Perfect partial reconstructions for multiple simultaneous sources
(2019) In Geophysical Prospecting 67(3). p.1486-1497- 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
- Wittsten, Jens LU ; Andersson, Fredrik ; Robertsson, Johan and Amundsen, Lasse
- organization
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Acquisition, Inverse problem, Mathematical formulation
- in
- Geophysical Prospecting
- volume
- 67
- issue
- 3
- pages
- 1486 - 1497
- publisher
- Wiley-Blackwell
- 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
- 2022-04-25 23:28:24
@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}},
keywords = {{Acquisition; Inverse problem; Mathematical formulation}},
language = {{eng}},
number = {{3}},
pages = {{1486--1497}},
publisher = {{Wiley-Blackwell}},
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}},
volume = {{67}},
year = {{2019}},
}