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| The HDBand toolkit was used to deghost seismic data from the Gulf of Mexico for delineating steep salt flanks. |
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One of the reasons why noise-cancelling headphones are so successful is that the digital music industry has figured out a way to retrofit the external noise with its own acoustical characteristics, and use it in conjunction with the signal (music or speech), and have them “work together” to produce a richer, cleaner signal.
GHOST INTERACTION
Without the noise-canceling technology, the sounds that people hear are a mixture of the music, summed with other external noises. The “sum” of all these signals may produce “amplified” or “suppressed” sounds in an almost random fashion, depending on the exact interaction of the two signals. This “summation” is a complicated process, because sound waves (or other types of waves) do not behave like particles.
Waves are made of two components. One is amplitude, which can be thought of as the intensity or “volume” of the signal, and the other, is phase. When two waves interact, they can amplify (constructive interference) or weaken (destructive interference) each other. The result depends on the exact relationship between the phases of each wave. When two or more sounds are in phase, they intensify each other. If they are out of phase, they diminish or cancel each other out. If the phases are perfectly miss-aligned, or out of phase, they could cancel each other completely, Fig. 1.
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| Fig. 1. Destructive and constructive interference between the primary and the ghost depends on the source depth. |
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The noise-cancelling idea used in the headphones hinges on the ability of the device to “hear” the outside noise and produce a digital filter that removes it from the signal, before it reaches the user’s ears.
Geotrace’s HDBand process was inspired by noise-cancelling headphones, since seismic waves are sound waves. The role of “noise” is played by anything that is not a primary reflection. In our case, “noise” can be made up of ambient incoherent (random) noise, or coherent, well-organized, but undesirable signals, such as multiples and ghosts. These are essentially echoes that interfere with the signal and mask the information. By removing these noises, the effect is not just a clean signal, but to actually produce a signal with increased bandwidth.
The HDBand process not only plays the role of noise-cancelling headphones in seismic, but has also been engineered to act as a digital equalizer, where different frequencies can be modulated and boosted, similar to a musical setting.
GHOST GENERATION
In marine seismic acquisition, an air gun (towed by a boat) generates a strong acoustic signal that travels to the earth and produces a series of reflections. These reflections are then recorded by a string of hydrophones in a towed cable or by an array of geophones planted across the sea bottom. A problem arises, because both sources and receivers are “submerged” within a layer of water. The water-air interface behaves like an acoustical mirror. Any signal that hits the interface is reflected back after a polarity change. These secondary reflections are very close in time to the primary signal, effectively producing an interference pattern that distorts the recorded signal, Fig. 2.
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| Fig. 2. Dynamics of ghost generation. |
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The interference pattern produced by the secondary signal generates a distorted signal, that complicates interpretation and, in some cases, may even eliminate reflections altogether. These secondary signals are commonly referred to as ghosts. Their effects can be understood better by analyzing the power spectrum of the signal, which indicates how the energy is distributed as a function of frequency.
Figure 3 shows the original air gun signal and its spectrum and ghosted version. As the ghosts interact with the signal, distortions appear in the spectrum. These distortions express themselves as notches in the spectrum—deep wedges of missing data. The location and severity of the distortions (depth and width of the notches) is a complicated issue out of the scope of this publication, interested readers should turn to a more technical publication by Yu, et al (2014) for more information. Ultimately, what’s important to understand is that these distortions appear, due to the destructive interference between the primary and the ghost signal, and the details depend on the depth of sources and receivers.
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| Fig. 3. Original and ghosted air gun signal: a) and b) show the time signal and its spectrum before any ghosting (far-field signature); c) and d) include the source notch; e) and f) include the receiver ghost. |
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ZERO-HZ NOTCH
One additional and very detrimental effect, and one of the main focus points of this article, is the notch that appears in the very-low-frequency part of the spectrum (Fig. 4), the “zero-Hz notch.” The severe loss of low-frequency information is a one-sided notch from a similar origin as all the other notches, but it is more pervasive and difficult to alleviate.
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| Fig. 4. Comparison of spectra, with and without ghosting. Note the severe loss of low-frequency data. |
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The zero-Hz notch comes from the fact that the low-frequency signal and ghost interact over a longer period of time than in the higher-frequency version, and the interference pattern is less sensitive to the depth of the sources and receivers. Figs. 5a and 5b show a synthetic, broadband zero-phase signal and its (source) ghosts. Fig. 5c shows the wavelet resulting from the interference pattern. The effect is to produce a well-defined and well-localized wavelet, although it appears to be 90° rotated. Figs. 5d and 5e show the same signal that now is restricted to only contain low frequencies. Because the wavelet is so much “longer” and less compact in time, when interacting, they nearly cancel each other. This effect produces the zero-Hz notch shown in Fig. 4.
