HANDBOOK OF» GEOPHYSICAL EXPLQRATI-ON "
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`, SEISMIC EXPLORATION ‘
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`Klaus Helbig and Sven Treitel, Editors
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`VOLUME 39
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`COding and OOOdmg:
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`by LUC IKELLE
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`SOiSmiO Om,
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`ThO OOnCOpI: Of multishOO‘Eing
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`WesternGeco Ex. 1012, pg. 1
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`WesternGeco Ex. 1012, pg. 1
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`Coome AND Drcoome: SEISMEC DATA
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`THE CONCEPT or MULTISHOOTING
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`LUC T. IKELLE
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`Robert R. Berg Professor
`CASP Project
`Geology and Geophysics, Texas A&M University, College Station
`Texas
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`5
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`mmmenMWMM/wlm)MM“wN
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`Amsterdam 0 Boston 9 Heidelberg 0 London 9 New York 6 Oxford
`Paris a San Diego 0 San Francisco 9 Singapore to Sydney 0 Tokyo
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`WesternGeco Ex. 1012, pg. 2
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`WesternGeco Ex. 1012, pg. 2
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`Elsevier
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`WesternGeco Ex. 1012, pg. 3
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`WesternGeco Ex. 1012, pg. 3
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`lkelle
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`lismic
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`Introduction 45
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`Box 1.3: A BRIEF REVIEW OF THE COCKTAIL—PARTY
`PROBLEM
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`The decoding of real rnultishot data is similar to a very well—known
`challenging problem in auditory perception, the cocktail—party problem.
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`This problem can be stated as follows: Imagine 1 people speaking
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`simultaneously in a room containing two microphones, as depicted
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`in Figure 1.24. The output of each microphone is the mixture of I
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`voice signals,just as multishot data are a mixture of data generated by
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`single sources. In signal processing, the I voice signals are the sources,
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`and the microphones’ recordings are the signal mixtures. To avoid any
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`confusion between seismic sources and the sources in the cocktail—
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`party problem, we simply continue to call the latter voice signals.
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`Solving the cocktail—party problem consists of reconstructing from
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`the signal mixture the voice signal emanating from each person. We
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`can see that solving this problem is quite similar to decoding multishot
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`data; in the cocktail—party problem, the voice signals correspond to
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`single—shot data and a mixture signal corresponds to one sweep of
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`multishot data.
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`If the two microphones in the cocktail—party problem represent
`human ears (constituting the organs of hearing), we end up with the
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`cocktail—party problem as first formulated by Colin Cherry and his
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`co—workers [Cherry (1953, 1957, 1961); Cherry and Taylor (1954);
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`Cherry and Sayers (1956, 1959); Sayers and Cherry (1957)]. In his
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`1957 paper, Cherry wrote: ‘One of our most important faculties is
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`our ability to listen to, and follow, one speaker in the presence of
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`others. This is such a common experience that we may take it for
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`granted. No machine has been constructed to do just this, to filter out
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`one conversation from a number jumbled together.’ In other words,
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`the cocktail—party problem refers to the remarkable (but not always
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`perfect) human ability to selectively understand a single speaker in
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`a noisy environment. The noise is primarily generated by the other
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`speakers attending the cocktail party. If the cocktail party is taking
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`place in a room, the noise will also include reverberations.
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`The earliest references, such as Cherry (1953) and Cherry and
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`Taylor (1954), use the term cocktail—party efikzt rather than cocktail-party
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`problem or cocktail-party phenomenon, which are commonly used today.
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`(continued)
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`WesternGeco Ex. 1012, pg. 4
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`WesternGeco Ex. 1012, pg. 4
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`Luc T. Ikelle
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`Mixture
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`Voice signal
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`WWW
`Mixing process
`Demixing process
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`Figure 1.24 Cocktail party problem. If I people speak at the same time in a room
`containing two microphones, then the output of each microphone is a mixture
`of two voice signals. Given these two signal mixtures, a decoding process aims at
`recovering the original I voice signals just like the decoding process of multishot
`data does.
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`There are also two basic approaches to the study of the audio
`cocktail—party problem:
`(1) Computational auditory—scene analysis
`(CASA) and (2) blind—source separation (BSS). The CASA approach
`consists of studying and imitating human hearing. To this end,
`computational models have been developed that mimic the several
`stages of auditory perception from the acoustical processing in the ear
`to the neural and cognitive processes in the brain. Readers are referred
`to van der Kouwe et al. (2001) for a m ore detailed review of recent
`progress in CASA.
`The blind—source separation (BSS) approach essentially uses the
`statistical properties of voice signals, and the mixtures or the mixing
`processes in an attempt
`to solve the separation problem from a
`purely mathematical point of View. As the term blind denotes,
`the mixing matrices and the voice signals are unknown — the
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`(continued)
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`WesternGeco Ex. 1012, pg. 5
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`WesternGeco Ex. 1012, pg. 5
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`introduction
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`47
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`Box 1 .3 continued
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`mathematical problems posed in 1385 are identical to the ones in
`(1.48) and (1.49) if we assume that x, is fixed. However, it is possible
`(and in fact absolutely necessary) to make assumptions about the
`statistics of voice signals. Two of the most successful BSS methods
`are the principal—components analysis (PCA) and the independent—
`components analysis (ICA). These two methods are also relevant to
`seismic—data decoding (see Chapters 2 and 3 for details).
`So what are the difierences between the cocktail—party problem
`and the seismic—multishooting problem? If we consider, for example
`the decoding aspect in these two problems, and compare Figures 1.23
`and 1.24, the only real difference is that in the seismic—multishooting
`problem, we have an extra degree of freedom through the receiver
`positions (Kr). This degree of freedom can be used to facilitate
`the decoding process, and even the imaging process, of seismic
`multishot data. Also, because we are dealing with relatively—controlled
`experiments in seismics, we automatically have an advantage in the
`seismic multishooting problem, as we have more control over the
`encoding process of source signatures. Actually,
`there are similar
`advantages in the cocktail-party problem, although these are not yet
`fully exploited in the decoding of the cocktail—party problem. One
`can use the differences between male and female voices, the accent of
`the speakers, the languages of speakers, etc. In fact, the human brain
`uses this knowledge in the decoding process.
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`1.5.2. Source encoding
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`Multishooting is similar to multiple—access technology (multiple access refers
`to the sharing of a common resource in order to allow simultaneous
`communications by multiple users), which is widely used in cellular
`communications to allow several subscribers to share the same channel.
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`The three basic decoding methods in communication applications are
`time—division multiple access (TDMA), frequency—division multiple access
`(FDMA), and code—division multiple access (CDMA). The characteristics
`of these methods are illustrated in Figure 1.25.
`In TDMA systems, time is divided into, say, I contiguous discrete time
`intervals, as shown in Figure 1.25(a). In FDMA systems, the total frequency
`bandwidth is divided into I contiguous discrete—frequency channels, as
`depicted in Figure 1.25(b). In CDMA systems, the signal is continuously
`distributed throughout the entire time or frequency axis. The frequency
`and time axes are not divided among subscribers, as is done in the FDMA
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`WesternGeco Ex. 1012, pg. 6
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`WesternGeco Ex. 1012, pg. 6
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