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oceanography, that addresses questions in biological, chemical, geological, and physical oceanography.
The rapid, theoretical advancement of sound propaga- tion through ocean internal waves in the 1970s contrasts sharply with the difficulty of carrying out ocean experi- ments to test the theories to better than orders of magnitude. Here a newly proposed acoustic remote- sensing technique by Munk and Wunsch (1979), termed ocean acoustic tomography, comes to the rescue. Ocean acoustic tomography utilizes precisely timed and navi- gated acoustic arrays to observe various acoustic path travel times between the array nodes, allowing a mapping of large to midscale ocean structures that are difficult if not impossible to sample with traditional instruments such as ships and floats (Worcester et al., 2005).
The observed variations in travel times are an indication of variations in ocean temperature along the acoustic paths. Thus, as the ocean warms/cools, the travel times decrease/ increase (Munk et al., 1994). The instrumentation of ocean acoustic tomography is precisely what is needed to quan- tify internal-wave-induced fluctuations because removing timing and navigation errors leaves signal fluctuations only due to ocean effects. In addition, the development of large- aperture vertical arrays proved useful for both fields. In tomography, large vertical apertures provide many addi- tional paths and increased horizontal resolution, whereas in fluctuation studies, the arrays provide a look at the cor- relation properties of the signals in both depth and time.
These acoustic-sensing technologies have been refined over nearly four decades. As an example, Figure 8 shows data from the 2010–2011 Philippine Sea experiment. Here, a six-mooring transceiver array and a water column-span- ning vertical receiver recorded 250-Hz center-frequency broadband transmissions over a whole year for ranges from 125 to 450 km (Figure 8b) (Colosi et al., 2019).
Figure 8a shows an example time front that is defined as the time history of wave front intensity as it sweeps by a vertical receiver at fixed range. Each point of the time front can be associated with a ray path that samples the ocean in a spe- cific way. The early-arriving paths cycle steeply through the ocean, whereas the late-arriving paths are confined closer to the sound-channel axis (Figure 7a). The variation in acoustic intensity along the time front is an indication of scintillation, and there are corresponding phase fluctuations.
Figure 8c shows that the scintillation index (normal- ized intensity variance) increases with the increasing propagation range, indicative of the transition from the unsaturated to the strong fluctuation regime. Phase fluctuations also drive the loss of coherence in depth increasingly so as distance from the source (range) increases (Figure 8d).
Finally, the development of the theoretical and obser- vational understanding of sound propagation through the internal-wave field has important implications for practical applications. Although the subject was born of naval needs (detection, localization, classification), the burgeoning remote-sensing applications in acous- tical oceanography often mean that internal waves are an irreducible noise that limits the recoverable informa- tion. But, at the same time, the acoustic fluctuations carry information about the ocean internal-wave field, a wave field that is an important link in the ocean energy cascade from large to small scales. And last, internal wave effects are an important consideration in the design and imple- mentation of underwater navigation and communication systems, most ambitious of which is an underwater GPS (UGPS) (Van Uffelen, 2021).
Concluding Remarks
This article introduced theoretical and experimental approaches employed by WPRM, particularly for sound propagation in a turbulent atmosphere and fluctuating ocean. Related phenomena occur in other branches of physics, which are amenable to the tools developed by Tatarskii and others. For example, the Earth’s lithoshperic crust is modeled as a stratifed medium with random heterogeneities, which scatters seismic waves (Sato et al., 2012). WPRM predicts the broadening of earthquake codas and peak arrival delays, which are used to retrieve lithospheric statistical properties.
There are also many other examples of WPRM in acoustics. Medical ultrasound tomography (Treeby et al., 2019), which predates tomography in the ocean and atmosphere, enables imaging of soft tissue using the effects of tissue inhomoge- neities on ultrasound attenuation, travel time, and scattering.
Although turbulence and internal waves exemplify con- tinuous random media, many discrete random media are also of interest, such as forests and fish schools. Clapping your hands in a forest creates a long echo, similar to the
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