Propagation of surface waves on a nonhomogenous spherically aeolotropic shell

Summary This paper studies the propagation of Surface Waves on a spherically aeolotropic shell surrounded by vacuum. The elastic constantsc _ij and density of the material of the shell are assumed to be of the form _ij r ^l and _o r ^m respectively, where _{ij o} are constants andl, m are any integers.     

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.     

The effect of the velocity of the centre of a cyclone on the generation of microseisms

Summary The influence of the velocity of the movement of the centre of the cycloneV _c.c. on the rate of amplitudes' change A/t and periods' change T/t of storm microseisms is investigated. The dependence A/t=k V _c.c. and T/t=k ¹ V _c.c. is obtained. Unmovable depression (V _c.c. =0) does not stipulate the change of A/t and T/t.

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u V _c.c. A/t T/t . A/t=k V _c.c. T/t=¹ V _c.c. . (V _c.c. =0) A/t T/t.

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Presented as a scientific communication to the IASPEI Assembly in Madrid, Sept. 1969.     

Propagation of surface waves on the surface of a non-homogeneous aeolotropic cylindrical shell

Summary The object of the present paper is to investigate the propagation of surface waves on a non-homogeneous aeolotropic cylindrical shell surrounded by vacuum. The elastic constantsc _ij (i, j=1,2...) and density of the material of the shell are assumed to be of the form and respectively, where _ij, ₀ are constants andk ₁,k ₂ are any integers.     

Anisotropic magnetic susceptibility of rocks under mechanical stresses

Summary The magnetic susceptibility of a rock under a uniaxial compression () decreases along the axis of compression and increases along the direction perpendicular to the axis, with an increase of . Thus, the magnetic susceptibility of a compressed rock becomes anisotropic.The decrease of longitudinal susceptibility,K (), and the increase of transverse susceptibility,K (), are theoretically derived from a model of rock which assumes the uniaxial anisotropy and the isotropic magnetostriction of magnetic minerals in rocks and a random orientation of the minerals. Results show thatK () decreases toward zero whereasK () increases and approaches a finite asymptotic value with an increase of , and –(/)K () is twice as large as /K () for small values of . These results are in good agreement with experimental data.

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Zusammenfassung Die magnetische Suszeptibilität eines Steines unter zunehmender uniachsigen Druckspannung () nimmt ab längs der Achse der Druckspannung und nimmt zu längs der Richtung senkrecht der Achse. Somit wird die magnetische Suszeptibilität des gedrückten Steines anisotrop.Die Abnahme der longitudinalen Suszeptibilität,K (), und die Zunahme der transversalen Suszeptibilität,K (), werden theoretisch von einem Modell eines Steines hergeleitet, das die uniachsige Anisotropie, die isotrope Magnetostriktion, und eine nichtbevorzugte Orientierung der magnetischen Minerals im Stein annimmt. Die Ergebnisse zeigen, dass mit einer Zunahme des ,K () gegen Null abnimmt, währendK () zunimmt und sich einem begrenzten asymtotitschen Wert nähert und, dass für kleine Werte des , –(/)K () zweimal so gross wie /K () ist. Diese Ergebnisse stimmen gut mit den Versuchangaben überein.

     

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 .

     

The mean energetic level. theory

Summary One of the important atmospheric levels, the mean energetic level (MEL), which in a sense reflects the energetics of the whole atmosphere, is defined. Its fundamental properties are shown. In order to describe the MEL correctly a new vertical coordinate is introduced and discussed. The new coordinate, , is defined as the ratio of height and temperature. The MEL is shown to be a level with constant value of . Some incorrect conclusions concerning the MEL, derived in the past, have been corrected.List of symbols used c _p specific heat of air at constant pressure - c _v specific heat of air at constant volume - e base of natural logarithms - E total potential energy - f Coriolis parameter - g acceleration of gravity - i specific internal energy - I internal energy - J enthalpy - k unit vector pointing upwards - p pressure - Q diabatic heating rate - R gas constant of the air - t time - T temperature - v horizontal velocity - v ⁽³⁾ three-dimensional velocity - w vertical velocity in thez-system - z height - temperature growth rate (T/z) - Pechala's vertical coordinate (z/T) - generalized vertical velocity in the -system (d/dt) - specific potential energy - potential energy - density of the air - Ruppert function - T(1–)^–1 - ( ) _S quantity at the sea level - ( )* quantity at the MEL     

