A remark on the hydrostatic approximation

Summary For an autobarotropic atmosphere the exact linearized equations of motion can be solved for the pressure oscillation when =0 and =2 (=frequency of oscillation, =angular velocity of the earth's rotation). The pressure computed in this way is shown to be in close agreement to the pressure computed by using the hydrostatic approximation.     

Solution of stochastic groundwater flow by infinite series,and convergence of the one-dimensional expansion

This paper investigates analytical solutions of stochastic Darcy flow in randomly heterogeneous porous media. We focus on infinite series solutions of the steady-state equations in the case of continuous porous media whose saturated log-conductivity (lnK) is a gaussian random field. The standard deviation of lnK is denoted . The solution method is based on a Taylor series expansion in terms of parameter , around the value =0, of the hydraulic head (H) and gradient (J). The head solution H is expressed, for any spatial dimension, as an infinite hierarchy of Green's function integrals, and the hydraulic gradient J is given by a linear first-order recursion involving a stochastic integral operator. The convergence of the -expansion solution is not guaranteed a priori. In one dimension, however, we prove convergence by solving explicitly the hierarchical sequence of equations to all orders. An infinite-order stochastic solution is obtained in the form of a -power series that converges for any finite value of . It is pointed out that other expansion methods based on K rather than lnK yield divergent series. The infinite-order solution depends on the integration method and the boundary conditions imposed on individual order equations. The most flexible and general method is that based on Laplacian Green's functions and boundary integrals. Imposing zero head conditions for all orders greater than one yields meaningful far-field gradient conditions. The whole approach can serve as a basis for treatment of higher-dimensional problems.     

Analysis of State of Stress During The 1997 Earthquake Swarm In Western Bohemia

Focal mechanisms of 70 events of the January 1997 earthquake swarm were analysed using the Gephart and Forsyth method to determine the state of stress in the West Bohemia/Vogtland region and to reveal possible stress variations during the swarm activity. The method was applied to the whole set of 70 focal mechanisms and to several subsets distinguishing magnitudes of events and the spatial and temporal distribution of the swarm. The three representative stress models A ( ₁ ,A: 0/45 (az/dip), ₂ A: 134/35, ₃ A: 243/25), B ( ₁ ,B: 162/38, ₂ B: 263/14, ₃ B: 10/49), and C ( ₁ C: 135/30, ₂ C: 1/50, ₃ C: 239/23) which could characterise the state of stress in the region were found. Model C can be considered to be the most probable stress model because of its consistency with the European stress field. The results of the stress analysis applied to the individual subsets of focal mechanisms indicate that the state of stress was more uniform during the first phase of the swarm. To distinguish between the fault plane and the auxiliary plane of fault plane solutions a statistical approach was used. The results showed that the fault planes striking NW-SE and dipping 45° to NE were activated during the swarm.     

Power radiated by a VLF loop antenna in the ionospheric plasma

Summary The radiation power a VLF loop antenna with an arbitrary orientation of the loop's plane relative to the direction of the external magnetic field is calculated and its portion, transferred to the electromagnetic part of the excited spectrum, is determined.

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am umaa m uu am c nu umau nmu uma n m¶rt; a¶rt;um¶rt; n u n¶rt;a ma am mu uu, u¶rt;a ma¶rt;um am am cnma ¶rt;a au.

     

Sensitivity of the Gs 12 gravity meter to vibrations

nuaa m¶rt;ua u mam unmauaumaGs 12 No. 129 a uauu ¶rt;uana amm 0.02–30. a uu a uau nam auu au u auma naamauma a mua ma u n¶rt;a mumm a ¶rt;uu ¶rt;ama ammau uu .     

