Accurate broadband gradient estimates enable local sensitivity analysis of ocean acoustic models

Sensitivity analysis is a powerful tool for analyzing multi-parameter models. For example, the Fisher information matrix (FIM) and the Cramer-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 50-400Hz band from a range-independent normal mode model for parameters of the sediment. Results demonstrate the utility of this methodology for obtaining Cramer-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.