sea surface 2 m 3 m Hydrophone Airgun 6 m
Figure 3.25: If these two airguns generate a peak pressure of 4 bars at 1m, the reflected signal from the sea surface measured at the hydrophone between the guns is approximately –1.3 bars, assuming linear theory. The hydrostatic pressure at the hydrophone position is 1.2 bars, which means that the total pressure – assuming that the pressure contribution from each source can be added linearly – is negative; cavitation will then occur.
more prominent, meaning that it is not easy to estimate exactly at which pressures cavitation will occur. Despite this, it is reasonable to assume that for compact and large airgun arrays we have a risk of cavitation formation in the area where the ghost reflections from several airguns coincide in time and space. Tis type of cavitation will be independent of the type
of airgun used, since it is simply a function of the geometry of the array. And this is the good news: if the major part of the high frequency signal generated by an array is generated by cavitation between airguns, this effect can be eliminated simply by increasing the distance between the guns. Plesset and Ellis showed in 1955 that it is indeed possible to
generate cavities by acoustic stimulation, as shown in Figure 3.24. Generally, the strength and length of this high frequency
68
Figure 3.28: Same traces as in Figure 3.27, but aligned, using NMO-correction, followed by taking the absolute value and smoothing. Notice that all ghost- cavitation signals show a gradual increase in amplitude followed by a sudden decrease at approximately 57 ms.
the abrupt decrease at approximately 57 ms. However, it is very weak, and close to zero amplitude, and we conclude that this weak ghost is probably related to the fact that the sea surface reflection coefficient decreases significantly for frequencies above 1 kHz if the sea surface is not perfectly flat. Tis skewness of the ghost cavity signal versus recording
Figure 3.26: Seven shots from a source shot line above a hydrophone located at the seabed. Notice the high-frequency noise occurring approximately 10 ms after the main peak. There are 2 ms between each time line.
Figure 3.27: Same traces as in Figure 3.26, filtered by a 10–20 kHz band-pass filter, which clearly demonstrates that the high frequency ghost-cavitation signal is repeatable in the sense that this phenomenon occurs at all traces and at the same time after the primary peak.
30 17 18 19 20 21 22 23 30 1 0.8 0.6 0.4 0.2 90 Shot number 300 0
time can be explained by a very simple and intuitive model. Let’s assume that the number of cavities (n) and the radius of each cavity is increasing to a maximum that occurs when the cavity cloud is at its maximum. Tis is shown in Figure 3.29, where we have assumed that the ghost cloud exists for
Figure 3.29: Simple model for number of cavities (n) created and initial radius (R) of the cavities versus time. The idea is that at 3.5 ms we have a maximum size of the ghost cloud, and a lot of small cavities with a maximum radius are then created. Note that both curves are normalised to 1 and therefore the two curves are identical.
Airgun 3.4.4 How Repeatable is the Ghost Cavitation Signal?
Landrø et al., 2013, investigated how repeatable the high frequency ghost cavitation signal is, and Figure 3.27 shows that the envelope signal is repeatable. Te details are of course different, since we imagine that the ghost cavitation process is random and chaotic. If we take the absolute value of each sample and smooth
the curve (and perform a move-out correction to align the curves), we observe another characteristic feature of the ghost cavitation signal (Figure 3.28): the strength increases gradually, followed by a relatively abrupt decrease to almost zero. Te ghost of the ghost cavitation signal is weak; we expect that this second order ghost signal should occur after
17 34 18 19 20 21 22 23
cavitation signal will therefore increase with the size and compactness of the airgun array.
0
1
2
3 Time (ms) 109
4
5
6
7
Time (ms)
Time (ms) Landrø et al., Geophysics, 2013 Normalised n or R Time (ms) Landrø (2000)
Landrø et al., Geophysics, 2016
Landrø et al., Geophysics, 2013
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