Underwater Acoustic Field Extrapolation: Theory and Sensitivity Analysis.

In some underwater acoustic applications, it is desirable to predict what an acoustic field will be at some distance away from a source. Numerical modeling based on environmental parameters (e.g., sound speed, bathymetry, sediment properties) is one possibility, but the amount of environmental information necessary for accurate long -range modeling is often beyond what is realistically measurable. Actual acoustic measurements are another possibility, but our knowledge of the fields is then limited to the points in the ocean where the sources and receivers are located. We present a hybrid method for predicting acoustic fields that takes limited acoustic measurements and extrapolates them over short ranges using modeled fields. The measured and modeled fields are combined in an integral formulation via a specialization of Huygens' principle. The basic theoretical formulation is stated and analyzed using the theory of normal modes. The formulation leads directly to modal-dependent (grazing angle dependent) "obliquity" factors, which are canceled to first order by averaging with a range derivative-based extrapolation. Sensitivity of the algorithm to the higher order components of the obliquity factors is studied. As with other model-based algorithms, environmental mismatch can degrade the results. The algorithm's sensitivity to mismatch in water column sound speed, and sediment sound speed, attenuation, and density are studied via a perturbational approach. Since the algorithm explicitly contains an integral and the measured field is collected at discrete locations, numerical quadrature techniques are studied. It is shown how undersampling can degrade the quality of the extrapolated fields, and how the spatial sampling required for reliable extrapolation can be obtained. A modal decomposition-based integration method is then shown, where the number of reference elements required is equal to the number of modes that contribute significantly to the fields. A modified version of this formulation can exactly cancel the obliquity factors.