Far-zone contributions to the gravity field quantities by means of Molodensky’s truncation coefficients

To reduce the numerical complexity of inverse solutions to large systems of discretised integral equations in gravimetric geoid/quasigeoid modelling, the surface domain of Green’s integrals is subdivided into the near-zone and far-zone integration sub-domains. The inversion is performed for the near zone using regional detailed gravity data. The farzone contributions to the gravity field quantities are estimated from an available global geopotential model using techniques for a spherical harmonic analysis of the gravity field. For computing the far-zone contributions by means of Green’s integrals, truncation coefficients are applied. Different forms of truncation coefficients have been derived depending on a type of integrals in solving various geodetic boundary-value problems. In this study, we utilise Molodensky’s truncation coefficients to Green’s integrals for computing the far-zone contributions to the disturbing potential, the gravity disturbance, and the gravity anomaly. We also demonstrate that Molodensky’s truncation coefficients can be uniformly applied to all types of Green’s integrals used in solving the boundaryvalue problems. The numerical example of the far-zone contributions to the gravity field quantities is given over the area of study which comprises the Canadian Rocky Mountains. The coefficients of a global geopotential model and a detailed digital terrain model are used as input data.     

Discussion of Mean Gravity Along the Plumbline

According to the definition of the orthometric height, the mean value of gravity along the plumbline between the Earth's surface and the geoid is defined in an integral sense. In Helmert's (1890) definition of the orthometric height, a linear change of the gravity with depth is assumed. The mean gravity is determined so that the observed gravity at the Earth's surface is reduced to the approximate mid-point of the plumbline using Poincaré-Prey's gravity gradient. Niethammer (1932) and later Mader (1954) took into account the mean value of the gravimetric terrain correction within the topography considering the constant topographical density distribution along the plumbline (for more details see Heiskanen and Moritz, 1967). Vaníek et al. (1995) included the effect of the lateral variation of the topographical density into the definition of Helmert's orthometric height. Recently, Hwang and Hsiao (2003) discussed the influence of the vertical gradient of disturbing gravity on the orthometric heights. In this paper, the mean integral value of gravity along the plumbline within the topography is defined so that the actual topographical density distribution and the change of the disturbing gravity with depth are taken into account. Based on the definition of the mean gravity, the relation between the orthometric and normal heights is discussed.     

Geophysical Field Pattern in The West Bohemian Geodynamic Active Area

Regional geophysical data from detailed gravity survey, airborne magnetometry and gamma-ray spectrometry were analysed in order to determine the subsurface extent of contrasting geological bodies and to highlight subtle anomalies which can be related to the occurrence of earthquake swarms. Potential field data were compiled into contour and colour-shaded relief maps suitable for detecting structural tectonic elements. A shaded relief map of the horizontal gradient of gravity was used to detect considerable structural and tectonic features. The results of airborne gamma-ray spectrometry, showing the regional total gamma-ray activity, abundance of uranium, thorium and potassium, were included in this study. Only the two most instructive maps – the total gamma-ray activity and the abundance of potassium are shown. The main line of epicentres Nový Kostel – Poátky coincides well with the N-S configuration of abundances of these natural radioactive elements. The epicentres of micro-earthquakes detected by the local seismological network KRASLICE for the 1991 to 1998 period were plotted in the geophysical maps. The hypocentres of earthquakes in the main epicentral zone at Nový Kostel were projected onto the crustal density model based on the interpretation of seismic reflection profile 9HR and gravity data. The average distance between the Nový Kostel epicentral zone and the seismic profile was 4-5 km. Based on the interpretation of gravity data the hypocentres of the main epicentral zone seem to be associated with the western margin of the Eibenstock - Nejdek (Karlovy Vary) Pluton and, beside that, they follow the depth level where the allochthonnous part of the Saxothuringian Zone is thrust over the European parautochton. A drawing of the geodynamic model of the area is also shown.     