Relations entre le creusement et le comblement des perturbations et leur déplacement

Résumé On commence par définir le creusement et le comblement d'une fonctionp(, t) du tempst et des points (, ) d'une surface régulière fermée en se donnant, sur cette surface, un vecteur vitesse d'advection ou de transfert tangent à . Le creusement (ou le comblement) est la variation dep sur les particules fictives se déplaçant constamment et partout à la vitesse , A chaque vecteur et pour un mêmep(, ,t) correspond naturellement une fonction creusementC (, ,t) admissible a priori; mais une condition analytique très générale (l'intégrale du creusement sur toute la surface fermée du champ est nulle à chaque instant), à laquelle satisfont les fonctions de perturbation sur les surfaces géopotentielles, permet de restreindre beaucoup la généralité des vecteurs d'advection admissibles a priori et conduit à des vecteurs de la forme: , oùT est un scalaire régulier, () une fonction régulière de la latitude , le vecteur unitaire des verticales ascendantes etR/2 une constante. Ces vecteurs sont donc une généralisation naturelle des vitesses géostrophiques attachées à tout scalaire régulier. Dans le cas oùp(, ,t) est la perturbation de la pression sur la surface du géoïde, le vecteur d'advection par rapport auquel on doit définir le creusement est précisément une vitesse géostrophique: on a alors ()=sin etT un certain champ bien défini de température moyenne.On déduit ensuite une formule générale de géométrie et de cinématique différentielles reliant la vitesse de déplacement d'un centre ou d'un col d'un champp(, ,t) à son champ de creusementC (, ,t) et au vecteur d'advection correspondant. Cette formule peut être transformée et prend la forme d'une relation générale entre le creusement (ou le comblement) d'un centre ou d'un col et la vitesse de son déplacement, sans que le vecteur d'advection intervienne explicitement. On analyse alors les conséquences de ces formules dans les cas suivants: 1^o) perturbations circulaires dans le voisinage du centre; 2^o) perturbations ayant, dans le voisinage du centre, un axe de symétrie normal ou tangent à la vitesse du centre; 3^o) évolution normale des cyclones tropicaux.Finalement, on examine les relations qui existent entre le creusement ou le comblement d'un champ, le vecteur d'advection et la configuration des iso-lignes du champ dans le voisinage d'un centre.Ces considérations permettent d'expliquer plusieurs propriétés bien connues du comportement des perturbations dans différentes régions.

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Summary The deepening and filling (development) of a functionp(, ,t) of the timet and the points (, ) of a regular closed surface is first of all defined, in respect to a given advection or transfer velocity field tangent to , as the variation ofp on any fictitious particle moving constantly and everywhere with the velocity . For a givenp(, ,t) and to any there corresponds a well defined development fieldC (, ,t). All theseC fields are a priori admissible, but a very general analytical condition of the perturbation fields in synoptic meteorology (the integral of the development fieldC (, ,t) on any geopotential surface vanishes at any moment), leads to an important restriction to advection vectors of the form: , whereT is any regular scalar, () any regular function of latitude, the unit vector of the ascending verticals andR/2 a constant. These vectors are a natural generalisation of the geostrophic velocities attached to any regular scalar. Whenp(, ,t) is the pressure perturbation at sea level, its development must be defined in respect to a geostrophic advection vector belonging to the above defined class of vectors with ()=sin andT a well defined mean temperature field.A general formula of the differential geometry and kinematics ofp(, ,t) is then derived, giving the velocity of any centre and col of ap(, ,t) as a function of the advection vector and the corresponding development fieldC (, ,t). This formula can be transformed and takes the form of a general relation between the deepening (and filling) of a centre (or a col) of ap(, ,t) and its displament velocity, the advection vector appearing no more explicitly. A detailed analysis of the consequences of these formulae is then given for the following cases: 1^o) circular perturbations in the vicinity of a centre; 2^o) perturbations having, in the vicinity of a centre, an axis of symmetry normal or tangent to the velocity of the centre; 3^o) normal evolution of the tropical cyclones.Finally, the relations between the developmentC (, ,t) of a fieldp(, ,t), the advection velocity vector and the configuration of the iso-lines in the vicinity of a centre are analysed.These theoretical results give a rational explanation of several well known properties of the behaviour of the perturbations in different geographical regions.

