Problems connected with the tangential metric coefficient in the Schwarzschild metric: A possible solution

Four situations are shown where the Schwarzschild metric cannot be used or is subject to unsurmountable problems. The first is the question of a metric useful for PPN-formalism checking different gravitational theories. The second problem occurs in connection with Mach's principle, when the flatness of the spacetime inside a massive hollow sphere is a generally accepted solution. The metrical discontinuity on the same spherical shell is a third problem. The fourth one is the anisotropy of the mass-energy of a test particle in the gravitational field. Three principles for solution are proposed:

1. The space is not dilated, but rather contracted, in the gravitational field; then the measurement-rods are shorter and measured distances have greater magnitudes.
2. The potential energy is to be related to a potential level where a stationary observer is placed and the general relativistic potential must be used.
3. A new metric must be introduced which is distinct from the Schwarzschild metric, so that the space in the gravitational field is warped isotropically.

Then the problems stated are shown to be easily solvable.     

Current estimates of the Earth's principal moments of inertia

Summary The principal moments of the Earth's inertia and their differences have been computed and their actual accuracy estimated on the basis of the most recent values of the 2nd degree geopotential parameters (model GEM-T2) and of the parameter H in the precession constant. The contributions due to the zero frequency zonal term in the tidal potential have been determined.

---

au m nmnmuaa 2- mnu (¶rt; GEM-T2) u naama nm nuu n¶rt; aua m uuu u u u amu u ¶rt;am u a mmu. u a¶rt; n¶rt; uu nm amu a a nuu nmuaa.

     

On the determination of the European gravimetric geoid

Summary The method of the automated computation of the gravimetric deflections of the vertical and of the geoidal heights for the European region is described. The work was carried out during the period 1986–1988 by the Topographic Service of the Czechoslovak Army. The computation applies to 20 sheets of the international map 1:1 000 000 (total area of =16^c, =30^c - see Fig. 1). The mean values of the free-air anomalies for each surface element =5, =7.5, approximately 9 × 9 km, were used with radius of integration of 300 km.     

Large-scale distribution of magnetic fields,green corona and prominences during an extended activity cycle

The interrelations of the latitudinal distribution of the coronal green emission maxima, maximal numbers and areas of prominences, magnetic fields, sunspots, and polar faculae in the 20th and 21st sunspot cycles have been investigated. It is again demonstrated how the behaviour of all studied data depends on their heliographic latitude. In the polar zone, well separated from the equatorial we observe following polarity magnetic fields transported only polewards, while the equatorial zone is occupied mostly by leading polarity fields, developed there, moving equatorwards, and crossing the equator to the other hemisphere with the new cycle during the minimum of sunspot activity.This magnetic field distribution is well emphasized by the places of maximal occurrence of prominences and by the distribution of coronal green emission maxima which also differ in dependence on latitude.The question of identifying the first and last evolutionary stages of an extended cycle of activity is discussed and the existence of a magnetic activity cycle lasting 15–17 years is suggested.     

Eruptive instability of magnetic arcades

Eruptive prominences trace disruptions of magnetic arcades in which they are embedded. The stability of an arcade containing an electric current filament at its axis is discussed. The model provides criteria for the onset of the eruptive instability in terms of prominence twist and overall geometry, i.e., the parameters which could be measured directly. The evolution of the eruption is analyzed, and the dependence of the acceleration and the pitch of field-lines on the height is established. The model is compared with the observations of one eruptive prominence where the development of helical structure was followed.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

The vulnerability of karst springs—a case study of the Hubelj spring (SW Slovenia)

The hydraulic behaviour of the karst aquifer in the Hubelj spring catchment area (SW Slovenia) was studied by using an indirect research method based on natural tracers. The variations of natural tracers (in precipitation and in groundwater) during the storm event made possible the separation of the Hubelj spring storm hydrograph by the three-component separation technique. The results produced information on the aquifer recharge, storage and discharge processes, as well as on the mechanisms that affected them. They verified the so-called epikarst hypothesis presuming that an important part of a karst aquifer recharge reaches rapidly and intensively from the epikarst zone. It was demonstrated that epikarst water could occupy up to 50% of the spring discharge during precipitation events. This phenomenon could have important consequences on protection and management of the problems of karst aquifers, including engineering problems in karst areas. With this respect the results could give way to new engineering ideas.     

Documentary Evidence of an Economic Character as a Source for the Study of Meteorological and Hydrological Extremes and their Impacts on Human Activities

This paper deals with documentary evidence of an economic character as a proxy for direct study of meteorological and hydrological extremes. Taxation records and reports of those who administrated domains and estates are described with respect to information about meteorological and hydrological extremes. Based on data from eight domains or estates from Moravia (in the Czech Republic), frequency series of floods and convective storms (including hailstorms) were developed for the period 1650–1849. One example of disastrous weather, which took place on 10 August 1694 in the Pern?tejn domain, is used to demonstrate the potential for such studies of the intensity of extremes and their impact on human activities. The importance of economic evidence in the instrumental period is shown through tax rebate data contingent upon hailstorm damage in Moravia (1896–1906). The benefits of employing documentary economic evidence for historical climatology and the study of the impact of meteorological and hydrological extremes on human activities are discussed.     

