Advanced

Perturbations of time shifts in signal apparition

Wittsten, Jens LU ; Andersson, Fredrik; Robertsson, Johan; Van Manen, Dirk Jan and Amundsen, Lasse (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.

(Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
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
SIAM Publications
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
2019-01-06 14:17:15
@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},
  keyword      = {Controlled source seismology,Fourier analysis,Inverse theory,Numerical solutions,Probability theory},
  language     = {eng},
  number       = {5},
  pages        = {2840--2864},
  publisher    = {SIAM Publications},
  series       = {SIAM Journal on Applied Mathematics},
  title        = {Perturbations of time shifts in signal apparition},
  url          = {http://dx.doi.org/10.1137/18M1165591},
  volume       = {78},
  year         = {2018},
}