Compactly supported radial covariance functions

Abstract

The Least-squares collocation (LSC) method is commonly used in geodesy, but generally associated with globally supported covariance functions, i.e. with dense covariance matrices. We consider locally supported radial covariance functions, which yield sparse covariance matrices. Having many zero entries in the covariance matrice can both greatly reduce computer storage requirements and the number of floating point operations needed in computation. This paper reviews some of the most well-known compactly supported radial covariance functions (CSRCFs) that can be easily substituted to the usually used covariance functions. Numerical experiments reveals that these finite covariance functions can give good approximations of the Gaussian, second- and third-order Markov models. Then, interpolation of KMS02 free-air gravity anomalies in Azores Islands shows that dense covariance matrices associated with Gaussian model can be replaced by sparse matrices from CSRCFs resulting in memory savings of one-fortieth and with 90% of the solution error less than 0.5 mGal.