Estimation of the value of the electric field in the upper ionosphere before an earthquake

Summary Plasma parameters were measured by the Intercosmos 24 satellite at altitudes between 2300 km and 2500 km about 40 hours prior to the strong shock of the Iranian earthquake of 6 July 1990. Anomalous concentrations of light ions and electrons were observed mainly above the active seismic zone up to two days before the shock (Boková et al., 1993, 1994). This paper presents a model which, with the use of the anomalous electric field, is able to describe the observed changes of light ion concentrations in the plasmasphere above regions of imminent seismic events. The value of the intensity of the anomalous electric field, required to explain the observed changes, is estimated. For the seismic event analyzed intensity of the anomalous electric field is comparable with the value of the ambipolar electric field, but of opposite direction.     

Do Solar Flares Affect Total Ozone?

An analysis of total ozone from Hradec Králové (50.25°N, 15.21°E) and of radio wave absorption in the lower ionosphere at 1539 kHz (reflection point 50.3°N, 11.8°E) shows that there is no detectable effect of strong solar flares in total ozone, no correlation between total ozone and absorption on a day-to-day time scale, and that strong solar flares do not affect this correlation. Thus the long-term correlation of monthly average values (Alberca et al., 1996) is not reproduced on a day-to-day time scale, and the effects of strong geomagnetic storms in total ozone (Latovika et al., 1992; Mlch and Latovika, 1996) have no counterpart in effects of strong solar flares.     

Far-zone gravity field contributions corrected for the effect of topography by means of molodensky’s truncation coefficients

A spectral representation of the topographic corrections to gravity field quantities is formulated in terms of spherical height functions. When computing the far-zone contributions to the topographic corrections, various types of the truncation coefficients are applied to a spectral representation of Newton’s integral. In this study we utilise Molodensky’s truncation coefficients in deriving the expressions for the far-zone contributions to topographic corrections. The expressions for computing the far-zone gravity field contributions corrected for the effect of topography are then obtained by combining the expressions for the far-zone contributions to the gravity field quantities and to the respective topographic corrections, both expressed in terms of Molodensky’s truncation coefficients. The numerical examples of the far-zone contributions to the topographic corrections and to the topography-corrected gravity field quantities are given over the study area situated in the Canadian Rocky Mountains with adjacent planes. Coefficients of the global elevation and geopotential models are used as the input data.     

Tectonosedimentary Evolution of the Cheb Basin (NW Bohemia,Czech Republic) between Late Oligocene and Pliocene: A Preliminary Note

A working model of tectono-sedimentary evolution is proposed for the Cheb Basin, a polyhistory sedimentary basin formed between the late Oligocene and Pliocene by reactivation of basement fracture systems in the northwestern part of the Bohemian Massif. The basin is located at the intersection of the Ohe (Eger) Graben structural domain, characterized by dominance of NE-striking graben systems in present-day geology, and the NW-striking Cheb-Domalice Graben, a major strike-slip – dominated structure in Western Bohemia. The first significant depositional episode in the Cheb Basin coincides with the deposition of late Oligocene-Miocene clastics in the whole extensional system of the Ohe Graben, controlled by E-W – trending depocenters. The main structural feature of the Cheb Basin region at that time was a palaeohigh caused by a NW- trending accommodation zone separating minor E-W – trending depocentres. The second, late Pliocene, episode of sedimentation occurred under a very different kinematic regime than the Oligo-Miocene rift basin evolution. During this time, the present-day structure of the Cheb Basin and the Cheb-Domalice Graben formed as a consequence of sinistral displacement on the Mariánské Lázn Fault Zone. Reactivation of this strike-slip fault zone led to the formation of a horsetail splay of oblique-extensional faults at the northern termination of the Mariánské Lázn Fault Zone, which contained the present-day Cheb Basin.     

Temporal Variations of Gravity in Western Bohemia: Period 1993 - 1996

The gravimetric investigation of the seismoactive area in Western Bohemia started in 1991 with local experimental measurements in a small area around the principal Mariánské Lázn fault close to Nový Kostel. With respect to the aims of the study, the method was designed for complex investigations in combination with GPS measurements, hydrological and geological research starting in 1993. Precise levelling was included into the project to specify vertical displacements with high accuracy in order to eliminate their influence on gravity. Temporal changes of gravity were observed during the initial stage in 1993 - 1995.     

