Determination of the geopotential scale factor from satellite altimetry

Summary The geopotential scale factor R ₀ =GM/W ₀ has been determined on the basis of satellite altimetry as R _{0=(6 363 672·5±0·3) m} and/or the geopotential value on the geoid W ₀ =(62 636 256·5±3) m ² s ^–2 . It has been stated that R ₀ and/or W ₀ is independent of the tidal distortion of surface W=W ₀ due to the zero frequency tide.

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¶rt;a nmu amumuu u ama amnmuaa R ₀ =GM/W ₀ =(6 363 672,5±0,3) m u/uu aunmuaa a nmuu¶rt;a W ₀ =(62 636 256,5±3) m² s^–2. m, m R ₀ u/uu W ₀ auum m nm amu a a nuu ¶rt;au nmu W=W ₀ .

     

To three aniversaries of czechoslovak geophysics in 1983

Summary 30 years from the foundation of the Czechoslovak and Slovak Academy of Sciences in 1953 are commemorated in connection with 40 years elapsed from the decase of Prof. V. Láska, founder of gephysics in Cezchoslovakia. The progress achieved in its main lines and the outlooks of further development are described.

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mam na 30-m u a u a aa¶rt;u a, ¶rt;a 1953-¶rt;, u u 40-mu m mu a . aa, amuuu auu. nua m mam u¶rt;au n anau u ¶rt;am nnmu ¶rt;a aumu.

     

On the possibility of utilizing grid reports in a local model of short-range forecast of meteorological elements

Summary In the experiment described, we test the possibility of utilizing forecasts of the pressure field, contained in GRID reports, to solve the problem of horizontal boundary conditions of a local model of short-range forecast of meteorological elements. We prove that the assumption of a linear tendency of the prognostic variables in the boundary region yields good results, using the Perkey-Kreitzberg method[1], even if applied to period T=24 hrs. In the Perkey-Kreitzberg method the effect of the horizontal diffusion in the boundary region is suppressed[2]. However, considering the diffusive term apart from the procedure of the method mentioned proves detrimental to the forecast.

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nua num n m unau n n ¶rt;au, ¶rt;au ¶rt; ¶rt; u numaau u a ¶rt;u am na muu m. aam, m n¶rt;nu u m¶rt;uu nmuu n au amu nu unauu m¶rt;a u- [1] ¶rt;am u mam ¶rt;a nu nuuu nu¶rt; T=24 a. m¶rt; u- nu¶rt;um n¶rt;au uuuma ¶rt;uuu au amu[2]. ama ¶rt;u a n¶rt; nu¶rt; m¶rt;a nu¶rt;um, ¶rt;a, ¶rt;u n.

     

Forecast of abnormally high solar activity in the next century and of its possible negative effects on the earth

Summary Based on the relation between the relative sunspot number R, the number of sunspot groups f ₀ generated per unit time on the Sun as a whole and their average lifetime T ₀ , and on the extrapolation of time behaviour of f ₀ and T ₀ , it is proved that abnormally high solar activity may be expected in the first half of the 21st century. At this time, the maximum annual relative sunspot numbers R_M of the 11-year cycles should reach values of about 300 units. This abnormally high solar activity in the next century can be understood as the antipole of the Maunderean minimum. This forecast is used to discuss some of the possible consequences of this abnormally high solar activity for the processes on the Earth: changes of climate (heat waves and draughts in Central Europe), in the higher layers of the Earth's atmosphere (anomalous propagation of radio waves, increased effect of the density of the upper atmosphere on the orbits of man-made satellites), in seismicity (increased seismic activity in Europe and Southeast Asia), for technical devices (induced electric currents), in the biosphere. etc.

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a mu ¶rt; uau a R nm, unn nm f ₀ uu ¶rt;uu u a ë u u ¶rt; n¶rt;ummu uu ₀ , u a manuu ¶rt;a f ₀ u ₀ , naa, m n nu ¶rt; 21 a u¶rt;am uum amum. aua¶rt;u ua a R m¶rt; 11-mu ua m u ¶rt;muam au 300 ¶rt;uu. m uum amum ¶rt; nuam a amun¶rt; a¶rt; uua. a m na ¶rt;am m n¶rt;mu m uum amumu a n nmau a : a uu uama (aa u a n¶rt;a ¶rt; n), a u u am u (aa anmau a¶rt;u, uu n nmmu u am a ¶rt;uu um m), a um (na ua amum n u -m uu), a muu mma (u¶rt;ua muu mu), a u u ma ¶rt;a.

     

Resonance frequencies in the sun's motion

Summary The position of the Sun with respect to the gravity centre of the Solar System for the beginning of every year of a 3100 — year time series was determined and the harmonic analysis of the parameters of the Sun's motion about the gravity centre was carried out.

