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Perfect partial reconstructions for multiple simultaneous sources

Wittsten, Jens LU ; Andersson, Fredrik ; Robertsson, Johan and Amundsen, Lasse (2019) In Geophysical Prospecting
Abstract

A major focus of research in the seismic industry of the past two decades has been the acquisition and subsequent separation of seismic data using multiple sources fired simultaneously. The recently introduced method of signal apparition provides a new take on the problem by replacing the random time-shifts usually employed to encode the different sources by fully deterministic periodic time-shifts. In this paper, we give a mathematical proof showing that the signal apparition method results in optimally large regions in the frequency–wavenumber space where exact separation of sources is achieved. These regions are diamond shaped and we prove that using any other method of source encoding results in strictly smaller regions of exact... (More)

A major focus of research in the seismic industry of the past two decades has been the acquisition and subsequent separation of seismic data using multiple sources fired simultaneously. The recently introduced method of signal apparition provides a new take on the problem by replacing the random time-shifts usually employed to encode the different sources by fully deterministic periodic time-shifts. In this paper, we give a mathematical proof showing that the signal apparition method results in optimally large regions in the frequency–wavenumber space where exact separation of sources is achieved. These regions are diamond shaped and we prove that using any other method of source encoding results in strictly smaller regions of exact separation. The results are valid for arbitrary number of sources. Numerical examples for different number of sources (three, respectively, four sources) demonstrate the exact recovery of these diamond-shaped regions. The implementation of the theoretical proofs in the field is illustrated by the results of a conducted field test.

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author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Acquisition, Inverse problem, Mathematical formulation
in
Geophysical Prospecting
publisher
EAGE / Wiley
external identifiers
  • scopus:85064045444
ISSN
0016-8025
DOI
10.1111/1365-2478.12761
language
English
LU publication?
yes
id
06ba02f3-b744-460e-97a6-2c8f73103b6b
date added to LUP
2019-05-09 12:27:54
date last changed
2019-11-25 09:29:47
@article{06ba02f3-b744-460e-97a6-2c8f73103b6b,
  abstract     = {<p>A major focus of research in the seismic industry of the past two decades has been the acquisition and subsequent separation of seismic data using multiple sources fired simultaneously. The recently introduced method of signal apparition provides a new take on the problem by replacing the random time-shifts usually employed to encode the different sources by fully deterministic periodic time-shifts. In this paper, we give a mathematical proof showing that the signal apparition method results in optimally large regions in the frequency–wavenumber space where exact separation of sources is achieved. These regions are diamond shaped and we prove that using any other method of source encoding results in strictly smaller regions of exact separation. The results are valid for arbitrary number of sources. Numerical examples for different number of sources (three, respectively, four sources) demonstrate the exact recovery of these diamond-shaped regions. The implementation of the theoretical proofs in the field is illustrated by the results of a conducted field test.</p>},
  author       = {Wittsten, Jens and Andersson, Fredrik and Robertsson, Johan and Amundsen, Lasse},
  issn         = {0016-8025},
  language     = {eng},
  publisher    = {EAGE / Wiley},
  series       = {Geophysical Prospecting},
  title        = {Perfect partial reconstructions for multiple simultaneous sources},
  url          = {http://dx.doi.org/10.1111/1365-2478.12761},
  doi          = {10.1111/1365-2478.12761},
  year         = {2019},
}