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$$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.

敏感性分析是分析多参数模型的强大工具。例如，Fisher 信息矩阵 (FIM) 和 Cramér–Rao 界 (CRB) 涉及正演模型关于参数的导数。然而，这些导数在海洋声学模型中很难估计。这项工作提出了一种与频率无关的方法，使用基于物理的参数预处理和理查森外推法准确估计数值导数。该方法通过 50-400 传输损耗的案例研究得到验证。$$Hz 频带来自沉积物参数的与范围无关的简正模态模型。结果证明了该方法在获得与模型灵敏度和参数不确定性相关的 Cramér–Rao 界 (CRB) 方面的实用性，从而揭示了模型中参数的相关性。该方法是一种通用工具，可以为不同应用中的反问题的模型选择和实验设计提供信息。