The factors that determine how much the sound's received level is reduced from its source level
From an AEI report on seismic airguns, which contains footnotes and bibliography, detailing all references .
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Sound is absorbed, scattered, and spread as it moves outward from its source. Researchers look at all of these as factors in "transmission loss," or the reduction in the sound level as it travels. The received level at any given distance is the source level, less transmission loss.
In the simplest models, assuming cylindrical or spherical spreading, the received level decreases simply by virtue of the sound energy being spread over a larger and larger surface area the farther from the source it is. In both spreading models, there is a relatively rapid decrease in the received dB level at close range, followed by a leveling off of the dB value out to many tens or hundreds of kilometers. High frequency sounds quickly fall victim to transmission loss (especially absorption and scattering), while low frequencies can travel vast distances at still-audible levels (see Section 2.3.2 below); in the ideal situation, the transmission loss of a 100Hz sound will nearly level off at about 100dB, so that an airgun noise (over 200dB at the source) will remain over 100dB a thousand kilometers or more away .
There are a number of factors that influence how loud a sound will be as distance increases.
Quieter near surface
Observations of the responses of many marine creatures indicate that they often take advantage of a "sound shadow" that exists near the surface of the sea. As sound waves bounce off the surface of the water from below, they interfere with themselves "destructively," meaning that the high point of the direct wave combines with the low point of a reflected wave to cancel each other out (similar to the way noise-cancellation headphones work). In this case, the cancellation is far from perfect, so there is no ?zone of silence,? but received levels can be significantly lower near the surface, offering refuge to animals escaping dangerous or annoying sound levels below.
Shallower water propagation is worse
In deep waters, sound waves can travel relatively undisturbed, so that transmission loss is mainly a factor of distance (and to some degree, time: gradients of temperature and salinity can influence the speed of the sound waves and thus affect the waveform patterns that are received). In shallow waters, however, the distance between the waters surface and the sea floor is too small for the sound waves, and they begin to break up and become scattered, greatly reducing their received levels if the bathymetry (seafloor topography) is rugged or varied, but allowing for excellent propagation if the seafloor is flat, as a wave guide is created.
Hard bottom/soft bottom radically different
The composition of the seabed plays a significantand hard to predictrole in horizontal sound propagation. Hard surfaces reflect most of the sound energy, while soft surfaces absorb/scatter the sound. So, transmission loss is greater in areas with soft surfaces. Unfortunately, the sea bed often contains patches of both hard and soft areas, making it very difficult to model likely transmission loss, and thus received levels. To take this one step further, models from any one area are likely to be of limited value in another place.
Examples of measured propagation at many km range
McCauley (2000) made direct measurements of the received levels around an active seismic survey vessel, at distances of 1km to 50km. At each distance, there tended to be about a 10dB variation in received level, likely the result of localized transmission loss differences. The two instances of greatest divergence from the overall transmission loss trends were both identified as being related to specific factors (a received level higher than predicted being related to being abeam the ship, where the source level was higher, and a received level lower than predicted being related to an upslope propagation path that increased transmission loss).
Distance, and Mean received level (dB re 1uPa2.s, equivalent energy; increase by 13dB for RMS, 28dB for peak to peak [SEE MEASUREMENT SYSTEMS])
Current regulatory consensus is that received levels of over 180dB (peak to peak) are likely to cause significant impacts on sea creatures; this compares to 152dB in equivalent energy. According to these measurements, then, the zone of significant impact will be out to almost 2 km from the ship. Behavioral, and likely perceptual, impacts are likely at far greater distances.