A mode-based measure of field sensitivity to geoacoustic parameters in weakly range-dependent environments

The most sensitive environmental parameters are often deemed most important because errors and uncertainties in their values are among the most likely sources of error in propagation modeling. The usual “snapshot” investigation of sensitivity (overlaying graphs of the modeled sound field before and after the environment is changed) falls short of measuring sensitivity because it fails to assign a physically meaningful quantity to each parameter, signifying its ability to influence the field. Here a new measure of sensitivity is formulated from the adiabatic-mode theory of sound propagation. The measure is practical because it applies as a statistical rule when the propagation scenario is uncertain. It is insightful because it can be explained physically as the combined effect of (1) a uniform change of the long-range phase common to all modes, (2) a nonuniform (jumbling) of the relative phase between modes, and (3) changes in energy loss. All three work together in a single analytic formulation, or they can be isolated to emphasize their particular roles. The measure is demonstrated for shallow-water environments.