Frechet derivatives for shallow water ocean acoustic inverse problems

Abstract

For any inverse problem, finding a model fitting the data is only half the problem. Most inverse problems of interest in ocean acoustics yield nonunique model solutions, and involve inevitable trade‐offs between model and data resolution and variance. Problems of uniqueness and resolution and variance trade‐offs can be addressed by examining the Frechet derivatives of the model‐data functional with respect to the model variables. Tarantola [Inverse Problem Theory (Elsevier, Amsterdam, 1987), p. 613] published analytical formulas for the basic derivatives, e.g., derivatives of pressure with respect to elastic moduli and density. Other derivatives of interest, such as the derivative of transmission loss with respect to attenuation, can be easily constructed using the chain rule. For a range independent medium the analytical formulas involve only the Green’s function and the vertical derivative of the Green’s function for the medium. A crucial advantage of the analytical formulas for the Frechet derivatives ...