default Multipath pulse shapes with refraction

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Multipath pulse shapes with refraction. NURC-FR-2006-005. April 2006.

All long range sonars have to contend with the effects of multipath propagation. One effect is that an impulse from a remote source or a reflected impulse from a point-like target will be significantly broadened. For example, in isovelocity water it has already been shown that one expects the tail of the pulse to fall off linearly in dBs with a decay constant that depends only on the bottom reflection properties and does not depend on the range of the target. Furthermore if neither sonar nor target have significant vertical directionality then the pulse shape is independent of their properties too. This finding has important implications for the design of sonars since integration times need to be matched to the characteristic arrivals of a target in its environment. The benefit of analytical solutions is that behaviour becomes immediately clear without having to cover an ndimensional parameter space. In addition one can make generalisations which would otherwise be impossible. This report extends the work to investigate the effects of upward or downward refraction. The known angle behaviour of the multipath arrivals can be converted into a time dependence to reveal the multipath pulse shape for a remote source (one-way path) or a target (two-way path). Exact solutions can be calculated numerically, explicit closed-form approximations are given for oneway paths, and these are converted to two-way paths by numerical convolution.