Eine Simulierung orographischer Effekte durch Quellsingularitäten zur Fixierung stromaufwärts gelegener Randwerte

Zusammenfassung Ein zweidimensionales, linearisiertes Strömungsmodell für orographisch induzierte Effekte wird vorgestellt: Unter Voraussetzung von Pseudo-Instationärität lassen sich in einem schwach-geschichteten, reibungsfreien Medium mittlerer Größenordnung dynamisch-thermodynamische Störungen parameterisieren. Beim Überströmen eines Hindernisses, das durch effektiven QuellflußQ simuliert wird, kann man für normierte Stromlinien eine inhomogene Helmholtz-Gleichung ableiten, deren vier Randbedingungen durch das Eingreifen zweier Zusatzterme, welche das instationäre Verhalten beschreiben, modifiziert werden. Man wählt im folgenden den Quellfluß derartig, sodaß vonQ ein aufz=0 aufliegender, endlich ausgedehnter Rücken (mit dem ungefähren Querschnitt eines Halbzylinders) beschrieben wird.Näherungslösungen für den stromaufwärts liegenden Teil eines Rechteckbereiches nach Erreichen eines stationären Strömungszustandes sind mit den Methoden von Laplace-Fourier bestimmbar. Die numerische Größenabschätzung dieser kolumnaren Wellen zeigt, daß die im Windfeld orographisch induzierten Scherungszonen noch in beträchtlicher Entfernung stromaufwärts eines endlichen Hindernisses auftreten. Ihre Größenordnung gleicht jener von Scherungen, welche aus Effekten des thermischen Windes entstehen können. Die horizontale Perturbation der Geschwindigkeit ist bloß um eine Größenordnung kleiner als die Fließgeschwindigkeit des Grundstromes.Die Vorteile des neuen Ansatzes werden diskutiert: Quellsingularitäten sind besser als die üblichen analytischen Darstellungen der Topographie geeignet, die mitunter über weite Distanzen laufenden Störwellen niedrigster Frequenzen mit kolumnarem Charakter zu erfassen.Im Anhang findet man die Verallgemeinerung auf ein analoges dreidimensionales Modell: Ein System zweier partieller Differentialgleichungen führt zu Pseudo-Stromlinien des dreidimensionalen Raumes.

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Source disturbances simulating orographical effects: The determination of upstream boundary values

Summary As outlined in an Appendix a system of partial differential equations is derived for the stream surfaces of a flow of a stratified fluid over an obstacle for the so-called pseudo-instationary case of an inviscid linearized model for mesoscale motions in three dimensions.The solution for the two-dimensional case, which is the basic part of this paper, results in a Helmholtz Equation, the four boundary conditions of which are partially modified by two additional terms characterizing the instationarity of the problem. The orographic effects are parameterized by the effective source singularity. (The latter corresponds roughly to a mountain range with a semi-circular cross-sectional profile).For the upstream part of a rectangular range steady-state solutions in the limit of long time are obtained by the methods of Laplace-Fourier. The numerical calculation shows, that a system of orographically caused shear-layers (columnar waves) exists. The wind shears induced are of the order of shears due to thermal wind effects, though quite apart from these effects. The perturbations of horizontal velocity are only one order of magnitude smaller than the velocity of the fluid-flow itself.The results show that source singularities are good means to represent topographical effects: Especially they may explain more precisely upstream influences due to horizontally propagating waves having near-zero frequencies than the usual analytical formulations of orography can do it.Finally the theoretical results are compared with some data-sets taken from fluid-tank experiments and from observations from instrumented aircraft.

     

