Perturbations of time shifts in signal apparition
(2018) In SIAM Journal on Applied Mathematics 78(5). p.2840-2864- Abstract
In the field of exploration geophysics, the method known as "signal apparition" offers a different perspective on how to separate signals acquired from simultaneously fired seismic sources. The method uses a periodic sequence of small time shift variations to encode the different sources, and this choice leads to exact separation of signals in diamond-shaped regions of the frequencywavenumber domain which are twice as large compared to those recovered by other methods. In this paper we investigate the signal apparition method's sensitivity to perturbations of the periodic time shift sequence. We model (measured or unknown) perturbations in a stochastic fashion and prove that the resulting inverse problem of separating the data is still... (More)
In the field of exploration geophysics, the method known as "signal apparition" offers a different perspective on how to separate signals acquired from simultaneously fired seismic sources. The method uses a periodic sequence of small time shift variations to encode the different sources, and this choice leads to exact separation of signals in diamond-shaped regions of the frequencywavenumber domain which are twice as large compared to those recovered by other methods. In this paper we investigate the signal apparition method's sensitivity to perturbations of the periodic time shift sequence. We model (measured or unknown) perturbations in a stochastic fashion and prove that the resulting inverse problem of separating the data is still well-posed, and we demonstrate the stability by numerical simulations on a finite-difference synthetic data set generated over a complex salt model.
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- author
- Wittsten, Jens LU ; Andersson, Fredrik ; Robertsson, Johan ; Van Manen, Dirk Jan and Amundsen, Lasse
- organization
- publishing date
- 2018
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Controlled source seismology, Fourier analysis, Inverse theory, Numerical solutions, Probability theory
- in
- SIAM Journal on Applied Mathematics
- volume
- 78
- issue
- 5
- pages
- 25 pages
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- scopus:85055797327
- ISSN
- 0036-1399
- DOI
- 10.1137/18M1165591
- language
- English
- LU publication?
- yes
- id
- 69f3cbf6-5059-415c-9994-81e7b9231999
- date added to LUP
- 2018-11-26 08:48:31
- date last changed
- 2022-04-25 19:24:20
@article{69f3cbf6-5059-415c-9994-81e7b9231999,
abstract = {{<p>In the field of exploration geophysics, the method known as "signal apparition" offers a different perspective on how to separate signals acquired from simultaneously fired seismic sources. The method uses a periodic sequence of small time shift variations to encode the different sources, and this choice leads to exact separation of signals in diamond-shaped regions of the frequencywavenumber domain which are twice as large compared to those recovered by other methods. In this paper we investigate the signal apparition method's sensitivity to perturbations of the periodic time shift sequence. We model (measured or unknown) perturbations in a stochastic fashion and prove that the resulting inverse problem of separating the data is still well-posed, and we demonstrate the stability by numerical simulations on a finite-difference synthetic data set generated over a complex salt model.</p>}},
author = {{Wittsten, Jens and Andersson, Fredrik and Robertsson, Johan and Van Manen, Dirk Jan and Amundsen, Lasse}},
issn = {{0036-1399}},
keywords = {{Controlled source seismology; Fourier analysis; Inverse theory; Numerical solutions; Probability theory}},
language = {{eng}},
number = {{5}},
pages = {{2840--2864}},
publisher = {{Society for Industrial and Applied Mathematics}},
series = {{SIAM Journal on Applied Mathematics}},
title = {{Perturbations of time shifts in signal apparition}},
url = {{http://dx.doi.org/10.1137/18M1165591}},
doi = {{10.1137/18M1165591}},
volume = {{78}},
year = {{2018}},
}