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     

Motion of particles in turbulent flow: Hyperbolicity,strange attractors and dynamic stochasticity of a system

¶rt;naa, m ma um uu maunuu m am muu ¶rt;uauu um. nua a mau ammama a, n¶rt; mnu ma u u au uu u¶rt;mu.     

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.

     

Heat flow in the upper-silesian coal basin: Re-evaluation of data with special attention to the lithology

Summary The area of the Upper Silesian Coal Basin was characterized by generally high heat flow ranging from 60 to 120 mWm^–2, mean 82±16 mWm^–2, which has been difficult to explain. Therefore all published data on the heat flow in this region (n=37) were summarized and re-evaluated. Special attention was paid to the detailed assessment of the lithological structure and the contribution of the individual rock types to the characteristic in-situ thermal conductivity. Also the thermal conductivity of the coal bearing layers was estimated and its effect on the temperature-depth distribution was investigated. The application of the data obtained for the representative thermal conductivity profiles of the whole drilled section considerably reduced the mean heat flow to 70±8 mWm^–2. The latter value is fully compatible with the tectonic structure of the northern part of the Carpathian Frontal Foredeep. Slightly increased geothermal activity compared with the heat flow field of the adjacent part of the Bohemian Massif corresponds to certain deep geological rejuvenation during the creation of the Western Carpathians.

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a -uu aa aamum nu uuau mn nma (m 60 ¶rt; 120 m.^–2 nu ¶rt; 82±16 m. ^–2), m ¶rt;a ¶rt u. m u u nm a nua ¶rt;a mn nma (n=37) ¶rt; ¶rt;a ua. ua ¶rt; ¶rt;ma aau umuu aa u u mnn¶rt;mu in situ ¶rt; a¶rt; muna n¶rt;. a a mnn¶rt;m m, a ma, a ma u¶rt;aa an¶rt;u mnam nu. nau n mam ¶rt; nuau mnn¶rt;mu m u amu aa nu am uum ¶rt;u mn nm ¶rt; 70±8 m.^–2. a uua n mam mmu u amu anam a nua. m uumu amumu n au mn n nuaa amu aua mmmmuuau amuuauu nu uauu um ana¶rdt; anam.

     

Definition of the normal gravity field including the constant part of tides

Summary One alternative of solving the problem of eliminating the effect of external masses, generating the constant part of the tidal field, from the perturbing potential is presented. The solution is founded on a new definition of the normal gravity field which contains this part of the tidal field. It is proved that two material circles in the plane of the Earth's equator, whose radii are approximately equal to the mean distances of the Moon and Sun from the Earth, can be considered as the source of this field. The new normal gravity field is first derived in the spherical approximation, which enables one to prove simply that the value of the normal gravity potential on the reference surface does not change, and that the change in the definition of the heights is insignificant. The normal gravity field for the equipotential ellipsoid is derived in the same way according to [1].

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¶rt;mam ¶rt;a amamua u ¶rt;umua n uu uu u a, au nm am nuu n, u a nmuaa. u a a n¶rt;uu a n u mmu, m m am nuu n aam. aam, m am umua m n umam a ¶rt; m nmu ama, a¶rt;u m nuuum a ¶rt;u amu u a m u. ¶rt; ¶rt; a n u mmu u nuuuu, m nm nm ¶rt;aam, m au a nmuaa u mmu a nmu m u m uu n¶rt;u m aum. ¶rt;ua n (. [1]) ¶rt; a n u mmu ¶rt; unu¶rt;a.

     

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     

Periodicity in the changes of the direction of the geomagnetic field

a au ¶rt;a a¶rt;u naam, m m uu anau n m aum u m u. aam u¶rt;a nuuu u u au am nmu m au. ¶rt;m nu¶rt;umu, m m m a mu u. n¶rt;mauau auumu aama u¶rt;a u um ¶rt; um aamu.     

Electromagnetic scattering by a perfectly conducting half-plane in a conductive half-space

FollowingDmitriev (1960) a rigorous theoretical solution for the problem of scattering by a perfectly conducting inclined half-plane buried in a uniform conductive half-space has been obtained for plane wave excitation. The resultant integral equation for the Laplace transform of scattering current in the half-plane is solved numerically by the method of successive approximation. The scattered fields at the surface of the half-space are found by integrating the half-space Green's function over the transform of the scattering current.The effects of depth of burial and inclination, of the half-plane on the scattered fields are studied in detail. An increase in the depth of burial leads to attenuation of the fields. Inclination introduces asymmetry in the field profiles beside affecting its magnitude. Depth of exploration is greater for quadrature component. An interpretation scheme based on a phasor diagram is presented for the VLF-EM method of exploration for rich vein deposits in a conductive terrain.List of symbols x, y, z Space co-ordinates - Half-space conductivity - ₀ Free-space permeability - Excitation frequency (angular) - T Time - h Depth of the half-plane - a Inclination of the half-plane - E _x x-Directed total electric field - E _x ^p x-Directed primary electric field - E _xo ^p x-Directed primary electric field atz=0 directly over the half-plane - H _y y-Component of total magnetic field - H _y ^p y-Component of primary magnetic field - H _y0 ^p y-Component of primary magnetic field atz=0 directly over the half-plane - H _z z-Component of total magnetic field - H _z ^p z-Component of primary magnetic field - J _x Surface density ofx-directed scattering current - G Green's function - k ₀,K Wave numbers - u,u ₀,u ₁,u ₂ Functions - Space co-ordinate - s Variable in transform domain - Variable of integration - Normalized scattering current - Laplace transform of - N Normalized - , ₀, ₁, ₂ Functions - t Variable of integration - Skin depth - H Total magnetic field - H ^p Primary magnetic field - H ₀ ^p Primary magnetic field atz=0 directly over the half-plane - M,Q,R,S,U,V Functions - N ₁,N ₂ Functions     