The Gravity Field of the Vogtland and NW Bohemia: Presentation of a Project

The Vogtland and NW Bohemia are characterized geoscientifically by periodically occurrence of swarm earthquakes. The basic geophysical mechanism is not yet sufficiently clarified, just like detail questions to geology in especially the deeper underground. Complex geophysical investigations in the seismoactive region indicate geodynamic phenomena like mass redistribution or stress accumulation and release (Spiák et al., 1998). According to Grünthal (1989) a weakness zone is suggested in the region of the swarm earthquakes. This zone can be caused by fluid-tectonics (Kämpf et al., 1992), a mantle plume (pers. com. J. Svancara, 1999) and/or by the geometry of the geological structures (Neunhöfer & Güth, 1988). A three-dimensional gravimetric model can clear up the underground situation. By means of high-resolution gravimetry a three-dimensional model will be developped for the Vogtland and NW Bohemia region. In the first step a homogeneous Bouguer map of the Vogtland and NW Bohemia was created (fig. 1) containing gravity structures analysed by Ibrmajer & Suk (1989) and Blízkovsky et al. (1985). The used gravimetric data were made available by the Saxonian National Office for Environment and Geology, by the Czech Geological Survey, Prague and by the GGA Hannover. In the context with the interpretation of the deep-seismic profile MVE 90 a two-dimensional gravimetric modeling was carried out (Behr et al., 1994), too. Anomaly-producing source bodies apparently do not offer themselves in a two-dimensional model, because after Jung (1961) the length of a gravimetric source structure must be about four times larger than it's width. The technique of the three-dimensional gravimetric modeling by means of any polyhedrons was developed by Götze (1976, 1984). Gravimetry is a potential method and supplies an infinite number of solutions, so the model has to be developed close to other geoscientific results. The aim is to construct a high-resolution three-dimensional underground model, which includes the upper earth's crust and the deep-seated structures of the middle and lower crust, too. The determination of the mass distribution in the underground supplies contradicting or supporting facts for geodynamic views in the Vogtland and NW Bohemia for example of Bankwitz et al. (1993). The interpretation of the Bouguer map of the Vogtland and a three-dimensional gravimetric model ought to contribute a substantial, also geodynamic part to understand the origin and the emergence of the swarm earthquakes in this region.     

Stress Analyses in the Epicentral Area of Nový Kostel (Western Bohemia)

The focal mechanisms of events from three micro-earthquake swarms (swarm in the years 1985/86, swarm of December 1994, and swarm of January 1997) in the epicentral area of Nový Kostel (West Bohemia region) were used as input data for stress analyses. The simple graphical method of Angelier and Mechler (1977) and inversion by the program BRUTE3 (Hardcastle and Hills, 1993) were applied to the data collections. The results of the stress analyses for the 1985/86 swarm and for the swarm of December 1994 are similar. For the January 1997 swarm, the results of the analyses differ from those for older swarms. The axis of maximum extension is oriented in the NE-SW direction and is subhorizontal, the axis of maximum compression is oriented in the NW-SE direction and perspicuously dips towards SE. These results are similar to older results of stress analyses carried out for the 1985/86 swarm (Antonini, 1988; Sonnleitner,1993). They are also consistent with most of other published results of stress analyses conducted at different sites in the western part of the Bohemian Massif. The orientation of the principal stresses confirms the sinistral strike-slip movement along the Nový Kostel-Poátky-Zwota line (the trend is about 355°) defined by the epicentres of the micro-earthquakes. The eastern tectonic limit of the Cheb Basin (and other respective parallel faults ) could be characterised by normal rather than strike-slip faulting.     

First Results of Hydrogeochemical Measurements in the Soos Area,Czech Republic

For some years, the Saxon Academy of Sciences at Leipzig (SAW) is engaged in the research project Contributions to Environmental Research by means of Radiometric-Geochemical Methods in the Vogtland area (Germany). The main goal is to investigate the hydrogeological and hydrochemical parameters of mineral springs in that region and their interrelations. Here, the high CO ₂ degassing rates are of particular interest. The isotopic signature of these gases indicates an anomalous high mantle/crust contribution (Weinlich et al., 1999). A further geoscientifically important phenomenon of this region is the high seismicity, in particular the Vogtland/NW Bohemian earthquake swarms. Therefore, we have tried to use the mantle-originated fluids as transport media for information from the seismogenic horizons. The variations of the parameters recorded continuously at the springs for years show a connection to the seismic events of the epicentral area of Nový Kostel in the Czech Republic. In particular, numerous anomalous degassing intervals were recorded at the mineral spring Wettinquelle (formerly: Radonquelle), Bad Brambach, prior to earthquakes occurred in the region of Nový Kostel.     

