Measurements of gradients of gravity in mines

¶rt;am mu ¶rt; m mua nu¶rt;nmuaa u nmm a u n¶rt;nuu, m nmm m u u amu m ma u. auam mam a¶rt;ua¶rt;um ama mamau, nu nu nu ¶rt;u m¶rt;.     

An attempt to determine long-periodic variations in the drift of horizontal pendulums

Résumé On donne les résultats de l'analyse de la dérive des pendules horizontaux de la station Píbram-Bezové Hory au cours des années 1927–1938. Différemment aux résultats publiés déjà antérieurement[2], on a tout d'abord séparé par la méthode des moindres carrés la dérive linéaire et le terme à période de durée d'un an exactement et ce n'est que le reste qu'on a analysé par la méthode de l'analyse spectrale spéciale[4, 6]. On a trouvé dans les deux éléments une période de 222, respectivement 223 jours, non considérée jusqu'alors et ne pouvant pas être interprétée jusqu'à présent du point de vue physique. Les autres résultats sont en bon accord avec ceux reçus à l'origine. On peut conclure de la comparaison des phases des composantes annuelles des pendules horizontaux et du mouvement du pôle[5] que les deux événements sont du même origine.     

Approximate spectral analysis by least-squares fit

An approximate method of spectral analysis called successive spectral analysis based upon the mean-quadratic approximation of an empirical function by generalised trigonometric polynomial with both unknown frequencies and coefficients is developed. A few quotations describing some properties of the method as well as one of the possible methods for numerical solution are given.     

综合利用地球物理和地震资料进行北天山地震危险性研究

综合分析地震学、地球物理学资料及地壳深部构造信息，对北天山地震危险性进行评价。作为研究的数学基础采用了对正交归一函数系统进行多维随机抽样的定量分析方法。最后对分析结果的成因进行了解释。     

A radar-based verification of precipitation forecast for local convective storms

Local flash flood storms with a rapid hydrological response are a real challenge for quantitative precipitation forecasting (QPF). It is relevant to assess space domains, to which the QPF approaches are applicable. In this paper an attempt is made to evaluate the forecasting capability of a high-resolution numerical weather prediction (NWP) model by means of area-related QPF verification. The results presented concern two local convective events, which occurred in the Czech Republic (CR) on 13 and 15 July 2002 and caused local flash floods. We used the LM COSMO model (Lokall Model of the COSMO consortium) adapted to the horizontal resolution of 2.8 km over a model domain covering the CR. The 18 h forecast of convective precipitation was verified by using radar rainfall totals adjusted to the measured rain gauge data. The grid point-related root mean square error (RMSE) value was calculated over a square around the grid point under the assumption that rainfall values were randomly distributed within the square. The forecast accuracy was characterized by the mean RMSE over the whole verification domain. We attempt to show a dependence of both the RMSE field and the mean RMSE on the square size. The importance of a suitable merger between the radar and rain gauge datasets is demonstrated by a comparison between the verification results obtained with and without the gauge adjustment. The application of verification procedure demonstrates uncertainties in the precipitation forecasts. The model was integrated with initial conditions shifted by 0.5° distances. The four verifications, corresponding to the shifts in the four directions, show differences in the resulting QPF, which depend on the size of verification area and on the direction of the shift.     

Electromagnetic induction of a three-dimensional conductivity inhomogeneity in the two-layered earth

Summary The calculation of the elements of Green's tensor function is presented for solving the problem of the electromagnetic induction by means of a vector integral equation. A two-layered Earth is considered as the medium, the surface layer including a three-dimensional conductivity inhomogeneity. Use is made of the boundary condition requiring the vertical component of the electric current to be zero at the Earth's surface which partly simplifies the theoretical computation. Long-period asymptotics of the individual complicated functions, occurring in Green's tensor function as well as in the tensor function required to calculate the components of the anomalous magnetic field at the surface of the halfspace, were effected. With the aid of these asymptotics one can obtain estimates of the functions occurring in the theoretical analysis of the problem.     

To the problem of noise reduction in sea-level records used in vertical crustal movement detection

The aim of this investigation is to develop a simple technique that would allow us to use the sea-level records for detecting contemporary vertical crustal movements of duration from several months to several years. The choice of auxiliary data needed for any such analysis is restricted to the regularly available meteorological data to make this approach possible in routine search for precursory movements in earthquake-prone areas. A linear mathematical model is designed to evaluate the effect of atmospheric temperature and pressure variations, river discharge, long periodic tides and Chandlerian motion. Spectra of the residual sea-level variations are also shown. It is concluded that local episodic crustal movements of a magnitude larger than some 10 cm may be detectable by this approach. If finer resolution is needed then it it necessary to also account for steric level, wind, and sea-current variations, for which data are largely non-existent.     

Tensor structure and the least squares

It is shown that for linear parametric adjustment models all the least-squares equations can be obtained from a commutative diagram, where the observation and parameter spaces are regarded as covariant. Their contravariant counterparts are defined through the metric property of the covariance matrix of the observations.     

Electromagnetic induction in a spherical earth with a circular bulge in the upper mantle

Summary Results of computing the anomalies of the variable magnetic field, generated by a harmonically variable field of the H_1,0-type in the model of a spherical Earth with an expressive bulge in the well-conducting part of the mantle, are presented. It was found that not only the radial, but also the tangential component of the magnetic field is disturbed above the bulge. The largest amplitudes of these changes can be observed over the area of the largest slope of the conductivity boundary if the exciting magnetic field is perpendicular to the surface of the interface.