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unu u u ¶rt; ¶rt;¶rt; u ¶rt; ¶rt;u 3100 u c¶rt;uu u n ¶rt;uu u.

     

Diurnal asymmetry of radio wave absorption on anomalous winter days

au uu nu a¶rt;u a amma a nu¶rt; 1966–1981 naa, m ¶rt;, auu m m, u nu u ¶rt; uu n n¶rt;, ¶rt;num nu aa ¶rt; ¶rt;a n n¶rt;. m uu aa ¶rt;u u mu u.     

Calculation of particle distribution by the data on spectral transparency

, , . . , , , . , , .Summary A general method for obtain the particle size distribution curve of the dispersed system is developed according to data of its spectral transparency, based onMellin's transformation. The method does not contain any arbitrary suppositions about spectrum character of particles. A simple calculation scheme is supposed, examples of inversion are given, the range of spectrum and the accuracy of transparency measurements necessary to obtain the inversion with a given accuracy are estimated. The calculation scheme is appropriate for every kind of errors of measurement and calculation and contains moderate requirements to their accuracy.     

Behaviour of quartz gravity meters under high frequency vertical motion

Summary Tests on the vertical vibrating table in the frequency range of70–110 Hz indicate that quartz gravity meters are10–100 times more sensitive at some frequencies than under low-frequency excitation. At high frequencies, the reading beam is at rest and deflected from the correct position. Slow fluctuations of amplitude and frequency near resonance could cause slow irregular motion of the beam with absence of low-frequency ground motion of sufficient intensity.

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unmauaum a mua um¶rt; ¶rt;uana amm 70–110u mam, m a m ammaaum 10–100 a mum nu uamm au. u amm au u a¶rt;um n m mu m nu. ¶rt; auauu anum¶rt; u amm au uu aa m am uamm u ua ¶rt;a mmmm uamm au n ¶rt;mam umumu.

     

On the gravitation absorption hypothesis

Summary It is recommended that the data from measurements with supraconducting gravity meters be also analysed with regard to verifying the gravitation absorption hypothesis. Based on theoretical data from a3-year period, the spectrum of the assumed effect of shielding the gravitational influence of the Sun by the Earth's body on the value of the acceleration of gravity has been calculated for the tidal station Brussels (Figs 2a–e).

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¶rt;aam aauuam ¶rt;a uu n¶rt;uaumau ma mu u nuunm n¶rt;auaumauu. a mmuu ¶rt;a a mmu nu¶rt; u nm n¶rt;naa ma auauaumau ¶rt;mu a m a uu u u mmu ¶rt; nuu mauu (u. 2a–).

     

Global geoidal undulations as inferred from the Bruns formula and from inversion of the geopotential series

Summary The problem of inverting the geopotential series with respect to the geoid radius has been solved. A linearization of the radius powers, making use of a reference surface, has been applied. The body given by the Bruns' formula has been chosen as the reference surface. Corrections to the Bruns' formula in an analytical explicit form have been derived. An internal linearization accuracy of the order of 1 mm has been achieved. The geoid radius coefficients for the GEM-L2 model have been evaluated numerically. The corrections have been found to range from –90 to 90 cm.

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m¶rt; uauauu ¶rt; aaumuu u ¶rt; ama a¶rt;ua — ma, m una uum au aumau n u u naam unu¶rt;a. u u¶rt; una um uum u nmuaa u uum au a¶rt;ua — ma. ¶rt;a¶rt;amua ua, aa uauau, n¶rt;a 1 . u¶rt; u am ¶rt; ¶rt;uaumau n GEM-L2. au na nm mm m am nu annuauuu¶rt;a, a a m a, n¶rt;a ± 90 .

     

Die heterogenen sphäroidischen Gleichgewichtsfiguren und das Normalsphärold der Erde

