On the propagation of finite Love Waves

Summary The problem of the propagation of finite Love Waves in a heterogeneous elastic half space lying over a homogeneous elastic half space, using the quasilinear stress-strain relation due toS. Ferhst [4] is considered in detail. The variations of the parameter in the layer assumed to be of the form 1= 0e ^z, 0e ^z where is a constant andz is distance measured from the surface into the layer.     

Hydromagnetic spin-up under conditions of the earth's core-mantle boundary

Summary The disturbances of the velocity and magnetic fields close to the Earth's core-mantle boundary, caused by sudden irregular changes in the Earth's rotation, are investigated. The problem leads to the investigation of the structure of the Ekman-Hartman hydromagnetic boundary layer, the magnetic diffusive region and the currentless region. Precise Laplacean inversions of the images of all disturbances in the Earth's core-mantle system are obtained for the limiting case of a zero magnetic Prandtl number, =0. The disturbance of the velocity in the direction of the axis of rotation (Ekman suction) in the currentless region has the nature of inertial oscillations with a frequency of 2. Additional disturbances (with respect to the case of =0) of the velocity in the azimuthal and radial directions, particularly for the EHL and MDR region, are determined for the case when 0< « 1. The disturbance in the velocity again has the character of inertial oscillations with the frequency 2, being exponentially damped in EHL asexp (–2²t) and in MDR asexp (–²t).     

Strong Potential Magnetic Field Influence on Slightly Differentially Rotating Spherical Shell

An electrically conducting viscous fluid-filled spherical shell is permeated by an axisymmetric strong potential magnetic field with large Elssaser number ² 1. We describe analytically the steady flow driven by a slightly faster rotation of the conducting inner boundary of the shell. The main flow is controlled by Ekman-Hartmann boundary layers with a small thickness /, where ² is the Ekman number. Asymptotics based on small ^–1 1 reveal the nature of a free shear layer O((/)^1/2) and a super-rotation that allows a part of the fluid to rotate faster than the inner sphere. The free shear is following an imposed field line that is tangent to the inner or outer sphere. Meridional flux is concentrated in the shear and boundary layers. Fluid tends to rotate with the inner sphere and to expel azimuthal magnetic field from an -region restricted by the free shear in the spherical shell. For an imposed axial uniform magnetic field, this -region is outside the cylinder tangent to the inner sphere and rotates with the outer sphere. Weak differential rotation O(/) is inside the cylinder, while almost all difference in rotation rates between spheres is accommodated in the thin O((/)^1/2) free shear. For an imposed dipole magnet, the region has a shape of a lobe touching the outer equator. Inside a super-rotation exists; this is the common case for such when the source of the imposed field is inside.     

Instantaneous photochemical rates in the global stratosphere

Starting with the average actual distribution of ozone (Dütsch [15]) and temperature in the stratosphere, we have calculated the solar intensity as a function of wavelength and the instantaneous rates (molecules cm^–3 sec^–1) for each Chapman reaction and for each of several reactions of the oxides of nitrogen. The calculation is similar to that ofBrewer andWilson [5]. These reaction rates were calculated independently in each volume element in spherical polar coordinates defined by R=1 km from zero to 50, =5° latitude, and ø=15° longitude (thus including day and night conditions). Calculations were made for two times: summer-winter (January 15) and spring-fall (March 22). As input data we take observed solar intensities (Ackerman [1]) and observed, critically evaluated. constants for elementary chemical and photochemical reactions; no adjustable parameters are employed. (These are not photochemical equilibrium calculations.) According to the Chapman model, the instantaneous, integrated, world-wide rate of formation of ozone from sunlight is about five times faster than the rate of ozone destruction, and locally (lower tropical stratosphere) the rate of ozone formation exceeds the rate of destruction by a factors as great as 1000. The global rates of increase of ozone are more than 50 times faster thanBrewer andWilson's [5] estimate of the average annual transfer rate of ozone to the troposphere. The rate constants of the Chapman reactions are believed to be well-enough known that it is highly improbable that these discrepancies are, due to erroneous rate constants. It is concluded that something else besides neutral oxygen species is very important in stratospheric ozone photochemistry. The inclusion of a uniform concentration of the oxides of nitrogen (NO_x as, NO and NO₂) averaging 6.6×10^–9 mole fraction gives a balance between global ozone formation and destruction rates. The inclusion of a uniform mole fraction of NO_x at 28×10^–9 also gives a global balance. These calculations support the hypethesis (Crutzen [10],Johnston [24]) that the oxides of nitrogen are the most important factor in the global, natural ozone balance. Several authors have recently evaluated the natural source strength of NO_x in the stratosphere; the projected fleets of supersonic transports would constitute an artificial source of NO_x about equal to the natural value, thus promising more or less to double an active natural stratospheric ingredient.     