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| Fig. 5. Primary and ghost signals interact differently, depending on the dominant frequency. |
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The zero-Hz notch can be very detrimental to the structural interpretation of seismic and the ability to identify and localize relevant prospects. Almost counter-intuitive, but well-documented in Stewart (1994), the loss of low frequencies compromises the ability to localize a reflection by producing very large side lobes on the wavelets and making the real events indistinguishable from spurious side lobes in the wavelet, Fig. 6. The low-frequency information also plays a critical role in seismic inversion of data into rock properties. Traditionally, because the low frequency is not present in the data, it is necessary to infer it from other sources such as migration velocity models, which may, at best, produce a crude estimate of the information needed.
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| Fig. 6. The lack of low frequencies compromises the ability to identify a reflection. Note that the resolution (width of the wavelet) has not changed, but the side lobes are now comparable to the main event. |
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BROADBAND THROUGH DEGHOSTING
Geotrace has developed a versatile, flexible HDBand toolkit to attack the ghost problem and to return the bandwidth of marine data to its original spectrum. The toolkit was developed to accommodate the different scenarios that can be encountered, based on the amount and type of data available. The technology is applicable for use before or after migration, and can be used in a post-stack mode. The HDBand suite of algorithms can accommodate any acquisition type, equipment and shooting geometry, geology, E&P objectives, budget, and turnaround time.
When a far-field signature is available, giving us the ideal response of the source-receiver system, it is used in HDBand to design the filters for deghosting. If this ideal response is not available, or due to the data complexity the initial approach does not work very well, a secondary technique is available, and it is well described in Yu, et al (2014).
Figures 7a and 7c represent the synthetic wavelet, with source and receiver ghosts and its corresponding spectra. Note the strong zero-Hz notch, in addition to the middle frequencies, resulting from the destructive interference of the ghosts with the primary signal. Figures 7b and 7d show the results after applying HDBand. The complex input wavelet has resolved itself into a zero-phase wavelet with an almost-white spectrum. Figure 8 shows the result of applying HDBand to real data from West Africa, courtesy of Polarcus seismic data acquisition company.
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| Fig. 7. HDBand on synthetic data: a) Input ghosted signal with its c) spectrum before HDBand; figures b) and d) are the results after the deghosting. Note the “healing” of the notches and the consequent broadening of the bandwidth. |
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| Fig. 8. HDBand toolkit applied to West African data: a) input stack with c) spectrum before HDBand; figures b) and d) are the results after deghosting. |
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Note the “healing” of the notches and the broadening of the bandwidth resulting from the removal of the ghosts. To reinforce the importance of taking out the zero-Hz notch, a portion of the data in Fig. 8 was low-pass filtered to 10 Hz and shown in Fig. 9. In particular, Fig. 9d reveals the additional structure unmasked by HDBand and only visible in the low frequencies.
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| Fig. 9. Magnified section from Fig. 7, before (a) and after (b) HDBand. Figures c and d are the result of low-pass filtering to 10 Hz. Note the appearance of a new “low-frequency structure” in d). |
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SURPRISE: SALT-FLANK IMAGING
Since HDBand processing has a remarkable effect on the low-frequency signal, it was used to enhance structures that can only be seen in the low frequency, namely very steep beds or salt flanks. By their very nature, a very steep or vertical structure has a small horizontal extent, so it has to be represented seismically by just a few traces (one if it is truly vertical), which imply very low frequencies.
HDBand was applied to a data set from the Gulf of Mexico that had already been depth-migrated and stacked. The results in Fig. 10 show a clearly identifiable (i.e., pickable) salt dome base that turns down into a salt flank. Halfway down the flank in Fig. 10a, it becomes unclear which way to proceed—to the right or to the left? The HDBand version of the same data shown in Fig. 10b has no such ambiguity and the salt flank is easy to interpret. The potential improvement coming from HDBand opens the door for applying it on data that have already been processed and imaged, and greatly improves their interpretability.
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| Fig. 10. Steep salt flanks get much clearer definition, when the low-frequency ghost is eliminated. |
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CONCLUSIONS
HDBand application improves the interpretability of seismic data, and increases the clarity and sharpness of events by eliminating the ghost reflection coming from the upward-moving waves bouncing off the water-air interface and producing a destructive interference pattern. This pattern makes seismic data appear “fuzzy” in the time/depth domain and introduces deep notches in the spectrum. The notches cut into the data, limiting the bandwidth of the signal. The loss of frequencies compromises the resolution and interpretability of the data.
HDBand is a versatile and robust toolkit that handles all kinds of acquisition parameters and geometries. Eliminating the ghosts broadens the spectrum and increases the data resolution. Special attention was paid to the loss of low frequencies and its consequences for structurally complex environments, in particular salt exploration.
The value of the deghosting technology was validated by applying it to several real data examples, one from West Coast of Africa and one from the Gulf of Mexico. The geological challenges are very different, but it was shown in both cases that the low-frequency components unmasked and restored by HDBand had a dramatic effect, and changed the interpretation and interpretability of the data. 
ACKNOWLEDGMENTS
The author would thank Polarcus for permission to show their data.
REFERENCES
- Martin, N. and R. Stewart, “The effect of low frequencies on seismic analysis,” CREWES Research Report Vol. 6, 1994.
- Yu, G.H., M. Smith and N. Shah, “Studying a spatially variant deghost technique for conventional streamer data,” EAGE Extended Abstract, 2014
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