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Computational Acoustics in Oceanography
 Figure 4. The 2-D time-sensitivity kernels for two different sound frequencies. The source is at left and the receiver is at right and are connected by a sound channel-trapped ray path continuously curving toward the sound speed minimum. (Two paths connect the source and receiver, each corresponding to an arrival.) Top: kernel for 250 Hz; bottom: kernel for 75 Hz. The bandwidth is 18.75 Hz. The alternating bands of color signify delay or advance of sound with respect to a positive perturbation of sound speed at the location. From Dzieciuch et al., 2013.
“line-of sight” model for the path (Huang et al., 2019), but long-range sensing requires a propagation model that yields the path taken by the sound (e.g., in the sound channel).
Ray tracing produces basic paths, but new computational methods give the so-called travel time-sensitivity kernel (Dzieciuch et al., 2013), which maps out locations where propagating sound is sensitive to the sound speed (mapping in a sense “where the sound goes,” although that is a simpli- fied notion for sound propagation). Figure 4 shows a kernel example. The wave nature of sound means that it cannot be sensitive to only an infinitesimal ray but instead responds to a broader zone where the phase is somewhat coherent. A key point is that the way the sound propagates is critical to the inverse problem, and the more precise this can be
computed, the better understood the tomographic inversion will be. For an ocean volume of arbitrary sound speed struc- ture c(x,y,z,t), the most trustworthy way to compute the kernel is with a full-wave computational simulation. This is because the kernel is a function of the geometry of the sound field itself (the structure of sound intensity and phase throughout the entire region). Here, the dueling particle and full-wave models of (sound) wave propagation, with Newton’s ray model treating waves as particles, meet again. In this situation, the ray model is a useful tool, but some- times a better result can be obtained with the full model.
The kernel arguments apply to generalized sound governed by the wave equation. But situations of propagation with strong bottom interaction and distance many, many times the water depth can instead be analyzed using normal modes. In the 1960 Perth, Australia, to Bermuda propa- gation study, sound from an explosive source (no longer permitted) was recorded near Bermuda about 20,000 km away about 13,360 s later. The arrivals were explained using adiabatic modal propagation (Heaney et al., 1991). The computation of rays on earth for propagating modes was essential to show how the sound moved and sensed an average sound speed (temperature proxy) because with- out horizontal modal ray refraction from temperature gradients, no sound could pass both south of Africa and north of Brazil. A similar modal study was subsequently performed with a PE (Collins et al., 1995), with different numerical strengths.
Signal-Processing Research
Detecting signals of interest, localizing the source point of the signal, and tracking source position over time are tasks common to many wave-based remote-sensing and surveillance systems. Research into improving methods for these using underwater sound has leaned on computational methods.
Detection is the first-order operation. In Figure 1, white areas have low sound energy, and in the presence of noise, sound from the modeled source would not be detectable there. On the other hand, many locations have ample sound for detec- tion. If currents are weak, sound propagation is reciprocal, so that one can see from an image like Figure 1 where sources would be detectable with a receiver at the modeled source position. Once detected, a source can be tracked over time if consistently received. The consistency of sound can be estimated and trackability evaluated by analyzing synthetic sound propagation patterns.
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