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A variational formulation for interpolation of seismic traces with derivative information

Andersson, Fredrik LU ; Morimoto, Yoshinori and Wittsten, Jens (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)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
interpolation, seismology, anisotropic diffusion
in
Inverse Problems
volume
31
issue
5
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
2015-05-18 14:42:28
date last changed
2017-09-03 03:32:34
@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.},
  articleno    = {055002},
  author       = {Andersson, Fredrik and Morimoto, Yoshinori and Wittsten, Jens},
  issn         = {0266-5611},
  keyword      = {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},
  volume       = {31},
  year         = {2015},
}