Advanced

Fixed point algorithms for detection of parabolic events

Andersson, Fredrik LU and Carlsson, Marcus LU (2016) In SEG Technical Program Expanded Abstracts 35. p.3997-4002
Abstract

In this paper we show how to convert the problem of estimating delay, slope and curvature of a parabolic event into a frequency estimation problem. Two dimensional data (time and offset) is converted into samples on a two-dimensional manifold embedded in a three-dimensional spaced. To conduct frequency estimation on this manifold we design general domain Hankel matrices and make use of a fixed point algorithm that is designed to find minima of convex envelopes of functionals using a combination of a rank penalty and a misfit function, under the constraint of a certain matrix structure. We illustrate that the proposed method can successfully detect the parameters of the parabolic events also in the case of unequally spaced spatial... (More)

In this paper we show how to convert the problem of estimating delay, slope and curvature of a parabolic event into a frequency estimation problem. Two dimensional data (time and offset) is converted into samples on a two-dimensional manifold embedded in a three-dimensional spaced. To conduct frequency estimation on this manifold we design general domain Hankel matrices and make use of a fixed point algorithm that is designed to find minima of convex envelopes of functionals using a combination of a rank penalty and a misfit function, under the constraint of a certain matrix structure. We illustrate that the proposed method can successfully detect the parameters of the parabolic events also in the case of unequally spaced spatial sampling and in the presence of rather high levels of noise.

(Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
SEG Technical Program Expanded Abstracts
volume
35
pages
6 pages
publisher
Society of Exploration Geophysicists
external identifiers
  • scopus:85019114895
ISSN
1052-3812
DOI
10.1190/segam2016-13869576.1
language
English
LU publication?
yes
id
b426582c-d017-4e75-8b16-98be1c5adc98
date added to LUP
2017-06-07 09:41:06
date last changed
2017-06-07 09:41:06
@article{b426582c-d017-4e75-8b16-98be1c5adc98,
  abstract     = {<p>In this paper we show how to convert the problem of estimating delay, slope and curvature of a parabolic event into a frequency estimation problem. Two dimensional data (time and offset) is converted into samples on a two-dimensional manifold embedded in a three-dimensional spaced. To conduct frequency estimation on this manifold we design general domain Hankel matrices and make use of a fixed point algorithm that is designed to find minima of convex envelopes of functionals using a combination of a rank penalty and a misfit function, under the constraint of a certain matrix structure. We illustrate that the proposed method can successfully detect the parameters of the parabolic events also in the case of unequally spaced spatial sampling and in the presence of rather high levels of noise.</p>},
  author       = {Andersson, Fredrik and Carlsson, Marcus},
  issn         = {1052-3812},
  language     = {eng},
  pages        = {3997--4002},
  publisher    = {Society of Exploration Geophysicists},
  series       = {SEG Technical Program Expanded Abstracts},
  title        = {Fixed point algorithms for detection of parabolic events},
  url          = {http://dx.doi.org/10.1190/segam2016-13869576.1},
  volume       = {35},
  year         = {2016},
}