(ϖμ/ϖT) P of the lower mantle

We estimate (/T) _P of the lower mantle at seismic frequencies using two distinct approaches by combining ambient laboratory measurements on lower mantle minerals with seismic data. In the first approach, an upper bound is estimated for |(/T) _P | by comparing the shear modulus () profile of PREM with laboratory room-temperature data of extrapolated to high pressures. The second approach employs a seismic tomography constraint ( lnV _S / lnV _P ) _P =1.8–2, which directly relates (/T) _P with (K _S /T) _P . An average (K _S /T) _P can be obtained by comparing the well-established room-temperature compression data for lower mantle minerals with theK _S profile of PREM along several possible adiabats. Both (K _S /T) and (/T) depend on silicon content [or (Mg+Fe)/Sil of the model. For various compositions, the two approaches predict rather distinct (/T) _P vs. (K _S /T) _P curves, which intersect at a composition similar to pyrolite with (/T) _P =–0.02 to –0.035 and (K _S /T) _P =–0.015 to –0.020 GPa/K. The pure perovskite model, on the other hand, yields grossly inconsistent results using the two approaches. We conclude that both vertical and lateral variations in seismic velocities are consistent with variation due to pressure, temperature, and phase transformations of a uniform composition. Additional physical properties of a pyrolite lower mantle are further predicted. Lateral temperature variations are predicted to be about 100–250 K, and the ratio of ( lnp/ lnV _S ) _P around 0.13 and 0.26. All of these parameters increase slightly with depth if the ratio of ( lnV _S / lnV _P ) _P remains constant throughout the lower mantle. These predicted values are in excellent agreement with geodynamic analyses, in which the ratios ( ln / lnV _S ) _P and ( / lnV _S ) _P are free parameters arbitrarily adjusted to fit the tomography and geoid data.     

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–).

     

A note on upper limits for hypothetic variation in the Newtonian constant of gravitation

Summary It has been demonstrated on the basis of recent astronomical, satellite and LLR data that the variations in the Newtonian constant of gravitation, if any, do not exceed5××10 ^–15 cy^–1 of its relative value.

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¶rt;a amuu u nmu a¶rt;u u a auu naa, m auauuaumau nm, u u um, n¶rt;m5×10 ^–15 mmu ^–1 mum au.

     

The magnetic observatory of Pendeli (Athens,Greece)

Summary A new magnetic observatory, named the Magnetic Observatory of Pendeli, was established and put in operation in 1958 near Athens (Greece). This Observatory was organized by and belongs to the Greek «Institute for Geology and Subsurface Research». The geographical position of the Pendeli Observatory is given by =38° 02.8, =23°51.8 andh=495 m (above sea level). The gemagnetic coordinates of the same are =36°.2, =102°.0. The Observatory is situated near Pendeli Mt. (18 km NEE of Athens). The site of the Observatory consists of marmor underlain by mica schists, both magnetically inactive.The building of the Observatory is constructed of stone and its roof made of tiles. The magnetograph room is in the underground of the building. The magnetic and thermal conditions in the variometer room are satisfactory enough.The variometers of the Observatory forH andZ are of the magnetic balance type. ForD a fibre suspension declinometer is used. The scale values of the variometers are _H =7.2 /mm, _D =1.0/mm (7.6 /mm), _Z =11.5 /mm. The speed of recording amounts to 12 mm/h and the width of the record is 9 cm.The Pendeli Observatory has been operating since April 1958. The record is changed every day. The scale and base-line values are determined every 10 days. The room for the absolute measurements is found in the ground floor of the building. A field magnetic theodolite is being used in the absolute measurements.D is measured with two magnets in a fibre suspension declinometer.H is measured by means of the deflection oscillation method and with a QHM as well. For the measurement ofI an earthinductor is available. The values of the magnetic elements are properly corrected in order to represent the external normal field.     

Analytical study of the energy rate balance equation for the magnetospheric storm-ring current

