A variational formulation for interpolation of seismic traces with derivative information
(2015) In Inverse Problems 31(5).- Abstract
- We construct a variational formulation for the problem of interpolating seismic data in the case of missing traces. We assume that we have derivative information available at the traces. The variational problem is essentially the minimization of the integral over the smallest eigenvalue of the structure tensor associated with the interpolated data. This has the physical meaning of penalizing the local presence of more than one direction in the interpolation. The variational problem is used to justify the solutions of a non-standard anisotropic diffusion problem as reasonable interpolated images. We show existence and uniqueness for this type of anisotropic diffusion. In particular, the uniqueness property is important as it guarantees that... (More)
- We construct a variational formulation for the problem of interpolating seismic data in the case of missing traces. We assume that we have derivative information available at the traces. The variational problem is essentially the minimization of the integral over the smallest eigenvalue of the structure tensor associated with the interpolated data. This has the physical meaning of penalizing the local presence of more than one direction in the interpolation. The variational problem is used to justify the solutions of a non-standard anisotropic diffusion problem as reasonable interpolated images. We show existence and uniqueness for this type of anisotropic diffusion. In particular, the uniqueness property is important as it guarantees that the solution can be obtained by the numerical schemes we propose. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/5386101
- author
- Andersson, Fredrik LU ; Morimoto, Yoshinori and Wittsten, Jens
- organization
- publishing date
- 2015
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- interpolation, seismology, anisotropic diffusion
- in
- Inverse Problems
- volume
- 31
- issue
- 5
- article number
- 055002
- publisher
- IOP Publishing
- external identifiers
-
- wos:000353548000002
- scopus:84928806242
- ISSN
- 0266-5611
- DOI
- 10.1088/0266-5611/31/5/055002
- language
- English
- LU publication?
- yes
- id
- 0ecaeeee-7ace-4547-ad74-fe451820b8ca (old id 5386101)
- date added to LUP
- 2016-04-01 11:10:43
- date last changed
- 2022-01-26 06:01:39
@article{0ecaeeee-7ace-4547-ad74-fe451820b8ca,
abstract = {{We construct a variational formulation for the problem of interpolating seismic data in the case of missing traces. We assume that we have derivative information available at the traces. The variational problem is essentially the minimization of the integral over the smallest eigenvalue of the structure tensor associated with the interpolated data. This has the physical meaning of penalizing the local presence of more than one direction in the interpolation. The variational problem is used to justify the solutions of a non-standard anisotropic diffusion problem as reasonable interpolated images. We show existence and uniqueness for this type of anisotropic diffusion. In particular, the uniqueness property is important as it guarantees that the solution can be obtained by the numerical schemes we propose.}},
author = {{Andersson, Fredrik and Morimoto, Yoshinori and Wittsten, Jens}},
issn = {{0266-5611}},
keywords = {{interpolation; seismology; anisotropic diffusion}},
language = {{eng}},
number = {{5}},
publisher = {{IOP Publishing}},
series = {{Inverse Problems}},
title = {{A variational formulation for interpolation of seismic traces with derivative information}},
url = {{http://dx.doi.org/10.1088/0266-5611/31/5/055002}},
doi = {{10.1088/0266-5611/31/5/055002}},
volume = {{31}},
year = {{2015}},
}