Schlumberger

Technical Paper: Bandwidth Optimization for Compact Fourier Interpolation

Society: EAGE
Paper Number: G026
Presentation Date: 2008
 

Abstract

COMFI is a minimum mean-square-error interpolation technique for data sampled at irregular locations. A particular application of interpolation is the estimation of data on a global, Cartesian grid (regularization). The sampling space can be of arbitrary dimension. The interpolated data are computed as a weighted sum of the actual data in a neighbourhood of the selected interpolation locations. The interpolation operator depends on the actual sampling locations and the interpolation location, but not on the data themselves. The operator is designed to have the minimum mean-square interpolation error among all linear operators over a suitable class of spatially band-limited basis functions. We consider, however, the spatial bandwidth as a parameter to be selected in an optimum way. Typically, we compute the COMFI operator to have the largest bandwidth that the actual sampling regime supports, in the sense that the mean-square interpolation error is below an acceptable threshold. We show that the quality of the operator can be strongly dependent on the bandwidth used for its design, and that the optimum bandwidth can vary significantly with spatial location.

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