A split-step Padé solution is derived for the parabolic equation (PE) method. Higher-order Padé approximations are used to reduce both numerical errors and asymptotic errors (e.g., phase errors due to wide-angle propagation). This approach is approximately two orders of magnitude faster than solutions based on Padé approximations that account for asymptotic errors but not numerical errors. In contrast to the split-step Fourier solution, which achieves similar efficiency for some problems, the split-step Padé solution is valid for problems involving very wide propagation angles, large depth variations in the properties of the waveguide, and elastic ocean bottoms. The split-step Padé solution is practical for global-scale problems.

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Conventional matched-field processing (MFP) requires accurate knowledge of the ocean-acoustic environment. Focalization, which simultaneously focuses and localizes, eliminates this stringent requirement by including the environment in the parameter search space. This generalization of MFP involves defining an appropriate high-resolution cost function, parametrizing the search space of the environment and source, constructing solutions of the wave equation, and utilizing a nonlinear optimization method to search the parameter landscape for the global minimum of the cost function. Focalization is implemented using cost functions based on ray theory and wave theory, empirical orthogonal functions for the environmental description, and simulated annealing for optimization. Numerical simulations are presented to demonstrate the feasibility of focalization.

Db measured with the BOD POD was higher than the criterion HW, thus yielding lower %fat scores for the BOD POD. In addition, BOD POD determined %fat was lower than DXA and 3C determined values in a subgroup of subjects. Assessment of %fat using the BOD POD is reliable and requires minimal technical expertise; however, in this study of collegiate football players, %fat values were underpredicted when compared to HW, DXA, and the 3C model.