Zusammenfassung Die Gleichgewichtsfiguren lassen sich gänzlich unabhängig vom Dichtegesetz durch die Eingeschaft charakterisieren, daß der Absolutbetrag des Formparametersf0 ein Minimum sein muß. Diese merkwürdige Eigenschaft liefert eine Gleichung zwischen der geometrischen Abplattung und den beidenStokesschen Konstanten und , mit deren Hilfe aus den ⁴ Lösungen desHelmertschen Gleichungssystems für eine bestimmte Masse die ³ Gleichgewichtsfiguren ausgesiebt werden können. Jede beliebige heterogene sphäroidische Gleichgewichtsfigur ist entweder durch die Masse und die Gestalt ihrer freien Oberfläche oder durch die Masse und drei physikalische Parameter gänzlich eindeurig bestimmt; sie hat ein streng individuelles Dichtegesttz. Aus der dreifach unendlichen Mannigfaltigkeit der Gleichgewichtsfiguren können linear Reihen herausgegriffen werden, indem man entweder zwei physikalische Parameter festhält oder indem man die Figuren aufsucht, welche eine gegebene Fläche zur gemeinsamen äußeren Niveaufläche besitzen oder die Reihe jener Gleichgewichtsfiguren, die sich aus der Schar der äußeren Niveauflähen einer gegebenen Gleichgewichtsfigur bilden läßt.Obwohl das HauptträgheitsmomentC keineStockessche Konstante ist, kann das durch ,W ₀ undC eindeutig definierte Normalsphäroid der Erde hypothesenfrei bestimmt werden, weil in der Reihe (,K) auch die Trägheitsmomente und damit die dynamische Abplattung konstant ist. Damit kann die empirisch bekannte dynamische Abplattung mittels des Rückganges auf die homogene Ausgangsfigur der Reihe (,K) durch die statische Abplattung ersetzt werden. Allerdings muß der Ableitung des Normalsphäroides an Stelle der primär unbekannten Werte für die Erdmasse und den Potentialwert des Geoides die Äquatorschwere und die Äquatorachse zugrunde gelegt werden.Abschließend werden noch die drei linearen Reihen (,W ₀), (,K) und (W ₀,K) diskutiert, welche sich im Normalsphäroid schneiden müssen. Auch kann in dem mit den Achsena, undh _m gebildeten Koordinatensystem die Hüllfläche der Gleichgewichtsfiguren angegeben werden; sie ist durch den Formparameterf=–3a²/2 gekennzeichnet.

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Summary The figures of equilibrium independant from the law of density in their interior can be characterized by the remarkable property that the absolute value of the «shape-parameter» must be a minimum. This gives an equation between the flattening and the twoStokes constant and , by which the ³ figures of equilibrium can be selected from the ⁴ solutions ofHelmert's equations for a given mass. Each inhomogeneous spheroidical figure of equilibrium is determined unequivocally by the mass and the shape of its free surface or by the mass and three physical parameters; the law of density is strictly individual. From the threefold infinite multiplicity of the figures of equilibrium linear series are to find out with two fixed physical parameters or you can compute a series of figures with a common level surface or the series built by all level surface of a given figure of equilibrium.Though the moments of inertia are notStokes constants the normal spheroid of earth unequivocally defined by ,W ₀ andC can be determined without hypotheses, because in the series (,K) also the moments of inertia and the mechanical ellipticity are constant. Therefore the empirically known mechanical ellipticity can be substituted by the static flattening returning to the homogenous figure in the beginning of the series. Of course the determination of the normal spheroid of earth demands the knowledge of gravity in equator and of the equator-axis instead of the unknown mass of earch series (,W ₀), (,K) and (K,W ₀), which intersect in the normal spheroid, are discussed. Also the boundary surface of the figures of equilibrium in the Cartesian system of the coordinatesa, andh _m is discussed; this surface is determined byf=–3a²/2.

     

Fracture surface energy of olivine

A relatively simple indentation technique for the rapid measurement of fracture surface energy, , of small samples is described. The reliability of this technique is assessed by testing soda-lime glass for which there are good independent fracture mechanics determinations of fracture surface energy. The indentation technique gives a value for of 4.33 J m^–2 which compares favourably with the accepted value of 3.8 J m^–2. Fracture surface energies of the {010} and {001} cleavage planes of single crystal olivine (modal composition Fo₈₈Fa₁₂) are then determined and compared with theoretical estimates of the thermodynamic surface energy, , calculated from atomistic parameters ( is equal to in the absence of dissipative processes during crack extension). The experimental values for _{010} and _{001} are respectively 0.98 J m^–2 and 1.26 J m^–2. The calculated values of _{010} and _{001} are respectively in the range from 0.37 J m^–2 to 8.63 J m^–2 and 12.06 J m^–2. The particular advantages of the indentation technique for the study of the fracture surface energies of geological materials are outlined.     

Absorption of direct solar radiation by water vapour

Summary Radiation absorption by water vapour plays an important role in the physics of the atmosphere. The calculation of the absorbed radiation energy by water vapour requires the amount of precipitable water in the atmosphere to be known. Actinometric and aerological measurements were used to establish the relation between vapour pressure and absorbed solar radiation.

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u a¶rt;uauu ¶rt; nam uam a amu uuu am. uu n a¶rt;uauu ¶rt; na a¶rt; am m a¶rt; ¶rt; am. u¶rt; mu ¶rt; ¶rt;au ¶rt; naa u n a¶rt;uau a amu muu u auu uu.