We present some results of the analytical integration of the energy rate balance equation, assuming that the input energy rate is proportional to the azimuthal interplanetary electric field, E_y, and can be described by simple rectangular or triangular functions, as approximations to the frequently observed shapes of E_y, especially during the passage of magnetic clouds. The input function is also parametrized by a reconnection-transfer efficiency factor (which is assumed to vary between 0.1 and 1). Our aim is to solve the balance equation and derive values for the decay parameter compatible with the observed Dst peak values. To facilitate the analytical integration we assume a constant value for through the main phase of the storm. The model is tested for two isolated and well-monitored intense storms. For these storms the analytical results are compared to those obtained by the numerical integration of the balance equation, based on the interplanetary data collected by the ISEE-3 satellite, with the values parametrized close to those obtained by the analytical study. From the best fit between this numerical integration and the observed Dst the most appropriate values of are then determined. Although we specifically focus on the main phase of the storms, this numerical integration has been also extended to the recovery phase by an independent adjust. The results of the best fit for the recovery phase show that the values of may differ drastically from those corresponding to the main phase. The values of the decay parameter for the main phase of each event, _m, are found to be very sensitive to the adopted efficiency factor, , decreasing as this factor increases. For the recovery phase, which is characterized by very low values of the power input, the response function becomes almost independent of the value of and the resulting values for the decay time parameter, _r, do not vary greatly as varies. As a consequence, the relative values of between the main and the recovery phase, _m/_r, can be greater or smaller than one as varies from 0.1 to 1.     

Local spatial nets derived from measurements of angles

Summary Some of the properties are discussed of local nets derived from measurements of angles by forward intersection. Their functionals and stochastic model indicate the way the effect of the initial data, of the model of determining refraction conditions can be taken into account, and the possibility of gradually obtaining the individual estimates of the coordinates of the points being determined.

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u¶rt; m ma a m, nm a auu nmam n au. a ua u mamu ¶rt;u mu m naam uu u¶rt; ¶rt;a, uu u n¶rt;u mua auu u m nmnz, m¶rt;z auau ¶rt;uam n¶rt; nm.

     

Some results of the comparison of Courvoisier,Schulze and Yanishevsky balancemeters

Summary Courvoisier, Schulze andYanishevsky type balancemeters have been compared in field exposure under different weather conditions and in the laboratory. Special attention has been devoted to the selectivity and the temperature regime of the detectors. The installation of the instruments is described and the main results of simultaneous measurements with the above-mentioned balancemeters are presented. , . v . .     

