“There’s nothing wrong with enjoying looking at the surface of the ocean itself, except that when you finally see what goes on underwater, you realise that you’ve been missing the whole point of the ocean. Staying on the surface all the time is like going to the circus and staring at the outside of the tent.”
Dave Barry
American writer, Pulitzer Prize winner 1988
Sinusoidal Ocean Waves
If we assume that the ocean surface is represented by a sine wave, analytical equations enable us to calculate the horizontal (u) and vertical (v) particle velocity and the pressure (p) as a function of depth (z) (Lighthill, 1978, Holmes, 2001):
Here H is the wave height, T the period of the ocean wave and λ the wave length, while x and t are the x-position and time, respectively. We have assumed that the water depth is large compared to the wavelength. The corresponding expression for the pressure has a similar exponential decay with depth. The particle velocity represented by these equations can be represented as circular (elliptical if the water depth is shallower) shaped particle orbits.
The dispersion relation for ocean waves depends on the water depth. However, if we assume large water depths, it is simply given as ω2 = gk where g is the gravitational acceleration (9.8 m/s2), ω is the circular frequency (ω = 2π/T) and k is the wave number. From the dispersion equation we can estimate the period of a sinusoidal ocean wave if the wavelength is known, since k = 2π/λ. It is clear that disturbances caused by the ocean wave will decrease with depth, and hence it might be a good idea to tow seismic streamers at large depths.
Typical time periods (T) for ocean waves are more than a second; sitting at a beach we can usually count eight seconds between each wave. This means that the noise both on the pressure component and the velocity component will be outside the typical frequencies of interest for a seismic experiment. However, as we are striving for lower and lower frequencies (see GEO ExPro, Vol. 10, No. 1) the noise caused by slow variations in particle velocity close to the streamer might influence our data. For streamer depths larger than 20m, the typical particle velocity caused by the ocean wave shown in the figure is less than 0.1 m/s and very low frequency (0.2 Hz). Since both the pressure variations and the velocities caused by water waves decay exponentially with depth, the direct influence is assumed to be minimal for normal seismic frequencies (above 4–5 Hz). This exponential decay rate is controlled by the streamer depth divided by the wave length (equations 1 and 2 above).
During heavy storms it is known that ships crossing the North Sea via, for instance, the Dogger area, which has shallow water ranging from 20 to 60m, get sand on deck, indicating that the waves have sufficient energy to lift sand from the sea bed to the surface. Close to shore this phenomenon is well known, as a thick layer of sand foam can be observed on the beach after a storm.
Wind Speed and Wave Height Correlation
Figure 2: The decay curve for particle velocity versus depth. Here we have used the exact dispersion relation without assuming that the water depth is much larger than the wavelength. The vertical velocity at the seabed (60m) is actually zero; the deviation is caused by the logarithmic plot. The period of this wave is 5 seconds, corresponding to a frequency of 0.2 Hz.
Figure 1: Smoothed measurements of wave height (black solid line) at the Gullfaks Field in 2012 and corresponding modelled wave heights by assuming a quadratic relation (red solid line) between wind velocity and wave height. The average wave height is 2.7m. (a=0.025 s2/m; b=1 m).The close relationship between wind speed and ocean wave height is well known. For fully developed ocean waves it is commonly assumed that the wave height increases with wind velocity squared, and a recent example showing wave data from the Gullfaks field in the North Sea is shown in Figure 1.
We observe a surprisingly strong correlation between the smoothed average wave height and the wind speed. Furthermore, we observe that the ocean waves for some periods lag behind the wind: first the wind calms down and then the waves. The average wave height measured at the Gullfaks Field in 2012 was 2.7m. Pierson and Moskowitz derived an empirical formula for the energy of a fully developed sea state as a function of frequency, known as the Pierson-Moskowitz-spectrum, which showed that the peak wave energy decreases as the wind velocity increases.
Another crucial parameter that is used to describe ocean waves is the wave steepness, s, which is equal to the wave height divided by the wavelength. If s is larger than 1/7, the wave will break. This value might vary significantly. Typical average values for the North Sea are between 0.06 and 0.006 (Torsethaugen, 1993). This means that for the Gullfaks example shown in Figure 1, assuming a steepness of 0.06, the average wavelength is 40m, corresponding to a period of 5 seconds. One of the largest waves observed precisely was reported by USS Ramapo in a storm in the Pacific Ocean in 1933. An officer on the deck used the crow’s nest to estimate the wave height and corresponding wavelength, knowing that the length of the ship was 146m. The estimated wave height was 34m and the corresponding wavelength was 342m, yielding a wave steepness of 1/10.
