Local Covariance Functions and Density Distributions.

Abstract

Abstract : The relationship between covariance functions and the density anomaly distributions generating the gravity field is studied using the ensemble averaging theorem, yielding interpretations of common well-known covariance functions in terms of simplified statistical mass models. Emphasis is on application for local gravity field modelling (e.g. assuming a high degree-and-order spherical harmonic reference field to be used), within the framework of the planar approximation. The very simple relationship existing between the planar power spectrum and the degree variances are treated in detail, and it is outlined how the shape of the power spectrum may be used as a geophysical inversion tool, to yield depths to density contrast interfaces within the earth. As a special application of the simple covariance functions associated with statistical mass distributions, it is shown how least-squares collocation may be interpreted as generalized point mass modelling. Finally, formulas are given for practically applicable local multi-layer covariance models (compensated Poisson model), and gravity anomalies in a number of sample areas in the United States are analyzed to yield empirical covariance functions, power spectra and degree-variances. Originator-supplied keywords included: Gravity, Covariance Functions, Density Distributions, Collocation.