Background Structure Functions for statistical acoustic propagation characterization

Wavefront distortion can affect the performance of underwater acoustic communication (a-comms) and imaging systems. A measure of wavefront distortion, the background structure functions (BSFs) are functions of sound speed profiles (SSPs) that are functions of depth. Long term, BSFs can use established commercial software to reduce wavefront distortion and forecast phase statistics for coherent systems. Historically, a suite of path-integral, ray tracing, and modal methods replaced the initial methods for statistical acoustics developed in the latter half of the last century. Underwater (UW) acoustics methods provide the amalgamation of deterministic and statistical expressions to help estimate Doppler and delay for UW acoustics by integrating the classical structure functions from the source to the receiver. In the interim years, non-acoustic communications industries used the older methods with algorithms and hardware that alleviated some of the old shortcomings in order to forecast communication performance. For acoustics, the use of databases of BSFs and SSPs recently helped simulate proof-of-concept forecasting of a-comms operating envelopes. These purely statistical BSFs have less than a quarter of the degrees of freedom (DOFs) in classical UW structure functions. Symmetries also drastically reduce the required background DOFs. For decades industry used these purely statistical structure functions to estimate wavefront wander, lensing (ducting), and fade. Commercial methods to estimate comms fade assume the medium has BSFs that are sufficiently symmetric in order to simplify the calculations. While these metrics can require re-calculation at different stations along the propagation path, extra phase screens are compatible with the evolution of computer technology during the past half century. Conditions of acoustical symmetry and invariance allow simplification of the acoustical calculations in most of the deep-water ocean and in littorals under iso-speed conditions. Results from shallow-sea measurements show that background BSFs in the littorals validate the simplified calculations for sufficiently symmetric sound speed fields. However, the complex calculations that arise from removing the simplifications are tractable with recent algorithms. Adaptive wavefront methods can use BSFs with arrays to guide the wavefront through less lossy paths. Nevertheless, even the value of the ability to forecast phase and throughput statistics in locations where measurements or estimates of sound speed fields exist is of adequate value to provide this foundation for the future use of these purely statistical methods.