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Linear acoustic sensitivity kernels and their applications in shallow water environments

Abstract

Time of arrival information from acoustic transmissions is the primary means through which ocean sound-speed structure is estimated. While initially limited to large scale coarse observations using ray theory to model the propagation of sound through the environment, ocean acoustic tomography evolved to incorporate a normal-mode representation of observed peak-arrivals. This wave- theoretic approach was enhanced, using the first Born approximation to perturbations in the wave equation, producing the travel-time sensitivity kernel (TSK): a linear relationship between sound-speed variations and observed changes in arrival times. This dissertation extends sensitivity kernel analysis to both the amplitude and phase of complex-demodulated broadband acoustic transmissions, producing both a qualitative and quantitative picture of how ocean sound-speed variability affects acoustic observations, and complementing prior work on travel-time sensitivity. The linearity and information content of these kernels is explored in simulation for a 3--4̃kHz broadband pulse transmission through a 1̃km shallow-water Pekeris waveguide, and in simulated inversions with a more realistic summer-type sound-speed profile, the results from which demonstrate the additional information amplitude contains over phase data alone. Differences in phase measurements were assumed to be directly relatable to travel-time changes, and thus the phase sensitivity kernel was expected to represent the same details as the travel-time sensitivity kernel. However, even a cursory visual inspection of the two kernel types shows that they have different spatial structures and hence different sensitivities to changes in the environment. A numerical survey was conducted comparing the performance of these sensitivity kernels (along with amplitude) to observations from perturbed simulations - including a synthetic time-evolving ocean - and the results suggest that phase and peak travel-time do indeed diverge in the presence of more complicated ocean sound-speed structure, with phase being the more linear observable. Additionally, the phase-derived sensitivity kernel is shown to be a better estimator of travel-time than the TSK, for which a possible explanation is suggested. The Born approximation has also been used to derive the acoustic sensitivity to perturbations at the boundary of an environment, in contrast to the volume perturbations discussed before. A sensitivity kernel for surface scattering is presented here, along with a numerical and experimental investigation of the acoustic response to surface displacements in an ultrasonic scale waveguide. The results are presented in both point-to- point and beam-to-beam formats, and suggest the potential use of sensitivity analysis in inverting for sea-surface structure

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