Sjøen Pedersen, Å., Amundsen, L., and
Robertsson, J. O. A.
Wavefield signal apparition, Part II:
Applications
EAGE, Vienna, 2016.
Introduction
A major trend on the marine seismic horizon is simultaneous shooting which has the potential to increase
the rate at which seismic data can be acquired and as well improve subsurface sampling by increased
shot density. The technique is established for land seismic data acquisition (Howe, 2008; Bouska, 2009).
The idea is to trigger two or more (encoded) sources sufficiently close together in time so that the
recorded signal energy interferes. The interference of signals is handled in data processing to decode or
separate the information generated from each source. The literature on the subject is vast. Key references
are Beasley et al., 1998; Ikelle, 1999; Stefani et al., 2007; Akerberg et al., 2008; Berkhout, 2008; Frømyr
et al., 2008; Hampson et al., 2008; Moore et al., 2008; Spitz et al., 2008; Moore, 2010; Kim et al., 2009;
Ikelle, 2010; Ji et al., 2012; Wapenaar et al. (2012); Chen et al., 2014; Amba et al., 2015; Kumar et al.,
2015; Langhammer and Bennion, 2015; and Mueller et al., 2015.
To date, the main principle in marine seismic multishooting has been to shoot with random dithering for
one or several sources acquiring seismic data simultaneously. The random dithers are known and can be
removed in processing to generate seismic data where all reflections generated by that source are
coherent (e.g., in the common-offset domain) whereas the signals from the other source(s) have a random
time distribution. One popular method to decode such simultaneous-source data is to consider the data
separation to be an underdetermined inverse problem, which can be solved through an iterative
procedure, assuming additional constraints, like sparsity and coherency. Moore et al. (2012) reported a
narrow azimuth survey with two source arrays firing simultaneously, one source-array being timedithered. The sources were separated using a modelling and inversion algorithm (Ji et al., 2012).
Langhammer and Bennion (2015) reported on triple-source simultaneous shooting to achieve higher
density seismic. They used an adaptive subtraction method for source separation.
In this abstract, we propose to change the way of thinking for simultaneous source acquisition. Instead of
using random time dithering we suggest to exploit periodic time dithering. By using the fact that seismic
data are spatially band-limited, decoding of densely sampled sources can be carried out without
inversion, namely by using the method of wavefield signal apparition (Robertsson et al., 2016, Wavefield
signal apparition, Part I: Theory, abstract submitted to EAGE), where responses are separated in 𝑓𝑘 domain. The method is applied to numerically modeled data, showing perfect separation of responses to
two adjacent sampled sources. We also discuss practical aspects of seismic acquisition related to the
principle of wavefield signal apparition.
Method of wavefield signal apparition
“Wavefield signal apparition” is a new method to sample time-discrete signals that allows for the
separation of interfering signals from multiple sources. The theory of wavefield signal apparition is
discussed in detail in a companion paper (Robertsson et al., 2016, submitted to EAGE). Essentially, by
changing a well-sampled conventional source sequence (…,1,1,1,1,1,…), where the wavefield in the
spectral 𝑓𝑘-domain is present in a cone around the spatial wavenumber 𝑘 = 0, to the source sequence
(…,1,A,1,A,1,…) where A is any function independent of spatial positions, the wavefield in the spectral
𝑓𝑘-domain will be present in two cones: one around 𝑘 = 0 and the other around the Nyquist
wavenumber 𝑘! . Then, in simultaneous shooting, where the combined source sequences
(…,1,1,1,1,1,…) and (…,1,A,1,A,1,…) are used, the data from the (…,1,A,1,A,1,…) sequence will be
solely apparent and isolated in the cone around the Nyquist wavenumber. The data from the two source
sequences thus can be separated in the 𝑓𝑘-domain.
