Adapting results in filtering theory to inverse theory, to address the statistics of nonlinear geoacoustic inverse problems

The intrinsically non‐Gaussian statistics of nonlinear inverse problems, including ocean geoacoustic problems, is explored via analytic rather than numerical means. While Monte Carlo Bayesian methods do address the non‐Gaussian statistics in nonlinear inverse problems, they can be very slow, and intuitive interpretation of the results are at times problematic. There is great theoretical overlap between recursive filters/smoothers, such as the extended Kalman filter, and methods of linear and nonlinear geophysical inversion. The use of recursive filters in inversion is not in itself new, but our interest is in adapting statistical developments from one to the other. Classic analytic methods in both filtering theory and inverse theory assume Gaussian probability distributions, but newer nonlinear filters do not all make this assumption and are explored for their potential application to nonlinear inverse problems. The similarities and differences between the frameworks of filtering theory and inverse theory...