Radioactivity and geochemistry of granulites and some related rocks from the saxonian granulite complex

Summary The distribution of radioactive(Th, U, K), major and selected trace(Rb, Sr, Ba, Y, Zr, V, Cr, Ni) elements of granulites from the Saxonian Granulite Complex was studied. Similarly to the South Bohemian granulites, the Saxonian granulites can be divided according to the contents of their major and trace elements into two main groups, groupA containing mostly acid and subacid granulites (K ₂ O>2.5%, SiO ₂ >68%), and groupB containing mostly intermediate and basic granulites (K ₂ O<2.5%, SiO ₂ <68%). Statistically significant differences between groupsA andB were found for all major oxides and several trace elements(Rb, V, Cr, Ni). The Saxonian granulites follow the same calc-alkaline trend as the South Bohemian, granulitesA being placed mostly in the rhyolite field and granulitesB mostly in the dacite, andesite and basalt fields of this trend. The investigated granulites are characterized by a considerable scatter ofTh andU contents accompanied by very variableTh/U ratios; theTh andU concentrations of granulitesA are substantially lower than is usual for rocks of corresponding acidity.

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¶rt;a an¶rt;u a¶rt;uamu(Th, U, K) u ua ¶rt;u(Rb, Sr, Ba, Y, Zr, V, Cr, Ni) m aum n¶rt;a aaum na. naa, m u¶rt;aum n uu aam n aaum u ¶rt;u am aua, u u uu. aum n u uu ma a¶rt;um ¶rt; ¶rt;nn; nnA nua¶rt;ama a au¶rt; u au¶rt;aum (K ₂ O>2,5%, Si O ₂ >68%), nnB ¶rt;u u aum (K ₂ O<2,5%, SiO ₂ <68%). ¶rt; muunnau mm mamumuu m au ¶rt; a u u ¶rt; m ¶rt;u m(Rb, V, Cr, Ni). auaum n¶rt;¶rt;m um- m¶rt; a u -uaum;aumA a¶rt;ma a uum n, uaumB a a ¶rt;aum, a¶rt;um u aam n m m¶rt;a. ¶rt;aum — u unnA — aamum uu ¶rt;au da¶rt;uamu mTh uU.

     

Rayleigh waves in an inhomogeneous medium

Summary Dispersion in Rayleigh waves is discussed for semi-infinite media with = ₁(1 ± cos s z) and = ₁(1 ± cosh s z), being the rigidity of the medium. A few workers tried with the above Fourier type of model but failed to find the dispersive nature. Because they neglected s due to the complexity of the calculation they arrived at a non dispersive frequency equation. This difficulty is removed in this paper and a dispersive frequency equation is obtained which shows both direct and inverse dispersion. The second model leads to non-convergent solution forz but shows many interesting results which are also discussed.     

Fundamental energy relations in the theory of compensation of non-equilibrium states in the earth's atmosphere