Structure and evolution of the terrestrial planets

Geo-scientific planetary research of the last 25 years has revealed the global structure and evolution of the terrestrial planets Moon, Mercury, Venus and Mars. The evolution of the terrestrial bodies involves a differentiation into heavy metallic cores, Fe-and Mg-rich silicate mantles and light Ca, Al-rich silicate crusts early in the history of the solar system. Magnetic measurements yield a weak dipole field for Mercury, a very weak field (and local anomalies) for the Moon and no measurable field for Venus and mars. Seismic studies of the Moon show a crust-mantle boundary at an average depth of 60 km for the front side, P- and S-wave velocities around 8 respectively 4.5 km s^–1 in the mantle and a considerable S-wave attenuation below a depth of 1000 km. Satellite gravity permits the study of lateral density variations in the lithosphere. Additional contributions come from photogeology, orbital particle, x-and -ray measurements, radar and petrology.The cratered surfaces of the smaller bodies Moon and Mercury have been mainly shaped by meteorite impacts followed by a period of volcanic flows into the impact basins until about 3×10⁹ yr before present. Mars in addition shows a more developed surface. Its northern half is dominated by subsidence and younger volcanic flows. It even shows a graben system (rift) in the equatorial region. Large channels and relics of permafrost attest the role of water for the erosional history. Venus, the most developed body except Earth, shows many indications of volcanism, grabens (rifts) and at least at northern latitudes collisional belts, i.e. mountain ranges, suggesting a limited plate tectonic process with a possible shallow subduction.List of Symbols and Abbreviations a=R _e mean equatorial radius (km) - A(r, t) heat production by radioactive elements (W m^–3) - A, B equatorial moments of inertia - b polar radius (km) - complex amplitude of bathymetry in the wave number (K) domain (m) - C polar moment of inertia - C _Fe moment of inertia of metallic core - C _Si moment of inertia of silicate mantle - C _p heat capacity at constant pressure (JK^–1 mole^–) - C _nm,J _nm,S _nm harmonic coefficients of degreen and orderm - C/(MR _e ² ) factor of moment of inertia - d distance (km) - d nondimensional radius of disc load of elastic bending model - D diameter of crater (km) - D flexural rigidity (dyn cm) - E Young modulus (dyn cm^–2) - E maximum strain energy - E energy loss during time interval t - f frequency (Hz) - f flattening - F magnetic field strength (Oe) (1 Oe=79.58A m^–1) - g acceleration or gravity (cms^–2) or (mGal) (1mGal=10^–3cms^–2) - mean acceleration - g _e equatorial surface gravity - complex amplitude of gravity anomaly in the wave number (K) domain - g free air gravity anomaly (FAA) - g Bouguer gravity anomaly - g _t gravity attraction of the topography - G gravitational constant,G=6.67×10^–11 m³kg^–1s^–2 - GM planetocentric gravitational constant - h relation of centrifugal acceleration (² R _e ) to surface acceleration (g _e ) at the equator - J magnetic flux density (magnetic field) (T) (1T=10⁹ nT=10⁹ =10⁴G (Gauss)) - J ₂ oblateness - J _nm seeC _nm - k ₍₀₎ (zero) pressure bulk modulus (Pa) (Pascal, 1 Pa=1 Nm^–2) - K wave number (km^–1) - K ^* thermal conductivity (Jm^–1s^–1K^–1) - L thickness of elastic lithosphere (km) - M mas of planet (kg) - M _Fe mass of metallic core - M _Si mass of silicate mantle - M(r) fractional mass of planet with fractional radiusr - m magnetic dipole moment (Am²) (1Am²=10³Gcm³) - m _b body wave magnitude - N crater frequency (km^–2) - N(D) cumulative number of cumulative frequency of craters with diameters D - P pressure (Pa) (1Pa=1Nm^–2=10^–5 bar) - P _z vertical (lithostatic) stress, see also _z (Pa) - P _n ^m (cos) Legendre polynomial - q surface load (dyn cm^–2) - Q seismic quality factor, 2E/E - Q _s ,Q _p seismic quality factor derived from seismic S-and P-waves - R=R ₀ mean radius of the planet (km) (2a+b)/3 - R _e =a mean equatorial radius of the planet - r distance from the center of the planet (fractional radius) - r _Fe radius of metallic core - S _nm seeC _nm - t time and age in a (years), d (days), h (hours), min (minutes), s (seconds) - T mean crustal thickness from Airy isostatic gravity models (km) - T temperature (°C or K) (0°C=273.15K) - T _m solidus temperature - T sideral period of rotation in d (days), h (hours), min (minutes), s (seconds), =2/T - U external potential field of gravity of a planet - V volume of planet - V _p ,V _s compressional (P), shear (S) wave velocity, respectively (kms^–1) - w deflection of lithosphere from elastic bending models (km) - z, Z depth (km) - z (K) admittance function (mGal m^–1) - thermal expansion (°C^–1) - viscosity (poise) (1 poise=1gcm^–1s^–1) - co-latitude (90°-) - longitude - Poisson ratio - density (g cm^–3) - mean density - ₀ zero pressure density - _m , _Si average density of silicate mantle (fluid interior) - average density of metallic core - _t , _top density of the topography - density difference between crustal and mantle material - electrical conductivity (^–1 m^–1) - _r , radial and azimuthal surface stress of axisymmetric load (Pa) - _z vertical (lithostatic) stress (seeP _z ) - _II second invariant of stress deviation tensor - latitude - angular velocity of a planet (=2/T) - ages in years (a), generally 0 years is present - B.P. before present - FAA Free Air Gravity Anomaly (see g - HFT High Frequency Teleseismic event - LTP Lunar Transient Phenomenon - LOS Line-Of-Sight - NRM Natural Remanent Magnetization Contribution No. 309, Institut für Geophysik der Universität, Kiel, F.R.G.     

Reservoir lifetime and heat recovery factor in geothermal aquifers used for urban heating

Simple models are discussed to evaluate reservoir lifetime and heat recovery factor in geothermal aquifers used for urban heating. By comparing various single well and doublet production schemes, it is shown that reinjection of heat depleted water greatly enhances heat recovery and reservoir lifetime, and can be optimized for maximum heat production. It is concluded that geothermal aquifer production should be unitized, as is already done in oil and gas reservoirs.Nomenclature a distance between doublets in multi-doublet patterns, meters - A area of aquifer at base temperature, m² drainage area of individual doublets in multidoublet patterns, m² - D distance between doublet wells, meters - h aquifer thickness, meters - H water head, meters - Q production rate, m³/sec. - r _e aquifer radius, meters - r _w well radius, meters - R _g heat recovery factor, fraction - S water level drawdown, meters - t producing time, sec. - T aquifer transmissivity, m²/sec. - v stream-channel water velocity, m/sec. - actual temperature change, °C - theoretical temperature change, °C - water temperature, °C - heat conductivity, W/m/°C - _r rock heat conductivity, W/m/°C - _aC_a aquifer heat capacity, J/m³/°C - _aC_r rock heat capacity, J/m³/°C - _WC_W water heat capacity, J/m³/°C - aquifer porosity, fraction     

On the further generalization of trochoidal frontal waves

Summary A non-linear model of trochoidal waves is presented which represents a geometrical and kinematical generalization of Gerstner's waves and of the results of[2–4].

