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Matched-field processing is a way to locate sound sources using receiver arrays. The structure of the sound phase and amplitude between the ocean surface and bottom is intricate across a receiver array and, to a large degree, is a unique function of the source and array locations (Jensen et al., 2011, Chap. 10). To locate the source, the received pattern is compared with patterns synthesized for all candidate source positions. Locations with good matches are considered likely source locations. The environmental conditions are usually complex enough that the patterns are best made with numeri- cal propagation models, but this can be computationally expensive (more on this in Simulations for Inversion).
Physics-based signal-processing research and application also improves with better simulation. A simple dichotomy illustrates the choices one must make when processing signals. Again, considering array receivers, an option is to use classical plane-wave beamforming to analyze com- plex sound arrivals in the ocean (i.e., not plane waves), thus degrading performance because the signals do not match the plane-wave model. Another option is to use the physics (e.g., multipath/multimode, Doppler) to improve performance. Interesting results can be found when this is applied to small-aperture arrays and even single hydro- phones. A popular current method is signal warping based on computed shallow-water waveguide modal dispersion. Figure 2 illustrates how modal dispersion causes a single pulse to morph into multiple pulses as the sound travels. Note that the various modes elongate uniquely. In signal warping, the time axis is adjusted (warped) to separate the modes in the frequency domain, which will work if the computed dispersion matches actual oceanic dispersion (Bonnel et al., 2019).
Simulations for Inversion
Because sound is very sensitive to environmental condi- tions, analyzing recorded sound can yield information about those conditions. This estimation of environmental properties is an example of data inversion (or the inverse problem) that pervades the earth sciences and other fields. To invert, one finds parameters of a natural state descrip- tion that can be connected to a dataset with a modeled process. In ocean acoustic data inversion, the process is wave propagation influenced by the natural state, which must be understood. The understanding is called the for- ward problem and often takes the form of acoustic field prediction in a given environment. It can be solved using propagation models, our main topic.
In many inversion techniques, one must quantify the match between simulated data (called replicas) and experimental data. Replicas are computed for many sets of environmen- tal parameters, and parameters are estimated by looking for the optimal fit between data and replicas. Inversion thus requires (1) powerful optimization algorithms to minimize a misfit function in a multidimensional space (the size of the space is the number of parameters to be estimated) and (2) effective propagation models that will be called on many times during the procedure. In Bayesian inversion, the trend is not only to estimate environmental parameters but also to infer the corresponding uncer- tainties. An approach to this uses Markov Chain Monte Carlo-like sampling methods (Dosso, 2002). It has been used to infer water column properties (Ballard and Becker, 2010), seabed properties (Bonnel et al., 2019), or both at the same time (Warner et al., 2015).
Interestingly, underwater acoustic inversion can have multiple aims. A clear goal is to learn geophysical/oceano- graphic information. We have already seen the tomography example where the objective is to sense ocean temperature structure. On the other hand, another goal for inversion is to infer parameters of a simplified ocean model, this model being physically inaccurate but acoustically equiva- lent to the true one. This specific application is particularly important for real-life users who need to run propagation models, from bioacousticians localizing whales to a navy assessing sonar performance.
Overall, today’s inversion research focuses more on the inverse methods or the inversion results than on the for- ward propagation models. This may indicate that propagation models are (thought to be) reliable enough. That being said, nonlinear inversion involves multiple calls of the forward models (sometimes millions), so fast models are beneficial, and using sophisticated models such as 3-D ones (Lin et al., 2013; Heaney et al., 2017) is impractical. For the same rea- sons, inversion usually does not allow the estimation of large parameter sets (like a range-dependent seabed). An approach to enabling larger efforts is using graphical processing units to run the forward propagation models (Belcourt et al., 2019).
Animal Studies
Locating vocalizing animals is an important step in marine mammal research. Not only is behavioral information provided when the animal is tracked over time, but passive acoustic local- ization is also important for accurate animal density assessment.
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