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Communication à la 2ème Assemblée de la «Società Italiana di Geofisica e Meteorologia» (Gênes, 23–25 Avril 1954).     

Approximative ray tracing and the accuracy of earthquake localization in media approximated by block structures

Summary Localization errors made by approximating a given medium by a homogeneous rectangular block model and due to the approximative solution of two-point ray tracing are estimated for four different structures. The separate influence of the individual characteristics of the medium is discussed. The iterative Geiger method supplemented by a generalized inversion of the damped least-squares and Marquardt algorithm is used for localizating five hypothetical hypocentres using 9 stations. Travel times in the original structures, used as input data for localization, are calculated using a special ray tracing system.

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am uu auauu a annuau a ¶rt; ¶rt; ma u ma ¶rt;¶rt; u annuau m a ¶rt; munau nuuum .

     

Reaction of linear gravimetric measuring systems to disturbances of equilibrium state

Summary The reaction is studied of measuring systems of quartz gravity meters to external disturbances. The actual elastic system is approximated by a model of a linear oscillator with one degree of freedom. The appropriate differential equation of motion is solved for some of the typical shapes of determinate and random disturbance input signals. The result represents expressions which describe the time behaviour of the output signals.

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¶rt;m au uum um aaum m u u. mua na uma annuum ¶rt; u uma ¶rt; mn ¶rt;. mmm au ¶rt;uu a ¶rt; m munuu u¶rt; n¶rt; a au ua a ¶rt;. mam m au, nuau n¶rt;u ua a ¶rt; auumu m u.

     

Normal density earth models

Summary Models of the Earth's density, close to thePREM model, have been derived, they reproduce the external normal gravitational field of the Earth and its dynamic flattening, and are referred to as normal density models. The Earth's surface is approximated by an ellipsoid of the order of the flattening, or of its square. Of the group of normal models sgtisfying the solution of the inverse problem, the normal density modelHME2 is recommended. The spherically symmetric density modelPREM, which was corrected in the course of solving the inverse problem, thus creating the modifiedPREM-E2 model, was used as the a priori information.

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¶rt; ¶rt;u an¶rt;u nmmu uu ¶rt;uPREM (m. a. a ¶rt;u nmmu), aumau n m u¶rt;mu na¶rt;am auaumau n u. m u annuum am unu¶rt; au. uau amu a ¶rt; mam H==0.003 273 994. ma ¶rt; a ¶rt; ¶rt;m ¶rt;HME2. am anu u a ¶rt; nmmu a unaa ¶rt; a¶rt;ua umua ¶rt;PREM. ¶rt;aam ¶rt;uuau m ¶rt;u n¶rt; aauPREM-E2.

     

On the rotational motion of deformable celestial bodies

¶rt;am au uu ¶rt; aam ¶rt;uu ¶rt;u ma; ¶rt;am am u ¶rt; a, ¶rt;a u¶rt; amua m uuu a; num n aaa auauu nm.     

Some possibilities of predicting radio wave absorption in the lower ionosphere

Summary An attempt is made to show possible ways of predicting radio wave absorption in the midlatitude lower ionosphere using relations between absorption and the intensity of solar ionizing radiation and/or common solar activity indices, and between absorption and f₀F2.

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aa mu nuau nu a¶rt;u ¶rt;um u u a mu ¶rt; nu u umum uuu uu (uu uu u¶rt;au amumu) u ¶rt; nu u f₀F2.

     

Effects of the imf sector structure in the midlatitude troposphere and stratosphere

Summary The data on geopotential heights and temperatures at 7 pressure levels between 1000-10 hPa above Berlin(52.5 °N, 13.4 °E) are analysed for the winters of 1963–1973. No demonstrable effect of the interplanetary magnetic field sector boundary crossing (IMF SBC) is found in the lower and middle stratosphere, but there is a demonstrable effect in the middle troposphere at the 500 hPa level. This effect is less important than the IMF SBC effect in the tropospheric vorticity area index and seems to be of a different type.

