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A variational formulation for interpolation of seismic traces with derivative information

In English

Författare

  • 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.

Publiceringsår

2015

Språk

Engelska

Publikation/Tidskrift/Serie

Inverse Problems

Volym

31

Issue

5

Dokumenttyp

Artikel i tidskrift

Förlag

IOP Publishing

Ämne

  • Mathematics

Nyckelord

  • interpolation
  • seismology
  • anisotropic diffusion

Status

Published

ISBN/ISSN/Övrigt

  • ISSN: 0266-5611