sparse nature of seismic data in the time- domain (i.e., seismic traces can be thought of as a subset of discrete reflections with ‘quiet periods’ in between). Figure 2.51 illustrates the results using such an approach by co-workers at Chevron and presented in a paper by Akerberg et al. (2008). A different approach to simultaneous
fm alias no signal
source separation has been to modify the source signature emitted by airgun sources, which comprise several (typically three) sub-arrays along which multiple clusters of smaller airguns are located. As, in contrast to land vibroseis sources, it is not possible to design arbitrary source signatures for marine airgun sources, in principle one has the ability to choose firing time (and amplitude i.e., volume) of individual airgun elements within the array, meaning it is possible to choose source signatures that are dispersed as opposed to focused in a single peak. Such approaches have been proposed to reduce the environmental impact in the past (Ziolkowski, 1987) but also for simultaneous source shooting. Abma et al. (2015) suggested using a library of ‘popcorn’ source sequences to encode multiple airgun sources such that the responses can be separated after simultaneous source acquisition by correlation with the corresponding source signatures, following a practice that is similar to land simultaneous source acquisition. Te principle is based on the fact that the cross-correlation between two (infinite) random sequences is zero whereas the autocorrelation is a spike. It is also possible to choose binary encoding sequences with better or optimal orthogonality properties such as Kasami sequences (discussed in Part I) to encode marine airgun arrays (Robertsson et al., 2012). Mueller et al. (2015) propose to use a combination of random dithers from shot to shot with deterministically encoded source sequences at each shot point. Recently, there has been industry interest in exploring the
-ks fm -ks -kn alias
Only signal from
periodic source
-kn 0 Wave Number (1/m) the spatial sampling frequency; and kn = ks 0 alias
Overlapping signals
Only signal from
periodic source
kn ks
Figure 2.52: (a) In geosciences, we plot time-offset data (not shown) in frequency-wave number (f k) diagrams to examine the direction and apparent velocity 2πf/k of seismic waves. Here fm frequency; ks
is the maximum /2 is the spatial Nyquist frequency. Typically,
seismic data plots into the f k signal cone bounded by the dashed white line, determined by the water speed. Observe that there is plenty of ‘space’ in f k that has no signal. This is utilised in seismic apparition by designing periodic source sequences that place seismic energy into this empty space. (b) For two sources shot simultaneously, the seismic apparition technique samples two source wavefields, sampled at spatial frequencies ks
and ks both source wavefields (overlapping signals). The cones centred around kn
/2 respectively. The cone centred around k=0 contains information about , however, only contain
information from the source that has been fired in a periodic way. By intelligent data processing, the data from the two sources can be decoded.
feasibility of marine vibroseis sources, as they would, among other things, appear to provide more degrees of freedom to optimise mutually orthogonal source functions beyond just binary orthogonal sequences, which would allow for a step change in simultaneous source separation of marine seismic data. However, we believe the engineering challenges of a marine vibroseis source are immense and the robustness and ability to provide the broad spectrum of the marine airgun array are very hard to match using other source technologies.
2.8.3 The Deterministic Approach: Seismic Apparition
A recent development, referred to as ‘seismic apparition’, suggests an alternative approach to deterministic simultaneous source acquisition. Robertsson et al. (2016) show that by using
90
simple modulation functions from shot to shot (e.g., a simple short time delay or an amplitude variation), the recorded data on a common receiver gather or a common offset gather will be deterministically mapped onto known parts of, for example, the f k-space outside the conventional ‘signal cone’ where conventional data is strictly located (Figure 2.52a). Te signal cone contains all propagating seismic energy with apparent velocities between water velocity (straight lines with apparent slowness of +-1/1,500 s/m in f k-space ) and infinite velocity (i.e., vertically arriving events plotting on a vertical line with wave number 0). Te shot modulation generates multiple new signal cones that are offset along the wave number axis thereby populating the f k-space much better and enabling exact simultaneous source separation below a certain frequency (Figure 2.52b). Robertsson et al. (2016) referred to the process as ‘wavefield apparition’ or ‘signal apparition’ in the meaning of ‘the act of becoming visible’. In the spectral domain, the wavefield caused by the periodic source sequence is nearly ‘ghostly apparent’ and isolated. Te word ‘spectrum’ was introduced by Newton (1672)
in relation to his studies of the decomposition of white light into a band of light colours, when passed through a glass prism (Figure 2.53). Tis word seems to be a variant of the Latin word ‘spectre’, which means ‘ghostly apparition’. A
fk signal cone
no signal kn ks b
a alias
Frequency (Hz)
Frequency (Hz)
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