This study presents the theoretical framework for variational data assimilation of acoustic pressure observations into an acoustic propagation model, namely, the range dependent acoustic model (RAM). RAM uses the split-step Padé algorithm to solve the parabolic equation. The assimilation consists of minimizing a weighted least squares cost function that includes discrepancies between the model solution and the observations. The minimization process, which uses the principle of variations, requires the derivation of the tangent linear and adjoint models of the RAM. The mathematical derivations are presented here, and, for the sake of brevity, a companion study presents the numerical implementation and results from the assimilation simulated acoustic pressure observations.
Signal excess (SE) is often used as a metric for determining acoustic performance through a waveguide or over an area. This quantity can limit the capability to assess the environment because SE is computed given a single acoustic source, receiver and frequency, and is a function of range from the source, thereby limiting the scenarios for which the environment can be assessed as well as the ability to visualize it over an area. Integrated SE (ISE) with phase tracking is proposed as an improved metric for evaluation of acoustic performance. For a given source location (in latitude and longitude), the SE is integrated over all possible source depths, a band of frequencies, and bands of ranges. Additionally, the phase variations across the regions are tracked. This metric is compared to various traditional SE fields and is shown to provide a better representation of the overall acoustic properties of a waveguide and an area. The ISE and the original SE are also examined across an ensemble of sound speeds and the variations of the acoustic environment are characterized. [The author appreciates and acknowledges the funding support from the Naval Research Laboratory Base Program.]
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.