A variational formulation for interpolation of seismic traces with derivative information

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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.

Detaljer

Författare
  • Fredrik Andersson
  • Yoshinori Morimoto
  • Jens Wittsten
Enheter & grupper
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematik

Nyckelord

Originalspråkengelska
Artikelnummer055002
TidskriftInverse Problems
Volym31
Utgåva nummer5
StatusPublished - 2015
PublikationskategoriForskning
Peer review utfördJa