Accurate Broadband Gradient Estimates Enable Local Sensitivity Analysis of Ocean Acoustic Models

Abstract

Sensitivity analysis is a powerful tool for analyzing multi-parameter models. For example, the Fisher information matrix (FIM) and the Cramér–Rao bound (CRB) involve derivatives of a forward model with respect to parameters. However, these derivatives are difficult to estimate in ocean acoustic models. This work presents a frequency-agnostic methodology for accurately estimating numerical derivatives using physics-based parameter preconditioning and Richardson extrapolation. The methodology is validated on a case study of transmission loss in the 50–400[Formula: see text]Hz band from a range-independent normal mode model for parameters of the sediment. Results demonstrate the utility of this methodology for obtaining Cramér–Rao bound (CRB) related to both model sensitivities and parameter uncertainties, which reveal parameter correlation in the model. This methodology is a general tool that can inform model selection and experimental design for inverse problems in different applications.