Variational formulation for sensitivity analysis of a two-dimensional energy flux model

Abstract

Energy flux propagation models have demonstrated promising results in efficiently approximating both incoherent and coherent field intensities in range dependent environments [Holland, J. Acoust. Soc. Am. 128, 2596 (2010); Harrison J. Acoust. Soc. Am. 133, 3777 (2013)]. The efficiency of energy flux models is advantageous when applied to solving complex problems in environments that would typically require much more computational effort with other propagation models. Some environmental range dependencies that have been investigated with the energy flux model include sound velocity, bathymetry, and sediment properties. Though comparisons have been made of static solutions between energy flux and other propagation models, there has been limited investigation of energy flux models in regards to variational sensitivity to perturbations in the environment. The applications for variational analyses are broad in a general sense, but the core goal is to capture the robustness of the forward model to perturbative inputs. This study seeks to establish the ground work for defining an adjoint-model-based sensitivity analysis of a 2-D range-dependent energy flux model.