Fixed point algorithms for detection of parabolic events
(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)
- author
- Andersson, Fredrik LU and Carlsson, Marcus LU
- organization
- publishing date
- 2016
- 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
- 2022-04-09 08:53:26
@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}}, doi = {{10.1190/segam2016-13869576.1}}, volume = {{35}}, year = {{2016}}, }