Covariance-Based Interpolation

Abstract

I test and extend an image interpolation algorithm designed for digital images to suite seismic data sets. The problem of data interpolation can be addressed by determining a lter based on global and local covariance estimates. Covariance estimates have enough information to discern the presence of sharp discontinuities (edges) without the need to explicitly determine the dips. The proposed approach has given encouraging results for a variety of textures and seismic data sets. However, when sampling is too coarse (aliasing) a proxy data set needs to be introduced as an intermediate step. In images with bad signalto-noise ratio, covariance captures the trend of the signal as well as that of the noise; to handle such situations, a model-styling goal (regularization) is incorporated within the interpolation scheme. Various test cases are illustrated in this article, including one using post-stack 3D data from the Gulf of Mexico.