Regularized Inversion for Towed-Array Shape Estimation

Abstract

This chapter describes a new approach to the inverse problem of estimating the shape of a ship-towed hydrophone array using near-field acoustic measurements. The data consist of the relative travel times of arrivals along direct and reflected paths from sources deployed by two consort ships maintaining station with the moving tow ship (the “dual-shot method”). Previous inversion algorithms typically apply least-squares methods based on simplifying assumptions, such as straight-line propagation and exact knowledge of the source positions. Here, a regularized inversion is developed based on ray theory, with the source positions included as unknown parameters subject to a priori estimates and uncertainties. In addition, a minimum-structure array shape is determined by minimizing the three-dimensional curvature subject to fitting the data to a statistically meaningful level, thereby reducing spurious fluctuations (roughness) in the solution. Finally, the effect of the survey geometry is investigated by defining a mean sensor-position error measure based on the a posteriori uncertainty of the inversion. The optimal source configuration is determined by minimizing this error with respect to the source positions using an efficient hybrid optimization algorithm. The inversion and optimization procedures are illustrated using realistic synthetic examples.