Author: Dr Alastair Godfrey, Founder and Director

Exploring Infra-Gravity Waves from Cables in the Deepest Reaches of the Ocean

Ocean waves with a very long wavelength are often called infra-gravity (or sometimes sub-harmonic or simply long period waves) are formed from groups of shorter period waves as they interfere with each other close to coastlines. It is in these shallow coastal waters where the waves are generally most apparent, and where they play a significant role in coastal erosion. They can also resonate in harbours of the right size to cause some interesting, and potentially damaging, “sloshing” effects. Far from the coast, these waves are very small in amplitude and generally not noticed or measured. Although DAS has incredible sensitivity to changes in the environment, we have to ask if such phenomena can be observed using opportunistic fibre sensing especially given the depths of the ocean at which they are present.

There are a few aspects of the deep ocean that make this job easier. First on the list is that it is very quiet, both thermally and acoustically. This means that we are largely limited by instrument noise, not environmental, which is a great start. Secondly, the waves are physically large in scale which allows the full advantage of a distributed sensor to come into play. Thirdly, the signatures move coherently, and by utilising a large DAS array this allows us to extract signal from instrument noise.

We are searching for waves with a frequency of around 4 to 40 mHz, and for water that is 1 km deep we would be expecting a speed of around 50 m/s. These waves would, therefore, have a wavelength of kilometres, which is greater than the water depth so attenuation of the pressure signal should be small, but we are expecting the signal to be very small in amplitude.

So, what is the sensitivity of DAS to waves?

First, the bad news. Silica, the material from which optical fibres are made, is actually quite insensitive to pressure. So, although we can calculate the expected signal from the pressure change of the water column above a fibre, the sensitivity is low. This problem is compounded by the construction of deepwater fibre optic cables. They are shielded from the water pressure as much as possible to prevent damage from the great height of water above them.

But then the good news. Two aspects of the environment around the fibre optic cable help magnify the pressure signal. The first is the construction of the cable. The spiral wrap of the stiffness elements (armour) of the cable actually acts as a mechanical lever to increase the strain seen by the cable from the change in pressure surrounding the cable. This can be visualised (in an inverse way) when watering your garden with certain types of hosepipes as they change in length significantly as the pressure changes inside. Incidentally, this effect is most noticeable on curved hose, so expect different fibre sensitivity round corners. The second bit of good news is that the seabed itself strains with the pressure change of the water column above it, so if the cable is mechanically coupled to the seabed (for example a buried cable) then this effect can become significant. With very small movements, static friction is enough to couple the cable as if it were welded to the seabed.

When taken together, we typically end up with a surprisingly high sensitivity to water column height change. We often see 100 nano-strain per metre of water height change on a cable. This might not sound a lot, but the system noise of a DAS unit can be down in the few pico-strain, so we end up with sub-mm sensitivity!

And what do we actually see?

A time series plot from one of the virtual sensors shows the IG pressure signal, but it is entangled with seismic signals, temperature change and noise (both background and instrumental). This plot is taken from DAS data on a fibre optic cable lying on the seabed in 1 km of water. It looks like this:

In this plot we can see that there is an oscillating signal with a period of around 50 seconds (20 mHz). This is a good start, but we need to know how fast it is moving and we want more spectral information.

One of the tricks of signal processing is to use an approach that shows data correlated over space and time. A convenient way to do this is an F-k transform. This involves doing a Fourier transform in both time on one axis, and space on the other. In such a plot, we see correlations in space (the patterns of the wave peaks over the length of the fibre), but also the temporal correlation (how the waves go up and down over time). Because different types of waves and different wave frequencies travel at different speeds, they appear in different parts of the plot. The direction is also shown by in which quadrant the data falls. Here is a plot of the same data from above but over a large number of channels:

What we can see is the correlation of a signal in both directions up to a cut-off frequency of around 40 mHz. The speed of the waves is seen to be around 50 m/s, so both the speed and the period correspond closely with expectations. Importantly the speed depends on wavelength (the correlated data changes gradient with frequency). Longer wavelengths are faster as would be expected from an infra-gravity wave. The amplitude of the waves can be estimated from the magnitude of the signal to be a few millimetres, but ideally the sensing system would be calibrated in some way to reduce the uncertainty of this value.

This measurement was carried out over only a short period of time (a few days), and ideally, we would like to see how these infra-gravity waves change in amplitude and direction with the seasons in a study never done before. Due to the methods used by Indeximate to compress and store the data without loss of this information, you can be sure that such long-term measurements will soon be happening.