Seismic Activity Around and Under Krakatau Volcano,Sunda Arc: Constraints to the Source Region of Island Arc Volcanics

There is general agreement that calc-alkaline volcanic rocks at convergent plate margins are genetically related to the process of subduction (Ringwood, 1974; Maaloe and Petersen, 1981; Hawkesworth et al., 1997). However, opinions on the mode and site of generation of primary magma for island arc volcanism differ substantially. The site of generation of calc-alkaline magma is thought to be either in the mantle wedge (Plank and Langmuir, 1988; McCulloch and Gamble, 1991) or in the subducting slab (White and Dupré, 1986; Defant and Drummond, 1990; Edwards et al., 1993; Ryan and Langmuir, 1993). We present seismological evidence in favour of the latter concept. A distinctive seismicity pattern around and under the Krakatau volcano was identified during systematic studies of the SE Asian convergent plate margins by means of global seismological data. A column-like cluster of events, probably associated with the dynamics of the volcano, is clearly separated from the events in the Wadati-Benioff zone. The accuracy of hypocentral determinations of the events of the cluster does not differ from the accuracy of the events belonging to the subducting slab. The depths of the cluster events vary from very shallow to about 100 km without any apparent discontinuity. On the other hand, there is a pronounced aseismic gap in the Wadati-Benioff zone directly beneath the volcano at depths between 100-150 km. The Krakatau cluster connects this aseismic gap to the volcano at the surface. The pervasive occurrence of earthquakes in the continental wedge between the subducting slab and the Earth surface bears witness to the brittle character of the continental lithosphere and casts doubt on the existence of large-scale melting of mantle material. The aseismic gap (Hanu and Vank, 1985), interpreted by us as a partially melted domain occurring in subducted slabs in practically all active subduction zones that reach depths greater than 100 km, is here used as evidence for the location of the primary source region of island arc volcanics in the subducting plate.     

The Bad Step Tuff: a lava-like rheomorphic ignimbrite in a calc-alkaline piecemeal caldera,English Lake District

Lava-like tuffs are lithologically indistinguishable from lavas, and form part of a temperature-and composition-controlled continuum from low-grade tuffs (which are non-welded or slightly welded), through high-grade (densely welded) tuffs, extremely high-grade tuffs (which may be agglutinated right to their upper and lower contacts), to spatter-fed lava flows. In some high-grade tuffs, a component of nonparticulate flow may postdate emplacement and deposition, but in extremely high-grade tuffs non-particulate deformation normally occurs during emplacement and deposition. In such cases, syn-depositional non-particulate deformation (previously called primary welding) and non-particulate slumping (previously called secondary flowage) processes overlap and are continuous, one into the other, so that distinction between them and their resultant structures is unrealistic and inapplicable. Therefore the term rheomorphism should be used to embrace all types of non-particulate flow. The Bad Step Tuff is the most lava-like of a sequence of rheomorphic calc-alkaline rhyolitic ignimbrites emplaced during a climactic caldera-forming eruption episode in the English Lake District. It is a ponded sheet, 40 to 400 m thick, which comprises a basal crudely stratified heterolithic breccia, a thick flow-laminated and locally vesicular central part, which beomes increasingly flow-folded upwards, and an upper autobreccia. Despite an absence of vitroclastic textures within the main laminated part, field relations show it to be a tuff. Diagnostic criteria are (1) a gradation, within a lithophysal zone, from unambiguous vitroclastic matrix of the basal lithic breccia upwards into the central flow-laminated tuff; (2) only rate autobreccia at the base of the sheet but ubiquitous autobreccia at the top of the sheet; and (3) close textural similarity with localized, intensely rheomorphic parts of associated ignimbrites that widely display unequivocal vitroclastic textures where their rheomorphism is less marked. The extremely high-grade character of the Bad Step Tuff may reflect its proximal setting in a piecemeal-type caldera. High emplacement temperatures resulted from high-rate but low-velocity vent emission from fissures along numerous cross-cutting calderafloor faults, producing very low boil over eruption columns and proximal ponding.     

