelated noise the linear/Bartlett processor results are identical to those of the minimum-variance/Capon processor. Finally, optimal source–receiver configurations have been determined by exhaustively computing the condition numbers for the associated matrices in the new linear formulation. Simulation results with the new linearization plus matrix inversion scheme show that three arrays located at optimal coordinates in a 250×250-km ocean region with shot sources distributed around the perimeter can result in 3-D sound-speed profiles determined to accuracies better than 0.07 m/s and better than 0.03 m/s for four arrays located at optimal coordinates (assuming perfect knowledge of sound-speed profiles at source and array coordinates, no array deformations, perfect elimination of bottom interacting energy). Such accuracies are not to be expected under experimental conditions.