Example
A 25Hz Ricker wavelet is used to simulate data at a receiver station. The data are acquired sufficiently
densely to avoid spatial aliasing according to the geometry shown in Figure 1. The simultaneous source
data with the apex to the left were generated by source ‘A’ shooting regularly (with source sequence
(…,1,1,1,1,1,…)). The data with the apex to the right were generated by source ‘B’ shooting with the
78th EAGE Conference & Exhibition 2016
Vienna, Austria, 30 May – 2 June 2016
periodic sequence (…,1,A,1,A,1,…) where A represents a time delay: 𝐴 𝜔 = 𝑒 !"# ; we have selected
T=10ms which gives on every second recording a somewhat “fuzzy” appearance of this part of the data.
The data are transformed to the 𝑓𝑘 domain, where the data generated from source ‘B’ are solely present
in the cone around the Nyquist number 𝑘! . These data are isolated and properly scaled (with a function
depending on the function A) before inverse Fourier transforming the source ‘B’ data to time-space
domain. Here, they are subtracted from the originally acquired simultaneous source data, recovering the
source ‘A’ data. As seen in Figure 1, the result is excellent and, apart from limited numerical artifacts at
the top and bottom (related to windowing of data before the temporal Fourier transform), no signal
leakage from source ‘B’ is visible.
Figure 1: Top left: Marine seismic model used to generate synthetic data for the simultaneous source
separation example. Data are recorded on the seabed 150m below the sea surface at 𝑥=3500m. Two
source profiles are acquired simultaneously. Source ‘A’ shoots regularly, from left to right. Source ‘B’
fires periodically, with a 10ms time-delay at every alternate shot position, and is moved from right to
left. Top right: Synthesized simultaneous source data, shown in the common receiver domain. The
horizontal axis refers to the coordinate of source ‘A’. Bottom left: 𝑓𝑘 spectrum of simultaneous source
data. The cone centred around 𝑘 = 0 contains data from both sources, while the cones centered around
the Nyquist wavenumber ±𝑘! contain only information from source ‘B’. Thus, the data from source ‘B’
is perfectly known in the 𝑓𝑘 domain. Bottom right: Separated simultaneous source data (for source ‘A’).
78th EAGE Conference & Exhibition 2016
Vienna, Austria, 30 May – 2 June 2016
Seismic acquisition – some practical aspects
The idea behind the proposed multi-shooting and decoding method (seismic apparition) was originally
conceived in a Statoil R&D-project for improving acquisition efficiency in seismic operations for PRM.
However, successful exploitation of this method will not only impact PRM and time-lapse seismic, but
will also be applicable in an exploration setting.
The proposed method will have several positive implications for seismic acquisition in addition to
perfectly separating/decoding simultaneous source data.
Residual shot noise can be dealt with in a similar manner, allowing for a moderate increase in source
vessel speed, which again could enable denser shooting (higher source fold) for acquisitions where such
an approach is desired. More efficient acquisition adds operational flexibility and weather robustness.
With real-time knowledge of position and firing times of other seismic vessels/sources, cancellation of
seismic interference is also possible with the method.
It is also worth mentioning that the seismic apparition method does not require much investment in new
acquisition hardware: Standard air guns can be used; so only minor modifications to existing equipment
may be needed; such as ensuring source firing control systems are upgraded and that capacity for air flow
and pressurizing air gun arrays is sufficient.
The proposed seismic apparition method is still in an early stage of development, and new aspects of its
use and potential will be further investigated in the near future.
Conclusions
The current main principle in seismic multishooting has been to shoot with random dithering for one of
the sources. We have demonstrated that by exploiting the method of seismic apparition, we can use
periodic shooting of one source while the master source shoots regularly. The numerical example shows
close to perfect signal separation from simultaneous source data. Such an excellent performance is
obtained easily for unaliased data. Our multishooting and decoding method can be generalized to more
than two sources.
Acknowledgement
We thank Statoil for permission to publish this paper related to proprietary data processing techniques.
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78th EAGE Conference & Exhibition 2016
Vienna, Austria, 30 May – 2 June 2016
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78th EAGE Conference & Exhibition 2016
Vienna, Austria, 30 May – 2 June 2016