An Equivalent Transform Method for Evaluating the Effect of Water-Column Mismatch on Geoacoustic Inversion

An "equivalent transform method" for quantitatively evaluating the effect of water-column mismatch on geoacoustic inversions is presented. This method is based on the concept of error transferral from one medium to another and is derived from linear perturbative inverse theory. To illustrate the method, geoacoustic inversions using adiabatic mode data, including wave numbers, group velocities, and travel times, are considered. In the test cases, both linear and nonlinear internal waves are considered as the causes of the water-column mismatch, and the inversion errors due to the water-column mismatch in each case are discussed. In the case of linear internal waves, range-averaged inversion errors are largely eliminated at the full cycle distance of the internal wave; however, in the case of nonlinear internal waves, the range-averaged inversion errors are accumulated but scaled down with increasing range. Furthermore, the inversion errors produced by water-column mismatch will be large if the modes used for inversion are sensitive to the mismatch; for instance, using higher order modes might lead to increased error even though it would normally improve inversion results. Using lower frequency signal, which penetrates deeper into the bottom, extends the effective depth of the inversion solutions, but this also allows the water-column mismatch to transfer error into the deeper bottom