In 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) scales and a variety of decibel types, that the attenuation (or decay) of sound in water can be represented (or misrepresented!). The attenuation (or decay) of sound in water is simply the fact that it becomes quieter (or lower in intensity) as it travels further from the source.

The key conclusions of the earlier article were that, although the attenuation of sound in water is considered a complex topic, if those who are interested just bear in mind just two simple principles:

a. doubling the distance, halves the sound level; and

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

then misrepresentation of the science of the attenuation of sound in water should be minimised.

The following 3 graphs, in which the same modelled sound attenuation curves are plotted on different logarithmic/linear scale axes, should assist in further visualising that the attenuation (or decay) of sound in water is significantly more rapid in the near-field than standard logarithmic displays appear to show (and hence many eNGOs claim).

log-log graph
Fig 1. Sound attenuation curve plotted on a logarithmic scale (dB) on the vertical axis with distance (m) plotted on a logarithmic scale on the horizontal axis.




First, for those who are interested, some definitions. Rather than explain cylindrical and spherical attenuation in this article, the difference between cylindrical and spherical sound spreading can be found on the Dosits website.  SEL stands for “Sound Exposure Level” and is a measure of energy over a period of time and is represented by the term dB re 1 µPa2.s (which is the logarithm [to the base 10] of the square of the acoustic pressure integrated over a period of time, generally either the duration of the seismic pulse or 1 second). Finally “RAM” stands  for Range-dependent Acoustic Model.

In this first display the sound attenuation curve is plotted using logarithmic scales on both axes. Logarithmic scales are used by scientists/researchers when they have a large range of quantities to display. Such a scale is based on “orders of magnitude”, as opposed to a standard linear scale, so each mark on the scale is the previous mark multiplied by a value (normally 10). In the above graph, the first mark on the horizontal axis is 100(102)m, the second is 1,000(103 – or 10 times more than the first mark)m. The next mark is 10,000(104)m and the final mark is 100,000(105)m.

In a similar way, each mark of the decibel scale on the vertical axis, although it appears to be linear (because it is annotated in decibels whereas decibels are logarithmic), is 10 times larger than the previous mark.

If we change the scale on the horizontal axis to linear, we get the following graph:

loglin graph
Fig 2. Sound attenuation curve plotted on a logarithmic scale (dB) on the vertical axis and distance (m) plotted on a LINEAR scale on the horizontal axis.

Despite these two plots being the same sound attenuation curves, they appear very different.  As opposed to Fig 1 showing that attenuation appears to be roughly a straight line, Fig 2 shows significant attenuation of sound in the near field (ie shorter distances) compared to the far field (ie longer distances).  Note that Fig 2 is plotted over the range from 0m to 50,000m. However, Fig 1 is plotted over the range from 100m to 100,000m.  Those who already had an understanding of logarithmic scales or even those who may have followed my (hopefully!) clear explanation, will now realise why the graph in Fig 1 has been curtailed at 100(102)m. Another mark to the right would take us to 10(101)m. A further mark to the right would take us to just 1m and a further mark to 0.1m. Thus, on a log scale, the distance on the graph representing the range 0.1m to 100m would actually be the same as the distance that represents 100m to 100,000m! Very confusing!?

Not only are distances plotted on a logarithmic scale confusing and do not accurately represent distance (in a linear sense), decibels are even more confusing as they do not intuitively represent changes in sound or pressure levels (in a linear sense). After all, decibels are referenced to a certain pressure level, with the reference level in water (1 micropascal or 1µPa) being different from the reference level in air (20 micropascal or 20µPa). More confusion!

To remove this confusion and represent pressure (or changes in pressure – the very property that creates sound) we need to convert our sound attenuation curves back to pressure units. After all, this was what was measured in the first place (but then the measured data was converted to decibels to enable us to plot a wide range of values).

Thus, changing the vertical axis to linear and retaining the horizontal axis as linear, we get the following:

linlin graph
Fig 3. Sound attenuation curve plotted on a LINEAR scale (pressure units) on the vertical axis and distance (m) plotted on a LINEAR scale on the horizontal axis.

This now becomes a true representation of the way the pressure (or changes in pressure, which produce sound) attenuate (or decay) in water with distance from a source. It also demonstrates that a marine animal would have to be extremely close to the source (and hence be at risk of collision) to be adversely affected by the pressure of seismic sounds.

Hence, why all the fuss?  The science (ie. physics) explains the facts that are observed on a day-to-day basis.