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A variational formulation for interpolation of seismic traces with derivative information

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Author

  • Fredrik Andersson
  • Yoshinori Morimoto
  • Jens Wittsten

Summary, in English

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.

Publishing year

2015

Language

English

Publication/Series

Inverse Problems

Volume

31

Issue

5

Document type

Journal article

Publisher

IOP Publishing

Topic

  • Mathematics

Keywords

  • interpolation
  • seismology
  • anisotropic diffusion

Status

Published

ISBN/ISSN/Other

  • ISSN: 0266-5611