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

Summary The 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.     

Determination of magnitude station corrections for a continental network of seismic stations

Summary A method for determining magnitude station corrections in a network of continental dimensions has been developed and tested for PV waves observed by eight selected Eurasian stations. Regional effects, observed for several stations, were taken into account. It appeared that station corrections could attain considerable values. The application of station corrections diminished both the dispersion of individual magnitude values and standard errors of mean network magnitudes.     

On the stochastic relations between the points of a geodetic network

Summary Three important characteristics of the stochastic relation between the position of one point of a geodetic network and the positions of the remaining points are investigated: a) Change of the ellipse of confidence of the position of a point of the network to the ellipse of confidence of the position of a point of the network, relative to any other point of the network. (This characteristic is called the change of the global ellipse of confidence to the relative ellipse). b) The regression between the positional vector of the investigated point and the positional vectors of some group of other points of the network and c) the so-called total correlation between any two points of the network. The latter characteristic is a question of determining a characteristic direction for each pair of investigated points, which would have the property that the correlation coefficient between the random displacement of the first point in its characteristic direction and the random displacement of the second point in its characteristic direction is maximum.     

Three new species ofSchizothrix Kützing (Cyanophyta) from marine algal mats

Three new species of the genusSchizothrix (Cyanophyta) have been described:Sch. gracilis, Sch. splendida andSch. constricta. They are significant members of many algal mat communities in marine shallow water and intertidal environments.     

Change in the spectrum of a gravity anomaly caused by expressing it discretely

Summary The spectral content of an operation which may be called the operation of selecting the step for treating a certain, discretely expressed datum, continuous by nature is shown.     

Structure function as a characteristic of geophysical fields

Summary Facts 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.     

On the problem of the existence and uniqueness of a discrete,surface, optimum wiener filter,applied to the filtering of geophysical fields

Summary Proof is given of the existence and uniqueness of a discrete, surface, optimum (in the Wiener sense) filter for filtering geophysical fields considering a spectral approach to the construction of the said filter. It is also shown that the filtration coefficients and the filtration errors of the filter, constructed with the help of statistical estimates of the required spectral densities, converge towards their theoretical values. From the mathematical point of view, this paper concludes the building-up of the mathematical model of the discrete Wiener optimum surface filtration, suitable for geophysical fields.     

Effect of station conditions on amplitudes and periods of seismic waves

Summary Station corrections for Prhonice, relating to Praha, were determined for body and surface waves using observations of Kirnos seismographs. The time stability of the station corrections was investigated and the possible causes of observed instabilities were discussed. A systematic difference in periods recorded at the stations was found.Dedicated to Academician Alois Zátopek on His 65th Birthday