Observables and prediction modeling in the presence of ultra‐wideband heterogeneity

Underlying virtually all propagation and scattering models is an intuitive understanding; the acoustic field is observable using a device of a sufficiently small size to obtain a sufficiently dense set of discrete measurements. This assumes the field variation cuts off at an inner length scale larger than the device size, assuring that no information is lost to the inherent spatial averaging in any measurement. This understanding is faulty in the presence of environment heterogeneity observed on an extreme range of length scales. The reason is that all physical devices have finite accuracy, which limits their ability to capture variation on scales significantly larger than their size, in the presence of variation on intermediate scales. A more refined understanding of the ability to observe a field requires multiple devices, an unbounded hierarchy in the limit, to obtain multiple dense sets of discrete ‘‘observables.’’ This, then, suggests a different class of prediction models for environments with ultra...