A normalmode formula for the derivative of a waveguide pressure field with respect to an arbitrary threedimensional sound speed perturbation
Abstract
Semianalytic expressions are derived for the first order derivative of a pressure field in a laterally homogeneous depth waveguide, with respect to an arbitrary threedimensional refractive index perturbation in either the water column or ocean bottom. These expressions for the environmental derivative, derived using an adjoint method, require a threedimensional spatial correlation between two Greens functions, weighted by an environmental parameter basis function, with the Greens functions expressed in terms of normal modes. When a particular set of orthogonal spatial basis functions is chosen, the threedimensional spatial integral can be converted into a set of onedimensional integrations over depth and azimuth. The use of the orthogonal basis permits environmental derivatives to be computed for any arbitrary soundspeed perturbation. To illustrate the formulas, a sensitivity study is presented that explores the impact of threedimensional plane wave and cylindrical perturbations on the environmental derivative. Under certain circumstances it is found that perturbation components outside the vertical plane connecting the source and receiver have nonnegligible effects on the pressure derivative. Potential applications of these formulas include benchmarking threedimensional propagation codes, computing CramerRao bounds for threedimensional environmental parameter estimates, and potentially inverting for small threedimensional refractive index distributions.
 Publication:

Acoustical Society of America Journal
 Pub Date:
 October 2003
 DOI:
 10.1121/1.4777452
 Bibcode:
 2003ASAJ..114.2376T