Summary The paper presents, in a condensed form, the fundamentals of global atmospheric energetics that have a bearing on the linear theory of compensation of non-equilibrium states in the Earth's atmosphere. The author introduces a new coordinate system with the vertical coordinate *=Z*/T*, which suits global atmospheric energetice.The relation between the energetics of the atmospheric system as a whole and the mean energetics level (MEL) is shown. Contrary to what has been assumed so far, it is proved that this level is neither an isopycnic level nor a physical surface, where */t=0 applies everywhere.List of Symbols Used x, y, z space coordinates in thez-system - x, y, space coordinates in the -system - t time - p, T, pressure, thermodynamic temperature and air density - p*, T*, pressure, temperature, density and geopotential on the mean energy level - g acceleration of the Earth's gravity - c _p ,c _v ,R specific temperature under constant pressure, volume and specific gas constant - = c _p /c _v Poisson's constant - E _k ,E _v ,E _p kinetic, internal and potential energies of the atmospheric system - r'(x,y) correction function to inhomogeneous atmosphere - v, v _n magnitude of motion velocity, magnitude of the normal component of velocity - O, S, S ₀ volume of the whole atmospheric system, surface limiting volumeO and the Earth's surface - Z _S height of surfaceS - arbitrary scalar quantity - _H , horizontal differential operators in thez- andp-systems Dedicated to Corresponding Member Vojtch Vítek, Director of the Institute of Physics of the Atmosphere of the Czechoslovak Academy of Sciences, at the occasion of his sixtieth birthday.     

Frequency dependence of crustalQ β in stable and tectonically active regions

Fundamental-mode Rayleigh wave attenuation data for stable and tectonically active regions of North America, South America, and India are inverted to obtain several frequency-independent and frequency-dependentQ models. Because of trade-offs between the effect of depth distribution and frequency-dependence ofQ on surface wave attenuation there are many diverse models which will satisfy the fundamental-mode data. Higher-mode data, such as 1-Hz Lg can, however, constrain the range of possible models, at least in the upper crust. By using synthetic Lg seismograms to compute expected Lg attenuation coefficients for various models we obtained frequency-dependentQ models for three stable and three tectonically active regions, after making assumptions concerning the nature of the variation ofQ with frequency.In stable regions, ifQ varies as , where is a constant, models in which =0.5, 0.5, and 0.75 satisfy fundamental-mode Rayleigh and 1-Hz Lg data for eastern North America, eastern South America, and the Indian Shield, respectively. IfQ is assumed to be independent of frequency (=0.0) for periods of 3 s and greater, and is allowed to increase from 0.0 at 3 s to a maximum value at 1 s, then that maximum value for is about 0.7, 0.6, and 0.9, respectively, for eastern North America, eastern South America, and the Indian Shield. TheQ models obtained under each of the above-mentioned two assumptions differ substantially from one another for each region, a result which indicates the importance of obtaining high-quality higher-mode attenuation data over a broad range of periods.Tectonically active regions require a much lower degree of frequency dependence to explain both observed fundamental-mode and observed Lg data. Optimum values of for western North America and western South America are 0.0 if is constant (Q is independent of frequency), but uncertainty in the Lg attenuation data allows to be as high as about 0.3 for western North America and 0.2 for western South America. In the Himalaya, the optimum value of is about 0.2, but it could range between 0.0 and 0.5. Frequency-independent models (=0.0) for these regions yield minimumQ values in the upper mantle of about 40, 70, and 40 for western North America, western South America, and the Himalaya, respectively.In order to be compatible with the frequency dependence ofQ observed in body-wave studies,Q in stable regions must be frequency-dependent to much greater depths than those which can be studied using the surface wave data available for this study, andQ in tectonically active regions must become frequency-dependent at upper mantle or lower crustal depths.On leave from the Department of Geophysics, Yunnan University, Kunming Yunnan, People's Republic of China     

A note on tidal current rotation

The rotational form of the vertically averaged equations of motion is applied to derive a formula, linear friction included, which establishes a direct connection between sense of rotation of tidal currents and features of tidal amphidromic systems. Two factors in the formula, called and , influence the sense of rotation of tidal currents; the factor involves the frequency of the tidal signal , the Coriolis parameter f, and the linear friction coefficient r. The sign of the cross-product of the logarithm of sea-surface elevation (), and phase () gradients determines whether the factor favors clockwise or anticlockwise sense of rotation. is a unit vector and is the angle between ln and . The limits ||0, ||0 and 0 lead to a clockwise sense of rotation in the Northern Hemisphere. 0 favors anticlockwise rotation in the Northern Hemisphere. Friction and low frequencies favor an anticlockwise sense of rotation. The theory works well in semi-enclosed regions like the North Sea. Although only linear friction and sea-surface elevation gradients were considered, there are ocean regions where the agreement between theory and observations is also good.Responsible Editor: Hans Burchard     

