A variational formulation for interpolation of seismic traces with derivative information

被引:2
作者
Andersson, Fredrik [1 ]
Morimoto, Yoshinori [2 ]
Wittsten, Jens [2 ]
机构
[1] Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden
[2] Kyoto Univ, Grad Sch Human & Environm Studies, Kyoto 6068501, Japan
基金
瑞典研究理事会; 日本学术振兴会;
关键词
interpolation; seismology; anisotropic diffusion; EDGE-DETECTION; RECONSTRUCTION; REGULARIZATION; FRAMEWORK; PDES;
D O I
10.1088/0266-5611/31/5/055002
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
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页数:32
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