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¶rt;aam ¶rt; mu¶rt;a , ma m u ma u am[2–4] mu umuu u uamu mm ¶rt;u.

     

Deformation of a homogeneous gravitating sphere by internal dislocations

Summary An explicit solution is obtained for the system of equations describing the spheroidal motion in a homogeneous, isotropic, gravitating, elastic medium possessing spherical symmetry. This solution is used to derive the Green's dyad for a homogeneous gravitating sphere. The Green's dyad is then employed to obtain the displacement field induced by tangential and tensile dislocations of arbitrary orientation and depth within the sphere.Notation G Gravitational constant - a Radius of the earth - A _o =4/3 G - Perturbation of the gravitational potential - Circular frequency - V _p ,V _s Compressional and shear wave velocities - k _p =/V _p - k _s =/V _s - k _p [(2.8)] - , [(2.17)] - f _l ⁺ Spherical Bessel function of the first kind - f _l ^– Spherical Hankel function of the second kind - x =r - y =r - x _o =r _o - y _o =r_o - x =r k _s - y =r k _p - x _o =r _o k _s - y _o =r _o k _p - =a - =a - [(5.17)] - _{m, l}      

Station factors of Khonsa and Yaongyimsen seismograph stations

Summary Body wave magnitudes of 384 and 440 teleseismic events in the distance range 9–100° are determined using short-period P-wave data obtained from the vertical component seismograms of Khonsa (Tirap district, Arunachal Pradesh) and Yaongyimsen (Mokukchung district, Nagaland) seismic stations. These magnitudes are compared with the corresponding body wave magnitudes reported by the National Earthquake Information Service of the United States Geological Survey. Average residuals for Khonsa and Yaongyimsen stations are found to be +0.09 and +0.48, respectively. It is observed that the average residuals (7) for both the stations decrease with respect to epicentral distance (), focal depth (h) and body wave magnitude (m_b). For the Khonsa station, the respective linear relations are: =0.12–1×10^–5 , M=0.22–7××10^–5 h, M=1.96–0.356m_b and similarly, for the Yaongyimsen station the relations are M=0.59–2×10^–5 , M=0.54–19×10^–5 h, M=2.56–0.391m_b. The nature of the variation of residuals is found to be nearly similar for both the stations.

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aum¶rt; uu m 384 u 440 muu u a amuu 9° – 100° u n¶rt; n mua mau a mau hna (a irap, Arunachal Pradesh) u Yaongyimsen (a Mokukchung, Nagaland). aum¶rt; auam mmmuu aum¶rt;au, nu m National Earthquake Information Service of United States Geological Survey. ¶rt;u amu ¶rt; mau Khonsa u Yaongyimsen a +0,09 u +0,48 mmm. aa, ¶rt;u u (M) ¶rt; u mau am amu m numa (),u aa (h) u aum¶rt; (m_b). mauu Khonsa mmmu u auumu ¶rt;u: M=0.12–1×10^–5 , M=0,22–7×10^–5 h, M=1,96–0,356m_b; ¶rt; mauu Yaongyimsen mmm M=0,56–2×10^–5 , M=0,54–19×10^–5 h, M=2,56–0,391m_b. m, m nu¶rt;a uu ¶rt; u mau nu ¶rt;uaa.

     

Some exact solutions for the flow of fluid through tubes with uniformly porous walls

Summary This paper considers an incompressible fluid flowing through a straight, circular tube whose walls are uniformly porous. The flow is steady and one dimensional. The loss of fluid through the wall is proportional to the mean static pressure in the tube. Several formulations of the wall shear stress are considered; these formulations were motivated by the results from Hamel's radial flow problem, boundary layer flows/and boundary layer suction profiles. For each of these formulations exact solutions for the mean axial velocity and the mean static pressure of the fluid are obtained. Sample results are plotted on graphs. For the constant wall shear stress problem, the theoretical solutions compare favorably with some experimental results.Notations A, B, D, E constant parameters - a, b constant parameters - Ai(z), Bi(z) Airy functions - Ai, Bi derivatives of Airy functions - k constant of proportionality betweenV andp - L length of pores - p,p mean static pressure - p ₀ static pressure outside the tube - p ₀ value ofp atx=0 - Q constant exponent - R inside radius of the tube - T wall shear stress - T ₀ shear parameter - t wall thickness - U free stream velocity - ,u mean axial velocity - u ₀ value ofu atx=0 - V,V mean seepage velocity through the wall - v ₀ mean seepage velocity - x,x axial distance along the tube - z transformed axial distance - z ₀ value ofz atx=0 - mean outflow angle through the wall - cos - density of the fluid - wall shear stress - dynamic viscosity of the fluid - over-bar dimensional terms - no bar nondimensional terms The National Center for Atmospheric Research is sponsored by the National Science Foundation     

