How quickly does sound attenuate in water?

Attenuation of sound in water in this article is defined as the way in which sound intensity levels decrease with distance.

As this is a long article, the following is a summary of the key points that will be made. Attenuation of sound in water is more rapid than most publicly available plots imply. Furthermore, given the rapid attenuation close to the source (ie as the distance doubles the sound level is roughly halved), seismic sound levels quickly attenuate to levels less than those generated at source by whales or natural processes. For example, as shown in articles on this site, the sound of a breaching humpback whale is the same as a seismic pulse at 68m and the sounds of calving/colliding icebergs are similar to seismic sounds at 1m. In addition, blue whales vocalise at 180-190 dB re 1 µPa(rms)@1m and sperm whales at 235 dB re 1µPa(rms)@1m. These levels are equivalent to seismic sounds within 250m of the source and at the source respectively.

The following discussion provides the scientific background.

Attenuation of sound in water is often discussed in the context of anthropogenic noise and marine life. Statements such as “attenuation of sound in water is slower than in air” and “sound in water can travel thousands of kilometres” often dominate such discussions. However, while both statements are true, they misrepresent the science. Yes, attenuation of sound in water is slower than in air, but it is still fairly rapid in the near-field (ie relatively close to the sound source). Yes, low frequency sounds can travel thousands of kilometres, if the sound gets into the deep sound (or SOFAR) channel, but such sounds are at very low amplitudes and can generally only be detected in very quiet environments. These facts get lost in the heat of any discussion about, for example, seismic surveys and marine life.

Any person involved or interested in this debate should familiarise themselves with the physical principles of the attenuation of sound in water. Unfortunately, it is difficult to access such information and, if it is accessed, acousticians appear to make the terminology so complicated that very few people can readily understand it.

A quick review of public referrals made under the EPBC Act to conduct seismic surveys will show that sound attenuation displays and the sound intensity values used in these referrals are confusing. In fact, while the use of logarithmic (log) scales is logical for the horizontal axis (which shows distance from source) they also give the impression that attenuation is slower than it actually is. For example, the following Figure 1 is figure 5 extracted from referral 2011/5969 on DoE’s website:

Fig 5 from Referral 2011/5969

Fig 1. Extracted from referral 2011/5969 (fig 5) showing modelling sound attenuation in 4 different directions 90 degrees apart

Key points to note regarding the above display:

1. Units used are Sound Exposure Level (SEL) represented in decibels (dB) as dB re 1 µPa2.s (which is the logarithm [to the base 10] of the square of the acoustic pressure integrated over the duration of an air gun pulse);

2. The minimum distance from the source shown on this display is 100m (and the SEL at 100m is approx 185dB re 1 µPa2.s);

3. The source energy levels in the zone from 1m to 99m are not shown on this plot. However, extrapolating the attenuation line back to 1m (a distance on the plot represented by the distance equivalent to that between 0.1km and 10km) gives a source level of approximately 229dB re 1 µPa2.s (which is also the theoretical SEL calculated for this array);

4. Thus, in the first 100m from the source, the SEL drops by about 44dB re 1 µPa2.s, whereas, as can be seen from the plot, it only drops about 6dB in the next 100m, 6dB in the next 200m, a further 6dB in the next 400m and so on (ie. as the distance is doubled, the sound level is roughly halved – note that 6dB steps represent a halving or doubling of energy levels); and

5. Of course, there are variations to the above simple attenuation trends due to a variety of factors and this can be very clearly seen in the red and blue plots in the display where there is very rapid attenuation of sound in the directions up the continental slope (the area of rapid attenuation coincide with the steep slope up to the continental shelf edge). Similarly, the light blue plot “flattens out” over 100km from the source in the oceanward direction where the sound has entered the SOFAR channel.

Another display (Fig 2 below) that appears in several different referrals made under the EPBC Act to conduct seismic surveys shows the measured sound attenuation curves of a variety of seismic arrays used in Australian waters. These measured results are recorded by sea-bed loggers generally deployed for the period before, during and after seismic surveys are conducted. This particular display is Fig 6 from referral 2013/7020.