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auum ¶rt;a nnmua m u mnam a 7 nm ¶rt;au ¶rt; 1000-10 a a¶rt; u(52,5 °.., 13,4 °.¶rt;.) ¶rt; u 1963–1973. ua ¶rt;aam m nu mau nam aum n( ) ¶rt;a amu u u ¶rt; mam, ma m a¶rt; ¶rt; mn a 500 a. mm m a, m u¶rt; na¶rt;u aumu am, u am m ¶rt; muna.

     

Les formes différentielles extérieures dans la géodésie II: Courbure moyenne

m m n¶rt;u mamu [7] m aa uu u aa a¶rt;u uu. uau ¶rt; u m¶rt;mu uu u u, a ¶rt;, u mu n nm. ¶rt;um a ama, ma m u¶rt; nm ¶rt; au ¶rt;amma m um. auu mamu ¶rt;um uua aa ¶rt; m unu¶rt;.     

Long period variations of the geomagnetic field and their spatial distribution in Europe

a 27 nu amu ama m¶rt;au nma aaua ¶rt; nu nma anum¶rt; 27-¶rt; auauu u ÿeau nu¶rt;au 13–14 u 9 ¶rt;. mam an¶rt;u nma anum¶rt; Z u H mau a n nuuuu auauuu uuP ₁ (cos ) u P ₁ /, mmm. mau mau a um auumu mau auau ¶rt; mmu mu Z/H ¶rt; a¶rt; amuu. au ¶rt; mmuuu u umu a¶rt;au muu ¶rt; ¶rt;am uau mu ¶rt;¶rt;mmu mu u. a aaua au mu Z/H ¶rt;m u uam n u m aa amu.     

Thermally driven hydromagnetic instabilities in a non-constantly stratified layer

Summary The convection in a rapidly rotating electrically conducting, fluid horizontal layer of non-constant stratification, permeated by an inhomogeneous magnetic field, is studied. In this connection, a temperature model of the layer is constructed, which creates a structure such that part of the layer is unstably and a part stably stratified. The results obtained are applied to the conditions in the fluid Earth's core.

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¶rt;m u m aa mn¶rt; u¶rt;uma , m um nm mamuuau u a¶rt;um ¶rt;¶rt; aum n. uaa nu m mna ¶rt; nu¶rt;um uu ma mm, nu m am mamuuum mau, a am — mau. mam unm ¶rt; aaua n, nu¶rt;u u¶rt; ¶rt; u.

     

The periodicity of aurorae in the years 1001–1900

Summary The sequence of aurorae, observed at latitudes up to 55° between the years 1001 and 1900 was processed by methods of spectral analysis. The same methods were applied to parts of various duration of this interval. The periods predominant in the time series under investigation were determined. In all the selected parts of the interval, these periods are always located within the same frequency band. Their position is related to the periods corresponding to mutual conjunctions of the large planets.

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¶rt; n uu, a¶rt;au a uma ¶rt; 55° nu¶rt; 1001–1900, ama nu nu m¶rt; nma aaua. a n¶rt; ¶rt; am a ¶rt;u m umaa. u n¶rt; na¶rt;au nu¶rt; u¶rt;a ¶rt;a. mu nu¶rt; ¶rt; a am umaa ¶rt;a a¶rt;m ¶rt;ua ¶rt;uaan amm. nu mum nu¶rt;au, mmmuu au u u nam.

     

Deep seismically active fracture zones in ecuador and northern peru

Summary A system of 8 seismically active fracture zones was delineated on the basis of the distribution of earthquake foci in the continental lithosphere of Ecuador. The position and width of the outcrop, thickness, dip and maximum depth of the individual fracture zones were estimated and correlated with surface geological and tectonic phenomena, volcanism and hydrothermal manifestations. The existence and strike of the fracture zones was independently confirmed by the occurrence of historical disastrous earthquakes.