On the free oscillations of a laterally heterogeneous earth model

Summary The equations of motion for the free oscillations of a heterogeneous spherical earth model are derived. It is found that the lateral variations of density and elastic moduli couple the odd(even) harmonics of the spheroidal oscillations with themselves as well as with the even (odd) harmonics of the torsional oscillations.List of symbols r, , Spherical coordinates;r is the radial distance from earth's center, is the co-latitude, and is the east longitude - r Space vector denoting a point with coordinatesr, , and - Gradient operator - ² Laplacian operator - _ij Kronecker's delta function - I Identity matrix - i      

Rotatory vibration of a thick spherical shell of isotropic non-homogeneous elastic material

Summary Rotatory vibrations of a thick spherical shell of isotropic non-homogeneous material with rigidity and density given by (i) = ₀ r ^-2 withQ =Q ₀ r ^-2 e ^2mr and (ii) = ₀ r ^m with =Q ₀ r ⁿ have been discussed and the frequency equation is derived with numerical enumeration of frequency in each case.     

The secular variation of the geomagnetic field in Egypt in the last 5000 years

The palaeo-intensities (F _a) of the geomagnetic field in Egypt at some ages are determined by archaeomagnetic measurements and found to be:F _a=36.2 T at 3100 B.C., F_a=46.8 T at 3000 B.C.,F _a=36.5 T at 2780 B.C., 49.0 T at 2500 B.C., 36.4 T at 2200 B.C., 57.5 T at 1990 B.C., 62.1 T atca 1400 B.C., 61.5 T at 1400 B.C., 69.9 T at 600 B.C., 59.3 T at 550 B.C., 79.9 T at 460 B.C., 73.7 T at 450 B.C., 69.7 T at 320 B.C., 56.2 T at A.D. 50, 64.9 T, at A.D. 400, 54.4 T at A.D. 300, 57.5 T at A.D. 700 and 43.0 T at A.D. 1975.The palaeo-inclinations (I _a) at some ages are found to be:I _a=24.2° at 420 B.C., 44° at A.D. 50, 60.7° at A.D. 703 and 42° at A.D. 1795.The measured values ofF _a are affected by the anisotropy of magnetic susceptibility of the samples by 13% to 20% of the expected correct value. The suitable correction of this effect is by multiplyingF by 1/((1+0.2(/90)) andF by 1/((1–0.13 (/90)), whereF andF are the resultant values ofF _a if the laboratory field is perpendicular or parallel to the wall of the sample during the Thelliers' experiments, respectively, and is the angle between the direction of natural remnant magnetization of the sample and the direction of the laboratory field.The results of this paper, together with the previous results for Egypt and the neighbourhoods, lead to the production of the secular variation curve of the geomagnetic field in Egypt for the last 5000 years. The intensity of the field shows a periodicity of about 400 years with multiples.     

Palaeointensity of the geomagnetic field during upper cainozoic derived from palaeo-slags and porcellanites in north Bohemia

Summary Porcellanites and palaeo-slags from North Bohemia are natural materials which can be used to derive the palaeomagnetic directions and palaeointensity of the geomagnetic field active at the time of caustic alteration. The origin of these rocks, called erdbrands, was due to the caustic alteration of predominantly pelitic sediments as a result of underground fires conditioned by spontaneous ignition of coal seams. The caustic alteration occurred during the Upper Pliocene to the Quaternary. Three procedure based on the methods by Thellier and Nagata are presented in the paper. The newly developed apparatus MAVACS (Magnetic Vacuum Control System) was used for the thermal demagnetization of samples. A procedure based on multi-component analysis was also proposed and tested. Besides some methodic results, it was found that the geomagnetic field intensity varied during the respective period within the limits of 48%±4% to 154%±32% of the present geomagnetic field intensity.

