Showing papers on "Covariance mapping published in 1976"
01 Jun 1976
TL;DR: In this article, the properties of covariance functions are discussed, and the authors show that a covariance function may be characterized by three essential parameters: the variance, the correlation length and a curvature parameter.
Abstract: : The report consists of two parts. Part A deals with the mathematical structure of covariance functions. The properties of isotrophy, harmonicity and positive definiteness are discussed, and it is suggested that a covariance function may be characterized by three essential parameters: the variance, the correlation length and a curvature parameter. Finally some spatial covariance models (planar and spherical) are considered. Part B treats the influence of covariances on the results of collocation. Formulas are developed for the standard error of collocation results when using non-optimal covariance functions, also for the case of stepwise collocation. Finally the behavior of interpolation errors with and without the additional use of horizontal gradients is studied by means of power series expansions for covariance functions and by means of Gaussian covariance functions. It is seen that non-optimal covariance functions have relatively little influence on the interpolated values but a very strong effect on covariances as calculated using the conventional formulas. (Author)
73 citations
18 citations
TL;DR: In this paper, the covariance functions and spectra of components of fluid particle velocity are obtained, taking into consideration the effects of free surface fluctuations, for a Gaussian, stationary and homogeneous random gravity wave field in deep water, using infinitesimal wave solutions.
Abstract: Covariance functions and spectra of components of fluid particle velocity are obtained, taking into consideration the effects of free surface fluctuations, for a Gaussian, stationary and homogeneous random gravity wave field in deep water, using infinitesimal wave solutions. Approximate representations of the covariance functions and spectra are also derived. It is shown that the covariance functions and spectra presented in this paper differ from those when the effects of free surface fluctuations are ignored, especially at, around and above the equilibrium surface.
3 citations
01 Apr 1976
TL;DR: A fixed-memory filter is applied to the covariance solution and linear predictor coefficients are sequentially updated on a sample-to-sample basis without requiring recalculated covariance values or inversion of the covariances matrix.
Abstract: A fixed-memory filter is applied to the covariance solution. Linear predictor coefficients are sequentially updated on a sample-to-sample basis without requiring recalculation of the covariance values or inversion of the covariance matrix.
1 citations