where c0 = 1,500ms-1 is a reference sound speed, z the depth below the pressure-
release surface, L the channel depth, and r the range from the source; l1 and l2 are parameters with the values l1 = 0.032L and l2 = 0.016L.
Consider two cases:
Case 4: Low-frequency, shallow water f = 25 Hz (frequency), L = 500 km (channel depth), R = 4 km (range coverage).
Case 5: High-frequency, deep water f = 100 Hz (frequency), L = 3 km (channel depth), R = 20 km (range coverage).
Figure 11.2 Analytical benchmark problem: plane-parallel waveguide for cases 4 and 5 (Jensen and Ferla, 1988).
The field should be computed for both source and receiver at depth z = L/2.
propagation paths such as bottom-reflected paths, bottom-refracted paths and Lloyd's Mirror interference. Ainslie and Harrison (1990) further demonstrated the utility of these analytical tools in assessing the performance of numerical models of acoustic propagation. They accomplished this by combining the intensity contributions from the individual propagation paths appropriate for any particular ocean environment and sonar system geometry. This approach allowed a path-by-path analysis of numerical model performance and illuminated any modeling pathologies in an instructive fashion. These tools were subsequently organized into a highly interactive sonar model called INSIGHT (Packman etal, 1992). (INSIGHT is described in more detail in Chapter 10, specifically Table 10.6.) The ability to alter a variety of environmental or sonar system parameters interactively and then rapidly visualize the resulting impacts on system performance makes INSIGHT especially attractive for instructional purposes.
Quantitative accuracy assessments of propagation models can be accommodated according to two procedures: difference techniques and figure of merit (FOM) techniques (McGirr, 1979).
Difference techniques measure the distance between the model prediction and a standard (which can comprise field measurements or outputs from other models) in terms of decibel differences at a given range, or over a set
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