Ludmila Kubáčková

Autocovariance function and the spectral density of the anomalous gravitational field, transformed by an integral operator of the convolution type

SummaryThe transfer of the fundamental statistical characteristics, i.e. covariance function and the density of the statistical power spectrum, of a random homogeneous field across a linear homogeneous filter is investigated. The results obtained are applied to the study of the said statistical characteristics of transformed anomalous gravitational field.

A Group of Gravimeters, Stochastical Problems and Their Solution

The study of recent crustal movements needs to perform simultaneously repeated levelling and gravimetric measurements, which have to be processed very carefully with respect to both the optimum estimators of parameters of the first and the second order. The difference between the corresponding components of the estimator of the vector first order parameters in different epochs is a subject for testing hypotheses on the existence or non-existence of significant recent crustal movements; here naturally the estimators of the second order parameters play the fundamental role.

Influence of atmospheric pressure variations on measurements made with Sharpe and Worden gravimeters

SummaryThe paper deals with the influence of the atmospheric pressure variations on Sharpe gravimeters CG 2 No. 226 and 280 and on the Worden gravimeter No. 978, equipped with a thermostat.

Statistical characteristics of geophysical fields in Hilbert's space

SummaryA review of the terms of functional analysis, which can be exploited for statistical treatment of geophysical fields, is given. The procedure for determining the statistical characteristics of the fields, defined by a single realization, which does not require the limiting assumption of homogeneity to be introduced, is outlined.

Correlation between gravity anomalies and the crust-mantle boundary in central Europe

SummaryMethods of simple and multiple linear correlation have been used in investigating the mutual statistical dependence of Bouguer anomalies, terrain elevations and the depths of the crust-mantle boundary determined by the method of Deep Seismic Sounding. Numerical results show a considerable degree of correlation among the quantities mentioned in Central Europe.

The fundamental statistical properties of the Vening-Meinesz and stokes integral transformations

SummaryThe stochastic properties of the vector function, formed by the components ξ and η of the deflection of the vertical and by the height of the geoid ς, are studied by utilizing the mathematical model in[4]. The properties of the error components of the said vector are also studied and a method is described for comparing the results when the vector function was obtained directly by means of astro-geodetic methods and when the vector function was generated by the Vening-Meinesz and Stokes transformation.

Structure function as a characteristic of geophysical fields

SummaryFacts about the statistical properties of random fields may be obtained by analysing their increments (i.e. the differences of values at two points). The properties of structure functions are described and the possibility of testing the statistical homogeneity of geophysical fields and their possible homogeneization are discussed.

Probability model for studying the spectral anomalous geophysical fields

SummaryThe paper is a contribution to the stochastic analysis of geophysical fields. Using Mercers theorem, the theorem of the resolution of Hilberts random field ξ(x), continuous with respect to the quadratic mean, into a general Fourier series which converges uniformly with respect to the quadratic mean to ξ(x), is proved.

Properties of the characteristics of linear transformations of geophysical fields

SummaryProof is given of the theorem which determines the relation between the characteristics of a random function prior to and after linear integral transformation. Moreover, only a single realization of the random function is available in a limited set and statistical homogeneity is not assumed. The characteristics are defined in Section 2 and they correspond to the actual estimates of the statical characteristics.

Mathematical background for studying the stochastical properties of vector geophysical fields

SummaryA mathematical model is constructed for studying the stochastical properties of plane vector geophysical potential fields under the assumption that these fields as a whole, or a particular component of the fields are studied as vector homogeneous random fields.