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aum u na au a mumuu uu n¶rt;mam nu¶rt; amua, m n¶rt;¶rt;um ¶rt; ¶rt;u naaum anau u naumumuaum n, ¶rt;m amu uu. mu n¶rt;, aa ¶rt;a¶rt;, uu n¶rt; uu amu uu num num a¶rt; n¶rt; ¶rt;mu aau . amu uu u m nu¶rt; m nua ¶rt; mmu nu¶rt;a. am n¶rt; mu umnmau nua, n¶rt;¶rt;u ¶rt; ¶rt;u naumumu, nuau a m¶rt; u aama. a aamaa annaama MAVACS (Magnetic Vacuum Control System) a unaa ¶rt; mu aauuau ¶rt; amu aa. n¶rt; u n n¶rt;¶rt;, a a munm aau amuauu. nu m¶rt;uu au, ma ma, m umumaum n u¶rt; nu¶rt; a n¶rt;a 48%±4%-154%±32% au umumu aum n.

     

On the possibilities of horizontal propagation ofPc1 pulsations in the ionosphere

Summary The vertical distribution of the contribution of the energy flux density due to the Alfvén(ordinary) wave, guided by the geomagnetic field(and propagating through the ionosphere to the Earth's surface) in the horizontal direction is demonstrated in the mechanism of the horizontal propagation of the Pc1 signal. The distribution with height is shown of the variations of the polarization characteristics of the propagating wave(e.g. the rotation of the polarization plane, changes in ellipticity, attenuation, etc.), which are the result of coupling in the denser layers of the low ionosphere in which also suitable isotropic(extraordinary) modes are generated. The results obtained using the method described in[4, 13] are demonstrated on a model of the daytime ionosphere under incidence of ordinaryL-modes, frequency f=0.3 Hz, and various meridional angles at the ionosphere.

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auauma anmau uaa Pc1 naa m an¶rt;u ¶rt;u nmmu ma uu uma anauu maum n n¶rt; , anma u nmu. naa m an¶rt;u uu aamumu nuauu anma (nauau nmu nuauu, uu unmumu, amau u m.¶rt;.), m m ¶rt;mu au¶rt;mu na uu u . ¶rt; mum n¶rt;¶rt;u umn() ¶rt;. mam num m¶rt; [4, 13] ¶rt;mua ¶rt;u ¶rt; u nu na¶rt;uu a u L-¶rt; amm f=0,3 n¶rt; au u¶rt;uau au.

     

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).     

Flow of non-Newtonian fluid through circular tubes

Summary According to Newton's law of viscosity _y = Dv_y/dy. But experiments have shown that _y is indeed proportional to –dv _x/dy for all gases and for homogeneous nonpolymeric liquids. There are however, a few industrially important materials, e.g. plastics, asphalts, crystalline materials that are not described by the equation given by Newton's law of viscosity and they are referred to as non-Newtonian fluids. The steady state rheological behaviour of most fluids can be expressed by the generalised form, _y = –(dv_y/dy) where may be expressed as a function of eitherdv _x/dy or _y (where is independent of the rate of shear, the behaviour is Newtonian with =). Numerous empirical equations or models have been proposed to express the steady-state relation between _y anddv _x/dy. The flow of Newtonian fluids through circular tubes have been discussed before by many. Here we shall discuss the case of two such models of non-Newtonian fluids through circular tubes. The flow of fluids in circular tubes is encountered frequently in Physics, Chemistry, Biology and Engineering.     

Density inhomogeneities in the upper mantle of Central Europe and their gravitational effects

Summary Problems of occurrence of density inhomogeneities in the upper mantle are discussed and their gravitational effects in the region of Central Europe are investigated. Attention is namely devoted to the density contrast between the asthenosphere and the lower lithosphere, and its possible dependence on depth.

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¶rt;am n nu nmm ¶rt;¶rt;m amuu u uaumau ¶rt;mu a mumuu ¶rt; n. uau ¶rt;m n¶rt; nmm mam ¶rt; am u um u auumu mu aau.