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Figure 8 illustrates verifi- cation vis-à-vis a non-FE analytical method, for the problem of scattering of a plane wave from a spheri- cal steel shell resting on the sediment (cf. Figure 6). The geometry of a sphere is very simple, so this problem is amenable to other, non-FE solution techniques, such as the T- matrix method, which is limited to very simple geo- metric shapes. The math- ematical formalism and computer codes are com- pletely different for FE and T-matrix analyses.
Since the sphere and its
environment are axisym-
metric about the vertical
(dashed line), the back-
scattered pressure is independent of the aspect angle, θ, so verification only needs to be done as a function of fre- quency. The two solutions in Figure 8, for the magnitude of the backscattered pressure vs. frequency, agree to about 3 significant figures over the entire three octaves of frequency, including the sharp spikes. Such strong agreements provide confidence in both mathematical techniques.
Validation
Validation is accomplished by comparing computer model predictions with data measured in experiments with real objects. This tests whether the correct physics is being used in the computer models (cf. Figure 7). For example, are Equations (2) and (3) adequate to capture all phenomena of interest or are additional equations necessary? Are there physical features in the real object that were intentionally omitted from the model to simplify the modeling, but per- haps shouldn’t have been omitted? Has all the experimen- tal equipment been calibrated properly? Validation tests the physics in the model against the real world, which involves ranges of uncertainty in physical properties, experimental imprecision, etc. Therefore, accuracies are generally much lower than those for verification; agreements to within a few dB are often considered very good.
Figure 10. (a) Fish and school of fish (cf. Figure 1). (b) Unexploded artillery shell partially buried in sediment. (c) Rock, mine and concrete conduit pipe on sediment (cf. Figure 2). (d) Unexploded Howitzer shells on sediment and bullet partially buried.
Figure 9 illustrates validation vis-à-vis experimental data, for the problem of scattering of a plane wave from a solid aluminum cylinder resting on the sediment (Williams et al, 2010). There is very good agreement (to within about 3 dB) over almost the entire range of frequencies and aspect angles. This provides some confidence that the computer simulation is based on the correct physics.
Some Models of Realistic Objects
This article has used simple objects – spheres and cylinders – to explain and illustrate the physics, mathematics and FE concepts for the computer simulation of acoustic scattering from submerged objects. This concluding section shows a variety of images from models of more realistic objects, all of which used the above-described techniques. In addition to these, much more complicated underwater structures have also been modeled, which have included a considerable amount of interior structural detail.
The Way Forward
The current PC-ACOLOR computer simulation system takes one or two days to compute a typical high-fidelity acoustic signature template using a dedicated in-house rack computer with 25 quad-core processors. This pace has been
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