Effect of the Acoustic Environment on Adjoint Sound Speed Inversions

Abstract

The recent prevalence of low cost robotic platforms such as oceanographic gliders has increased the availability of long--term measurements of the ocean environment. Gliders can take direct measurements of the ocean sound speed environment, which is of interest in many ocean acoustic problems, including source localization and tomography. These measurements, however, have a low spatial--temporal resolution that makes them difficult to use directly. These measurements have the potential to provide an accurate environmental parameterization for acoustic inversions, which could in turn be used to measure the sound speed field at a much higher spatial--temporal resolution. This study uses glider measurements to provide the environmental parameterization used in the adjoint inversion method. The adjoint method calculates the gradient of a cost function describing the mismatch between observed data and acoustic model predictions with respect to the ocean sound speed. This gradient is a measure of how changing the sound speed at any point in the acoustic environment would affect this misfit. This cost function and its gradient information is then used as inputs to a numerical optimization routine, which efficiently finds a local minimum. There are two challenges of this method addressed in this study; the first is restricting the search space of this inversion. Proper parameterization of the inversion will ensure that the local minimum found in the numerical optimization routine is the correct result of the inversion. This parameterization allows for the combination of the relative strengths of both methods of measuring the sound speed field, the robust direct measurement of the glider and the near instantaneous result of an acoustic inversion. A covariance matrix is created from glider measurements of the range dependent sound speed field, which is then decomposed into an empirical orthogonal function (EOF) base. The mean profile and the significant EOF bases then form the search space of the adjoint method. The second issue is the proper treatment of the acoustic interaction between the ocean and its sea floor. The adjoint method uses the implicit finite difference form of the Parabolic Equation, which has a few possible bottom treatments. Two simple bottom interface treatments are the local boundary conditions of McDaniel and Lee [J. Acoustic. Soc. Am. 71 , 855-858 (1992)] and the non--local boundary conditions of Papadakis \emph{et al.} [J. Acoustic. Soc. Am. 92 , 2030-2038 (1992)]. Local boundary conditions treat the interface by altering sound speed values at the interface to account for