Turbulent Flow Around Streamers
Figure 4: Noise spectra with and without superhydrophobic (SHS) surface on the streamer. We observe a significant noise reduction for frequencies between 1 and 10 Hz.In addition to noise created by ocean waves, there are currents in the water layer, and close to the streamer the flow is not necessarily laminar, as shown in Figure 3. Elboth et al. (2010, 2012) studied this flow in detail, and demonstrated that the surface material of the streamer is crucial. By using a superhydrophobic surface material they revealed that the towing noise could be lowered by approximately 10 dB in the frequency range between 1 and 10 Hz. This observation is crucial for broadband seismic, where especially the lower frequencies are important. The broadband paradigm shift that we witness today is multi-causal: the streamer depth has increased, the manufacturing of various types of streamers has improved significantly, especially with respect to noise attenuation, and finally the algorithms for data processing have also improved. The result is high quality data, enabling an improved image of the subsurface.
Noisy Birds and Tugs
Figure 6: Noise comparison of solid streamer (traces 0–100) and fluid-filled streamer (traces 100– 450), measured for moderate seas.
Figure 5: Measured noise in calm seas (practically no wind). The noise level is lower than 0.5 microbar for the mid streamer, and shows significant increase close to the birds and the front and tail end of the streamer. Notice the slight decrease in noise level away from the ship (trace 120 is closest to the ship). This is a normal, fluid-filled streamer.In order to control its depth, a streamer is equipped with devices that enable adjustment of the vertical (and in some cases also the horizontal) position. These devices are called ‘birds’ and are attached to the streamer at certain intervals, typically a couple of hundred metres. A noise record obtained in calm weather is shown in Figure 5, where we can notice a significant increase in noise level close to the birds and also close to the front and tail ends of the streamer. Trace 120 is closest to the seismic vessel, and we observe a slight decrease in noise level (red dashed line) as we get further away from the ship. This indicates that some of the noise observed is actually vessel noise caused by the ship propellers and engine.
The slightly increased level at the head and tail (6–8 microbars) is probably caused by tugging from the vessel, tail buoys and lead-in sections. As the sea condition gets more marginal, this tugging noise will increase and create unwanted vibrations along the streamer. As the streamer depth increases, the angle between the head and tail buoys rises, leading to extra tug noise. This additional problem is normally solved by introducing passive sections prior to the active receiver sections in the streamer. However, there is no doubt that when we are solving one problem by towing the streamer deeper we create a new problem by introducing a more complex towing pattern for the streamers. Furthermore, introducing passive sections (with rapid depth variations) limits the available near offset information somewhat.
During the last two decades most seismic contractors have replaced the fluid surrounding the receivers in the streamer with a gel-like or solid material, which reduces or completely removes the noise caused by movement of the fluid inside the streamer, as shown in Figure 6.
It is reasonable to assume that the difference shown in this figure will increase for acquisition in more marginal weather conditions.
Broadband Seismic Development
There has been tremendous development in new streamer design, new ways of towing streamers and new ways of processing and utilising the data acquired by broadband systems. Most contractors have developed their own system aiming for increased bandwidth and improved signal-to-noise ratio. Compared to a decade ago, it is evident that more and more seismic is acquired using deep towing depths, often down to 20–30m below sea surface. In the next issues we will present some of these new technologies and show examples demonstrating the progress made up to now.
References
Dowle, R. 2006, Solid streamer noise reduction principles, SEG Annual Meeting, p 85-88.
Elboth, T. et al., 2010, Investigation of flow and flow noise around a seismic streamer cable, Geophysics, 75, Q1-Q9.
Elboth, T. et al., 2012, Flow noise reduction from superhydrofobic surfaces, Geophysics, 77, P1-P10.
Holmes, P., 2001, A course in coastal defense systems, CDCM Professional Training Programme, Chapter 5.
Lighthill, 1978, Waves in fluids, Cambridge University Press, ISBN 0521 21689 3.
Pierson, W.J. and L. Moskowitz, 1964, A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii, J. Geophys. Res. 69, 5181-5190.
Torsethaugen, K. and S. Haver, Simplified double peak spectral model for ocean waves, Paper No. 2004-JSC-193, ISOPE 2004 Touson.