Measured decay curves

Fig 2. Measured sound attenuation curves from a variety of seismic surveys acquired in Australian waters

This display is also plotted on a log scale along the horizontal axis. Except for one anomalous magenta curve, all curves are less than 180dB re 1 µPa2.s at 100m, which, as can be seen from Fig 1, are about 10dB lower than the theoretical curves for the 4130 cubic inch (cui) array used in that analysis. The difference between measured and modelled curves will be the subject of another article at a later date.  The reason I include this figure is to show simply that measured sound curves correlate with modelled sound curves but, when plotted on a log scale on the horizontal axis, both give an inaccurate impression of the significant attenuation in the near field. This is simply due to log scales being used in the graphical representation for convenience.

Furthermore, this impression of low attenuation is magnified in both figures because the vertical axis, being in dB, is a log scale. If both axes were displayed as linear scales, the actual attenuation shown graphically would be dramatic, especially in the near-field. Unfortunately, as the units are in dB, this is not possible.

The following display, with the horizontal distance plotted on a linear scale, shows the sound levels along one seismic traverse at different distances from a sea-bed logger and has been extracted from a 5-day plot as displayed in an article on sounds in the vicinity of a seismic survey on this site:

Sound attenuation along traverse

Fig 3. Measured sound levels at different distances along a seismic traverse.

Key points about this display are:

i) The horizontal scale on both plots is actually time but it has been converted to distance in metres (ie the vessel speed was known);

ii) The vertical scale on the lower plot is frequency in Hertz (Hz) whereas for the upper plot it is sound level in dB re 1 µPa (this form of dB is different from dB re 1 µPa2.s but I won’t complicate this article with explanations as we are simply looking at attenuation);

iii) The sound level in the lower plot is represented by colour and ranges from 80dB re 1 µPa2/Hz (dark blue) to about 148dB re 1 µPa2/Hz(brown). These values are the sound level values for every 1 Hz of frequency and are called spectral values. These spectral (or component) values are lower than the sound level value of the full frequency range of the signal and need to be integrated (a form of summation) to arrive at the dB levels we are familiar with; and

iv) The top plot shows the overall signal values but, as mentioned above, even these dB values can be represented differently. The red plot is in dB re 1 µPa(p-p) whereas the blue plot is in dB re 1 µPa(rms) meaning that the former represents the peak-trough range of the signal and the latter represents the energy intensity of the signal. An introduction to signal levels can be found on the DOSITS website

Some of the conclusions that can be drawn from this display are:

1. The measured signal, even at 144m barely gets above 140dB re 1 µPa2/Hz and most of this energy is in the 20Hz range. At this distance (ie 144m), the equivalent sound levels in dB re 1 µPa are about 190 (p-p) and just under 180 (rms).

2. The attenuation seen on all 3 plots (spectral, rms and p-p) is rapid, with the dB levels at 4km having dropped to approx 110, 140 and 160 respectively.

3. Both upper and lower plots of Fig 3 give a more realistic impression of the rate of sound attenuation in water than Figs 1 and 2.

4. However, as the vertical axis of the spectral plot is linear (as it is in HZ not dB) it provides a more realistic representation of the rate of attenuation of sound in water than displays that have 1 or 2 log scale axes.

In conclusion, although the attenuation of sound in water is a complex topic, those who are interested should bear in mind two simple principles:

a. double the distance, halve the sound intensity and

b. log scales distort the representation of the actual rate of attenuation.

Perhaps only then will misrepresentation of the science of the attenuation of sound in water will be minimised.

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  1. […] the sounds of breaching whales, Antarctic ice sounds, the reaction of cetaceans to seismic sounds, attenuation of sound in water, etc, is covered in articles on this website. Perhaps this is why seismic personnel often see […]

  2. […] an earlier article entitled “How quickly does sound attenuate in water?“, I provided a series of graphs to demonstrate the different ways, using logarithmic (log) […]

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