Sensitivity analysis of normal mode algorithms using automatic differentiation

Acoustic propagation underwater is affected by dynamic and spatial variations of the sound speed, both of which can be observed in underwater environments. In this work, a differentiable implementation of the KRAKEN normal mode model is presented. By applying automatic differentiation to the discretized algebraic eigenvalue problem, we obtain sensitivities of every modal quantity with respect to a full set of geoacoustic parameters and frequency. These sensitivities are accurate to machine precision. This opens gradient-based methods for inversion purposes, such as source localization and geoacoustic inversion. The utility of this approach is demonstrated by performing sensitivity analyses on classical benchmark problems. These analyses provide insight into parameter significance, validate our implementation, and offer a foundation for developing more efficient gradient-based inversion techniques.