Analysis and optimization of wide-band force-balance seismometer responses

¶rt; aau n¶rt;am uu, umu,au mummu u ¶rt;uau ¶rt;uanaa mu um. am n a nmua amm aamumuu um ¶rt; au uu nuu. ¶rt;ma ummuu m¶rt; nmuau mu um a a¶rt;a an¶rt;u n n¶rt;am uu n nmu.     

Boundary conditions in the hydromagnetic dynamo problem

au am nu¶rt;, nuau ¶rt;u¶rt;aum ¶rt;ua, a u ¶rt; ma aum u¶rt;uu aam ma¶rt;am . a a au ¶rt; uuauu u nm nmu a u m muna, mm m¶rt; ma a anma n u. uunua muau u m¶rt; nua [4, 5]. n¶rt; am nuam m¶rt; u, u¶rt;u u m¶rt;a a u a nm nu nu¶rt;um au m u m¶rt;.     

The response of the total electron content to the interplanetary magnetic sector boundary crossing

¶rt;m uu n ¶rt;au m uu nu mau nam aum n. mu uu auam mmmuu uuu ¶rt;u u naam. a¶rt;am auu ¶rt; uuu n ¶rt;au m u u. a auu a¶rt;am nuu amm 245 . ¶rt;aam umnmau m a¶rt;a uu.     

Regional trends in European induction data

n ¶rt;a, n¶rt;mau 531 au ¶rt; u aum m u¶rt;uu n mumu ana¶rt;, ¶rt; u -m n, aauum ¶rt;um u u amuaa n¶rt;naa ma ua aama. uu nmam an¶rt;u ¶rt; u aum aam ¶rt;au cuu uP _n ^m , n¶rt;am mn n=1, 2, 3 u 5 (m n). u uua ¶rt;a¶rt;amu uu n¶rt;mauu uum au (a. 1) u u n aumam uu nmu, m n¶rt;mam u¶rt; am uuu ¶rt; u aum (u. 1–4). annuau 2 u 5 mn nm ma am mmmu m (u. 5, 6). ama uuu u m aam amu uu uma.     

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 .

     

Palaeomagnetism of the Börzsöny Mountains (Hungary)

Summary Mean directions of magnetization (29 normal and 31 reversed) were recorded for 60 magmatic localities of middle Miocene age from the Börzsöny Mountains (Hungary). The overall mean direction of RM, irrespective of polarity, isD=0,9°;I=59,8°; withk=8,3 and ₉₅=6,8°. The coordinates of the corresponding geomagnetic north pole are =82,7°, A=193,8 with p=7,7° and m=10,2°.     

The optimal shape design method applied to modelling thermal thinning of the oceanic lithosphere near hot spots

Summary Using the optimal shape design method, which is generally described, and von Herzen's et al. measurements of the heat flow, the shape of the lithosphere and its thermal field is computed in the vertical plane parallel to the hot spot source versus the plate velocity at a distance of about 250 km from the axis of the Hawaiian Island chain. The results are compared with the computations based on Crough's idea of thermal rejuvenation of the oceanic lithosphere above a hot spot source. If we assume that the lateral cross-section of the lithospheric bottom is described by the Gaussian curve h=h₀ exp (–y²/2²), we obtain h₀35 km and 130 km, where h is the value of lithospheric thinning and y the lateral coordinate. We thus obtain the lower limit of the lateral dimension of the Hawaiian anomaly.

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u m¶rt; nmua nua amu, m u ma nuam, u ¶rt;a mn nm, ua a um u mn n mua nmu, naa mu um mum umua mu u ¶rt;a nuuum 250 m uuuaa aunaa. mam a uuu, au a u¶rt;u aa (Crough), aauu mn mu au um a¶rt; umu mu. u n¶rt;num, m ama nn u umu ¶rt;a nuam u aa h=h₀ exp (–y²/2²), m num h₀ 35 u 130 ,¶rt; h—umu mu u —amaa ¶rt;uama. ¶rt;am, =130 m u n¶rt; ama aaaa aauu.