     

Molecular refraction in the Earth's mantle

The Drude law (molecular refraction) for the temperature radiation in a monoatomic model of the Earth's mantle is derived. The considerations are based on the Lorentz electron theory of solids. The characteristic frequency (or eigenfrequency) of independent electron oscillators (in energy units, ) is identified with the band gapE _G of a solid. The only assumption is that solid material related to the Earth's mantle has the mean atomic weight A21 g/mole, and its energy gap (E _G) is about 9 eV. In this case the value of molecular refraction (in cm³/g) is (n ²–1)/=0.5160.52, where andn are the density and the refractive index at wavelength _D=0.5893 m (sodium light), respectively. The average molecular refraction of important silicate and oxide minerals with A21, obtained byAnderson andSchreiber (1965) from laboratory data, is , where denotes the mean arithmetic value calculated from three principal refractive indices of crystal. For the rock-forming minerals with 19A<24 g/mole the new relation was found byAnderson (1975).     

Approximate solutions of the surface mass loading of a spherical Earth model

Summary Simple linear representation of the components of an approximate plane solution of point mass loading of the Earth's surface in a conveniently chosen coordinate system leads to selection of a 2nd-degree curve which is the best fit of the spherical solution for the given Earth model. The new approximate solution, which, analogously to the plane solution, can be called a parabolic solution, enables the simple input parameters of the plane solution to be used also for substantially larger angular distances. The comparison with the spherical solution is carried out by computing the effects of the M₂-wave of ocean tides. The results of the computations for the tidal station Brussels prove the two solutions to be in sufficient agreement for global problems as well.

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m nu uau aa nuuum nm u m m au nmu u n¶rt;¶rt; um ¶rt;uam ¶rt;m ma u m mnu, ma auu a n¶rt;¶rt;um u u ¶rt; ¶rt;a ¶rt;u u. nuuum u, m n aauu nm u aam naauu u, nm unam nm ¶rt; ¶rt;a nm u ¶rt;a ¶rt; m u amu. au uu u m uu uu ₂ u nuu. mam uu ¶rt; nuu mauu ¶rt;aam ¶rt;mum au u u ¶rt;a ¶rt;a a¶rt;a.

     

НЕКОТОРЫЕ СВЯЗЫ ЭЛЕКТРИЧЕСКИХ ПАРАМЕТРоВ ГОРНЫХ ПОРоД И ИХ ХИМИЧЕСКОГО СОСТАВА

au aa ¶rt;a, nuau uuu ma n¶rt; u m muu uu, n¶rt; m¶rt;a nm (). u a m u ¶rt; uuu ma u muuu uuau.

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Summary Analysis of the data set describing the chemical composition of the rocks and their electrical parameters was performed by the principal component method. Some relations between chemical composition and electrical parameters were established.

     

Accuracy in measurements and the temperature and volume dependence of thermoelastic parameters

To obtain the temperatureT and volumeV (or pressureP) dependence of the Anderson-Grüneisen parameter _T , measurements with high sensitivity are required. We show two examples:P, V, T measurements of NaCl done with the piston cylinder and elasticity measurements of MgO using a resonance method. In both cases, the sensitivity of the measurements leads to results that provide information about _T (,T), where V/V ₀ andV ₀ is the volume at zero pressure. We demonstrate that determination of _T leads to understanding of the volume and temperature dependence ofq=( ln / lnV) _T over a broadV, T range, where is the Grüneisen ratio.     

Lamé's elastic constants determined from the results of geodetic measurements

m¶rt; n¶rt;u amu mam a u , a a ¶rt;a an¶rt;uu ¶rt; a um ¶rt;auua u a mama uu uu, un uu ¶rt; a nu¶rt; n¶rt; anu ¶rt;auua u n anu. u u¶rt;um u n¶rt;nu, m nuuum ¶rt;muma na nnuam ¶rt; uu uu nu m, u au mam uuau, u nmua u numu ¶rt; a mu ma. ¶rt; n¶rt;nam, m uu nu aum m amu mam ¶rt; (mam a u ). mm m¶rt; nu amu ¶rt;auua aua a au, a muu uu =(0,69±0,03)×10¹¹ a mmmm uua ¶rt;u a ¶rt;u m 100 ¶rt; 200 .     

Is there any relation between the sun's motion and global seismic activity?

Summary The seismic energy released by global earthquake activity with time was correlated with F=||, where || is the absolute value of the change of the Sun's acceleration with time. For deep earthquakes and probability P=0.95, the coefficient of correlation was found to be around 0.4. For shallow earthquakes, the dependence was not proved.

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¶rt;a u uu (1900–1982.) ua ¶rt; F=||,¶rt; || am au uu u a. mu (h>60 ) u ¶rt; mmu =0.95 uum uu ¶rt;muam0.45. nm mu auum a n¶rt;m¶rt;a.

     

On the propagation of finite Love Waves

Summary The problem of the propagation of finite Love Waves in a heterogeneous elastic half space lying over a homogeneous elastic half space, using the quasilinear stress-strain relation due toS. Ferhst [4] is considered in detail. The variations of the parameter in the layer assumed to be of the form 1= 0e ^z, 0e ^z where is a constant andz is distance measured from the surface into the layer.