Closed-form and Numerical Reverberation and Propagation: Inclusion of Convergence Effects

• Main Author: Harrison, Chris
• Other Authors: CENTRE FOR MARITIME RESEARCH AND EXPERIMENTATION LA SPEZIA (ITALY)
• Format: Text
• Language: English
• Published: 2013
• Subjects: Numerical Mathematics; Acoustics; Fluid Mechanics; *ACOUSTIC REFRACTION; *CONVERGENCE; *NUMERICAL METHODS AND PROCEDURES; *PROPAGATION; *REVERBERATION; AMPLITUDE; DEPTH; EIGENVALUES; FLUX(RATE); RANGE-DEPENDENT ENVIRONMENTS; ARTEMIS MODEL; ORCA MODEL; RAY CYCLE DISTANCE; ENERGY FLUX; Orca
• Online Access: http://www.dtic.mil/docs/citations/ADA598651; http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA598651

The flux formulation of propagation has already been used to calculate bistatic, range-dependent reverberation, target echo, and signal excess very efficiently in a model developed by Harrison called Artemis. This model is used in the operational planning aid MSTPA at CMRE. Propagation in this formulation behaves like acoustic energy flux and falls off monotonically with range. The goal of the ONR-funded work is to improve the propagation accuracy by including convergence and focusing effects in a range-dependent environment without compromising the simplicity and efficiency of the approach. The objective has been first to write out the theory for the range-independent case, i.e. start with the modulus-square of the coherent mode sum and reject rapidly oscillating terms to leave fluctuations on a scale of a ray cycle distance. These formulations have been evaluated in Matlab and compared with each other and with runs of other well-established models, in this case the normal mode model Orca. In the second part of this work the theory is extended to range-dependent environments and to include reverberation. The final goal is to document the work and supply updated code for the Artemis model. The flux method is exactly equivalent to an incoherent mode sum with only the smooth amplitude of WKB modes and a high mode density (i.e. treated as a mode continuum). One can start the derivation instead with the modulus-square of the coherent mode sum but retain some of the cross-terms instead of rejecting them all, as in the incoherent sum. It can be shown that the ray cycle distance is related to the difference between adjacent mode eigenvalues, so retaining just these terms adds a ray convergence peak structure to the otherwise monotonic decay. This theory with some examples was documented in Refs 1 and 2. The major task now is to extend this theory to operate in range-dependent environments, to include reverberation, and finally to embed it in the model Artemis.