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 intensity of the main phase of geomagnetic storms in relation to the parameters of the solar wind

Summary On the basis of investigating 10 storms (1965–1967) good correlation was found between the density of the solar wind energy (₂=1/2mNv²) and the intensity of the main phase of the geomagnetic storms, expressed in terms of the maximum decrease of the horizontal intensity (B=H/cos). The relation between ₂, or Nv², and B could then be used to determine the quantities and ₀ ( is the factor expressing the increase in energy density in the magnetosphere, ₀ is the energy density of the particles in a quiet magnetosphere). A comparison with the directly observed distribution of the energy density of the particles in the magnetosphere indicates that the computed value of ₀ seems to be realistic. The magnitude of the factor will have to be checked again.     

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.

     

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}      

Magnitudes of detectable and localizable shocks in nw bohemia

Summary The effectiveness of recording seismic phenomena in the Kruné hory (Mts.) region in NW Bohemia by selected stations in the CSR, GDR and Poland has been estimated. Magnitude isolines of the weakest earthquakes, which can be localized and detected with an 0.9 probability, were calculated on the basis of the level of seismic disturbances at the individual stations and of the empirical dependence of the attenuation of seismic waves with distance.

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a a mum umauu uu u amu ¶rt; ana¶rt; uu uau mauu a mumuu , u a a uu n a m¶rt; mau u nuu auumu amau uu m amu u auma uuuu aum¶rt; a a mu, m mm 0.9 auuam u aum.

     

On the recent dynamics of the earth's surface of the Little Carpathians

a mam 10-mu u¶rt;au ¶rt;uauu nmu a anam. auum aam mua ¶rt;uu u nu amu uu, a , muu, u auauu n u mmu u uu umaa u ¶rt; nmu uuau.     

Transfer impedance of a probe in a drifting plasma

au un¶rt;a umu ¶rt;a na nu nauuu ¶rt;a uam mmu amm na aa. amau aa auum m mnam u mu ¶rt;a, m unam ¶rt; ¶rt;uamuu u na.     

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 .     

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.     

Effect of the additional low-sensitivity channel on the amplitude response of the electromagnetic seismograph

u¶rt;m ¶rt; anum¶rt;-amm aamumu maum a aa nu mummu (). ma¶rt;am aamumu uu mau auma uu am auu a uu aaa aa.     

Explosive source and its influence on ground motion dynamics

Summary In adjusting measured values in sets A(r*), v(r*) and f(r*) by means of a power function in the form of P=Kr^* a region of discontinuity of the approximating curves was found at the distance r*11.5 m kg ^–1/3. It is assumed that this discontinuity was caused by the varying character of the source of seismic waves. For scaled distances r*>11.5 m kg ^–1/3 the explosion was considered to be a spherical source from the point of view of the charge geometry and of the distance of the pick-up from the centre of the charge, whereas if r*<11.5 m kg ^–1/3 the explosion in the borehole had the character of a cylindrical source. The difference of the two types of sources was reflected in the exponent with both the functions A(r*) and v(r*), so that for r*>11.5 m kg ^–1/3 –4.0 and–2.4, and for r*<11.5 m kg ^–1/3 –2.5 and–1.5. For the same intervals of scaled distance in the set f(r*)1.4 and1.2.     

Relation between the field of surface heat flow and the distribution ofP n -wave velocities for continents

Summary The dependence between P_n-wave velocities and the surface heat flow, temperature at the core-mantl boundary and thickness of the Earth's crust for continents (Europe, Asia, North America and Australia) was investigated statistically in connection with the problem of lateral inhomogeneities in the upper mantle. The relations obtained were compared with those determined under laboratory conditions. The conclusion is that temperature and pressure effects may provide additional explanations of the regional variations of P_n-wave velocities observed in most continents.

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auum ¶rt;auu mu n¶rt; a nmu uua(P_n ), nm mn nm, mnam a u m mum a u¶rt;aa u n uuuma ¶rt;¶rt;m mu P_n. nua ¶rt;a mama aam u¶rt;au nu m n¶rt; amuu u u ¶rt;au u mnam a¶rt;um mmmuu mamau n¶rt;aa am. am ¶rt;, m ua uu m P_n- ¶rt; amu muma n¶rt;m auu m¶rt;uauu u a nmu muua.