Quantification of karst aquifer discharge components during storm events through end-member mixing analysis using natural chemistry and stable isotopes as tracers

Karst aquifer components that contribute to the discharge of a water supply well in the Classical Karst (Kras) region (Italy/Slovenia) were quantitatively estimated during storm events. Results show that water released from storage within the epikarst may comprise as much as two-thirds of conduit flow in a karst aquifer following rainfall. Principal components analysis (PCA) and end-member mixing analysis (EMMA) were performed using major ion chemistry and the stable isotopes of water (δ¹⁸O, δ²H) and of dissolved inorganic carbon (δ¹³C_DIC) to estimate mixing proportions among three sources: (1) allogenic river recharge, (2) autogenic recharge, and (3) an anthropogenic component stored within the epikarst. The sinking river most influences the chemical composition of the water-supply well under low-flow conditions; however, this proportion changes rapidly during recharge events. Autogenic recharge water, released from shallow storage in the epikarst, displaces the river water and is observed at the well within hours after the onset of precipitation. The autogenic recharge end member is the second largest component of the well chemistry, and its contribution increases with higher flow. An anthropogenic component derived from epikarstic storage also impacts the well under conditions of elevated hydraulic head, accounting for the majority of the chemical response at the well during the wettest conditions.     

Petrology and geochemistry of orthoamphibolites from the Variscan metamorphic sequences of the South Tisia in Croatia – an overview with geodynamic implications

In the southern Pannonian Basin, the Variscan Barrovian- and overprinted Abukuma-type progressive metamorphic sequences of the South Tisia in Slavonian Mts. (SM) and Mt. Moslava)ka Gora (MG) are interlayered with orthoamphibolites. These sequences represent part of a disrupted Variscan belt that extends southeastwards of the Bohemian Massif through the Carpathians to the Caucasus. Orthoamphibolites contain hornblende (Mg-hornblende, tschermakite, pargasite, and edenite), plagioclase An_48-98 (MG) and An_26-35 (SM), biotite, grossular (MG) and almandine (SM) enriched garnet, diopside (MG), with accessory ilmenite, titanite, and clinozoisite. Based on major and trace element analyses and CIPW norms, these orthoamphibolites, which originally were olivine tholeiites to slightly alkalic basalts, can be correlated with tholeiites of consuming plate margins. '¹⁸O of orthoamphibolites varies from 5.8 to 7.1‰, the measured ⁸⁷Sr/⁸⁶Sr ratio from 0.70435 to 0.70665, which indicates slight continental crust contamination, and the calculated ratio from 0.70262 to 0.70535, indicating an upper mantle origin of the original basaltic melts. For associated penecontemporaneous I-type granitoids, the calculated initial ⁸⁷Sr/⁸⁶Sr ratio also have upper mantle values ranging between 0.70293 and 0.70368. Geochemical data for orthoamphibolites and the associated penecontemporaneous I-type granites, and the occurrence of alpine-type ultramafic bodies within the Barrovian sequence, indicate that they have many features in common with orogenic associations related to recent subduction-related settings. Some characteristic element ratios suggest back-arc basin environments and the Ce/K vs. Ce diagram suggests a pargasite-lherzolite source. Its partial melting gave primitive basaltic melts of olivine tholeiite to slight alkalic affinities that produced at first differentiated mafic rocks by olivine fractionation (future orthoamphibolites) and, afterwards, a strongly differentiated suite of I-type granitoids by amphibole fractionation. Magma emplacement and subsequent AFC processes took place in subduction environments preceding the main Variscan deformational metamorphic event during which orthoamphibolites were generated. This interpretation is compatible with geodynamic modeling of this part of the Paleotethys.     

Experimental validation of the wavefield transform of electromagnetic fields

The wavefield transform is a mathematical technique for transforming low-frequency electromagnetic (EM) signals to a non-diffusive wave domain. The ray approximation is valid in the transform space and this makes traveltime tomography for 3D mapping of the electrical conductivity distribution in the subsurface possible. The transform, however, imposes stringent frequency bandwidth and signal-to-noise ratio requirements on the data. Here we discuss a laboratory scale experiment designed to collect transform quality EM data, and to demonstrate the practical feasibility of transforming these data to the wavefield domain.
We have used the scalable nature of EM fields to design a time-domain experiment using graphite blocks to simulate realistic field conditions while leaving the time scale undisturbed. The spatial dimensions have been scaled down by a factor of a thousand by scaling conductivity up by a factor of a million. The graphite blocks have two holes drilled into them to carry out cross-well and borehole-to-surface experiments. Steel sheets have been inserted between the blocks to simulate a conductive layer.
Our experiments show that accurate EM data can be recorded on a laboratory scale model even when the scaling of some features, such as drill-hole diameters, is not maintained. More importantly, the time-domain EM data recorded in cross-well and surface-to-borehole modes can be usefully and accurately transformed to the wavefield domain. The observed wavefield propagation delay is proportional to the direct distance between the transmitter and receiver in a homogeneous medium. In a layered medium, data accuracy is reduced and, hence, our results are not so conclusive. On the basis of the experimental results we conclude that the wavefield transform could constitute a valid approach to the interpretation of accurate, undistorted time-domain data if further improvement in the transform can be realized.