Stochastic analysis of multiphase flow in porous media: II. Numerical simulations

The first paper (Chang et al., 1995b) of this two-part series described the stochastic analysis using spectral/perturbation approach to analyze steady state two-phase (water and oil) flow in a, liquid-unsaturated, three fluid-phase porous medium. In this paper, the results between the numerical simulations and closed-form expressions obtained using the perturbation approach are compared. We present the solution to the one-dimensional, steady-state oil and water flow equations. The stochastic input processes are the spatially correlated logk where k is the intrinsic permeability and the soil retention parameter, . These solutions are subsequently used in the numerical simulations to estimate the statistical properties of the key output processes. The comparison between the results of the perturbation analysis and numerical simulations showed a good agreement between the two methods over a wide range of logk variability with three different combinations of input stochastic processes of logk and soil parameter . The results clearly demonstrated the importance of considering the spatial variability of key subsurface properties under a variety of physical scenarios. The variability of both capillary pressure and saturation is affected by the type of input stochastic process used to represent the spatial variability. The results also demonstrated the applicability of perturbation theory in predicting the system variability and defining effective fluid properties through the ergodic assumption.     

Explanation of the internal air pressure effect on the worden gravity meter dial constant

Summary A model, explaining the effect of air pressure changes in the space of the measuring system on the fine dial counter constant of the Worden and similar gravity meters, is presented. It is based on the changes of the bellows volume with compensating the gravity changes. It is shown that the resetting the gravity meter in the whole range has practically no influence on the fine dial counter constant.

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La vitesse de phase des ondes de Rayleigh et les structures de la croûte et du manteau supérieur entre Machhad et Chiraz (Iran)

Résumé A partir de sismogrammes enregistrés dans deux stations sismologiques longues périodes identiques (WWSSS) installées à Machhad (36°1840N, 59°3516E) et à Chiraz (29°3040N, 52°3134E), la vitesse de phase des ondes de Rayleigh a été calculée dans cette région. D'après les résultats obtenus par l'étude des ondes de volume dans cette même région des modèles ont été établis. Le modèle s'accordant le mieux avec les résultats expérimentaux a une croûte d'environ 50 km d'épaisseur et comporte une couche à faible vitesse située entre 100 et 200–250 km de profondeur.     

Models of sub-grid variability in numerical simulations of solute transport in heterogeneous porous formations: three-dimensional flow and effect of pore-scale dispersion

Modeling transport of contaminants in the earths subsurface relies on numerical solutions over grids with blocks larger than Darcys scale. The hydraulic conductivity is homogenized over the grid blocks and the plumes spreading is reduced as a consequence of the wiped-out variability. To compensate for this loss Rubin et al. (1999) proposed to augment mixing by block-effective dispersion coefficients, and Rubin et al. (2003) showed, by means of two dimensional simulations, how this concept can be applied in practice. In this paper, we present new solutions of the block-effective dispersion tensor for an axisymmetric exponential covariance model. In addition, we discuss the influence of pore-scale dispersion in both two- and three-dimensional applications.     

Sensitivity of secular trends in precipitation data to observational errors

There has been considerable interest in estimating secular trends in precipitation data in various regions of the world. It is therefore important to ascertain the manner in which errors of observation affect estimated trends. For this purpose we have compared trends at 1219 stations in the contiguous United States for two data sets: (a) original observations, also called raw observations, and (b) the observations, adjusted to compensate for suspected errors. The adjustments were made at the National Climate Data Center, Asheville (Quinlan et al., 1987;karl andWilliams, 1987), In order to focus on the effects of observational errors we attempted to avoid the effects of filling of missing data by limiting the analysis to the period 1940–1984 for which the number of missing values is much smaller than earlier periods. A least-square linear regression was performed on the raw and adjusted data for each station and the slopes of the fitted lines were compared. The comparison was made for monthly, seasonal and annual precipitation values.The results for annual precipitation showed that 23 percent of the stations have trends of opposite signs in the raw and adjusted data. The trends were identical in annual data at only 11 percent of the stations. When monthly data are combined to form seasonal and annual averages the magnitude of the difference between the slopes of the adjusted and the raw observations generally increases, indicating that the errors in the individual monthly observations are correlated. When the station data were averaged to obtain state-wide averages, the effects of the errors became less pronounced in most of the states. These results indicate that obtaining trends in precipitation from station data is a more difficult problem than has been realized.