Mathematical model of the spectral decomposition of periodic and non-periodic geophysical stationary random signals

Summary A model is discussed for the spectral decomposition of stationary periodic and non-periodic functions, suitable for studying various geophysical signals. The properties of the individual components of the random spectrum of the periodic stationary random function was shown in the geometry of Hilbert space of random quantities, and these were used to construct the periodic continuation of the random stationary function, given in a finite interval.     

Contribution to the estimation of the co-ordinates of the centre of gravity of a disturbing body

Summary It has been proved that the formulae for determining the horizontal co-ordinates of the centre of gravity, derived by Gamburtsev in 1938 and adopted in many textbooks of gravimetry and other works, are not accurate. A method of estimating the co-ordinates of the centre of gravity of a disturbing body has been elaborated under the assumption that just the values of the vertical gradient of the disturbing gravitational potential in the xOy-plane are known.     

Computation of synthetic seismograms in 2-D and 3-D media using the Gaussian beam method

Summary The Gaussian beam method is applied to vertical seismic profiling in 2-D and 3-D models. A simple approach to the computation of Gaussian beam seismograms in the vicinity of structural interfaces is proposed. The effects of (a) the radiation pattern of a point source, (b) noncausal attenuation, (c) transverse inhomogeneities in synthetic seismograms are studied on numerical examples.

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Statistical characteristics of geophysical fields in Hilbert's space

Summary A 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.     

A note on the superluminal velocity in cosmological models

This note removes a misunderstanding in the interpretation of solutions of the equations of motion in Friedmann's model.     

Reconstruction of a large runout landslide in the Krušné hory Mts. (Czech Republic)

The aims of this study were to summarize current knowledge of a large runout prehistoric landslide, critically review all of the existing data and, in particular, gather new data in order to estimate the age of the accumulation and reveal the movement mechanism. The reconstruction of a large rockslide-rock avalanche in the NW part of the Czech Republic was supported by the analysis and interpretation of 216 boreholes and by GIS analysis of the original 1950s pre-mining surface using digitized old military topographic maps. For the age estimation, we used the Schmidt hammer test. The total volume of the quaternary deposit was calculated to be between 25.4 and 27.4 mil m³, occupying an area of 778,000 m² and consisting of six to eight generations of colluvial sediments. Three main landslide events were identified based on extensive Schmidt hammer sampling, and the approximate age was established using a regression equation assembled by Engel (2007). All three of the documented events occurred around the time of significant climate change. The oldest event occurred due to the Oldest Dryas warming, the largest event probably occurred at the end of the Younger Dryas (11,700 yBP), and the youngest of the documented events was purely of a Holocene age, with the highest landslide frequency being during the Atlantic temperature fluctuations (approximately 8200 yBP). The slope deformation occurred on a fault slope with a relative height of over 400 m and in tectonically weakened rocks. Sediments in the Most Basin were weakened from meltwater during rapid warming periods, which allowed mobilization of rockslide deposits and runout of up to 1000 m from the mountain foothills.     

Magma hybridization in the Western Tatra Mts. granitoid intrusion (S-Poland, Western Carpathians)

In the Variscan Western Tatra granites hybridization phenomena such as mixing and mingling can be observed at the contact of mafic precursors of dioritic composition and more felsic granitic host rocks. The textural evidence of hybridization include: plagioclase?CK-feldspar?Csphene ocelli, hornblende- and biotite-rimmed quartz ocelli, plagioclase with Ca-rich spike zonation, inversely zoned K-feldspar crystals, mafic clots, poikilitic plagioclase and quartz crystals, mixed apatite morphologies, zoned K-feldspar phenocrysts. The apparent pressure range of the magma hybridization event was calculated at 6.1?kbar to 4.6?kbar, while the temperature, calculated by independent methods, is in the range of 810°C?770°C. U-Pb age data of the hybrid rocks were obtained by in-situ LA-MC-ICP-MS analysis of zircon. The oscillatory zoned zircon crystals yield a concordia age of 368?±?8?Ma (MSWD?=?1.1), interpreted as the age of magma hybridization and timing of formation of the magmatic precursors. It is the oldest Variscan magmatic event in that part of the Tatra Mountains.     

Eclipsing Binaries with Possible Light-Time Effect

The period changes of six eclipsing binaries have been studied with focus on the light-time effect. With the least squares method we also calculated parameters of such an effect and properties of the unresolved body in these systems. With these results we discussed the probability of presence of such bodies in the systems with respect to possible confirmation by another method. In two systems we also suggested the hypothesis of fourth body or magnetic activity for explanation of the "second-order variability" after subtraction of the light-time effect of the third body.