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uma 8 uu amu a a aa a auu an¶rt;u a mu muma um a¶rt;a. u n¶rt; nu u uua a nmu, mua, u auaaua m¶rt; a . mau mu auu n¶rt;m¶rt;am a¶rt;u umuu aum mu u nmau nmu, mmu, au uu¶rt;mau nuu.

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Visiting professors at Instituto Geofísico and Facultad de Geología, Minas y Petróleos, Escuela Politécnica Nacional, Quito (Ecuador).     

Heat flow variations in the presence of an irregular contact of different rock type

Summary The effect of an irregular contact of two different rock types on the surface heat flow was analysed for the Zlatý Kopec region in northwest Bohemia. The 2-D geothermal model of subsurface structures was compiled according to measured values of the thermal conductivity and heat sources and by using isobaths map of the metamorphite-granite boundary. The heat flow was computed numerically from the temperature distribution obtained as a finite-difference solution of the heat conduction equation. It was found that the heat flow variation, corresponding to the most probable model, amounts approximately to the half of the actually observed changes. The surface heat flow is affected strongly by the thermal conductivity contrast between the overlying metamorphites and underlying granites and, on the contrary, it is little sensitive to the heat production difference between both rock types. It seems, therefore, that, despite the big heat production contrast observed, the main source of the heat flow variability are thermal conductivity inhomogeneities.

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¶rt;am uu mama ¶rt; m¶rt; mun n¶rt; a nm mn nm ¶rt; amu am n ana¶rt; uu. a u au mnn¶rt;mu u mnauu u n amu aauauaum — mauu n¶rt; a maa ¶rt;a ¶rt; nunm mm. n nm auma n -am u au mnn¶rt;mu. mam ¶rt;m, m auau mn nma ma a m ¶rt;u, n¶rt;mam nuuum nu a¶rt;a uu. a nm m u um aua mnn¶rt;mu ¶rt; aauu mauuu n¶rt;au u uaauaum, u am, nm a mum auu mnauu ¶rt; muu n¶rt;au. aum, m, m a a¶rt;a au mnauu,a umu auau mn nma m ¶rt;¶rt;mu uma mnn¶rt;mu.

     

Identity of the characteristics of electrodynamic seismographs with non-standard periods of seismometers and galvanometers

Summary The maximum changes of magnification were determined for electrodynamic seismographs with standard characteristics and for some experimental long-period seismographs, the constants of which are given in Tab. 1, when the period of the seismometer or galvanometer has a deviation of not more than 5% from the standard value. Under the assumption of control of the other constants of the seismograph, identical amplitude and phase responses with a small change of the absolute magnification of the seismograph may be achieved with characteristicsAII ( ² >0.2), AIV ( ² 0.4), B ( ² >0.3) Nos28, 32 and33. This deviation can also be compensated by adjusting the optical distance. The procedure of adjusting the identical characteristics is suitable for systems with which an accurate setting of the period is difficult and for systems with an uncontrollable period, provided their values are within the limits of allowed deviations from the standard constants.     

Single- and inter-station transfer functions for non-synchronous geomagnetic arrays-II. the results of the field data analysis

Summary The theory of methods of computing single- and inter-station transfer functions in both the spectral and time domains was developed in paper[1]. Both approaches are applied to the variation data recorded at field stations along two non-simultaneous profiles traversing the eastern margin of the Bohemian Massif, where a zone of anomalous induction seems to mark an important geological boundary of formations with different histories of development. The results of both analyses are found to coincide within reasonable bounds of 20–30% in the principal induction characteristics.

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u m¶rt; ama ¶rt;-u -mau n¶rt;am u nma u am a ua am[1]. am nua m am a n¶rt;¶rt;a nu ¶rt; aaua ¶rt;aaum auau aumua a n mau ¶rt; u nu, nau m au aua,¶rt; aa a aa u¶rt;uu. a, u¶rt;u, mamau a¶rt;a ¶rt; ¶rt; ¶rt;uuau au umuu aumu. mam aau nma u am auam a 20–30% ¶rt; u¶rt;u naam.