Meridional equatorial electrojet current in the American sector

Huancayo is the only equatorial electrojet station where the daytime increase of horizontal geomagnetic field (H) is associated with a simultaneous increase of eastward geomagnetic field (Y). It is shown that during the counter electrojet period when H is negative, Y also becomes negative. Thus, the diurnal variation of Y at equatorial latitudes is suggested to be a constituent part of the equatorial electrojet current system. Solar flares are known to increase the H field at an equatorial station during normal electrojet conditions (nej). At Huancayo, situated north of the magnetic equator, the solar flare effect, during nej, consists of positive impulses in H and Y and negative impulse in Z field. During counter electrojet periods (cej), a solar flare produces a negative impulse in H and Y and a positive impulse in Z at Huancayo. It is concluded that both the zonal and meridional components of the equatorial electrojet in American longitudes, as in Indian longitudes, flows in the same, E region of the ionosphere.     

The derivatives of the lunar disturbing potential harmonics with respect to euler's angles

Summary The derivatives of the harmonicsP _n ^(k) (sin _O)cos kT_O andP _n ^(k) (sin _O)sin kT_O, occurring in the development of the lunar disturbing potential, are derived upto n=4 and for k== 0, 1, ..., n. The equatorial co-ordinates _OT_O are referred to the Moon's mass centre; the procedure for the solar disturbing potential is formally identical.     

Single and multiple dislocation models of extended earthquake sources

Summary A short review of simple theoretical models for extended earthquake sources visualized as single and multiple dislocations is presented. Formulas for the duration of the radiation t _i ^s from the starting point of the destruction up to the region forming the amplitude maxima of body waves are given. A method for determining some basic parameters of extended earthquake sources (length and depth of the dislocation, azimuth of the first dislocation and the angles between every two consecutive dislocations) from the seismogram data for t_i ^s is presented. The procedure is applied to yield some practical results.     

A new dissipation model based on memory mechanism

Summary The model of dissipation based on memory introduced by Caputo is generalized and checked with experimental dissipation curves of various materials.List of symbols unidimensional stress - unidimensional strain - Q ^–1 specific dissipation function - c(t) creep compliance - m(t) relaxation modulus - c ₀ instantaneous compliance - m equilibrium modulus - (t) creep function - relaxation function - () spectral distribution of retardation times - spectral distribution of relaxation times - c ^*() complex compliance - m ^*() complex modulus - tang loss-tangent     

Isotopic ratio and concentration of sulfur in the undersaturated alkaline magmas of Vulture Volcano (Italy)

Both the ³⁴ value and the total S content of products from Vulture Volcano, Italy are mainly controlled by the separation of S gases, predominantly SO₂, from high f _O2magmas containing S predominantly as SO _2- ⁴ . The addition of evaporites to such magmas appears to be a relatively uncommon and limited phenomenon. The total S content of the most primitive product of Vulture Volcano (5600 mg/kg) is very high. The high ³⁴S value of 4 indicates an origin through the partial melting of a mantle containing high S, enriched in ³⁴S of unknown origin.     

Origin of the fumarolic fluids of Vulcano Island,Italy and implications for volcanic surveillance

Variations in D and ¹⁸O values with H₂O contents and outlet temperatures indicate that the fumaroles of La Fossa crater have discharged mixtures of magmatic water and marine hydrothermal water, since 1979. The contribution of meteoric water was low in the period 1979–1982 and very low afterwards. The ¹⁸O values of the marine-hydrothermal component of +5 to +7.2 are due to isotopic exchange with the ¹⁸O-rich silicates of the rocks under high-temperature and low-permeability conditions. The ¹⁸O value of the magmatic end-member is generally +3.5 to +4.3, although values as high as +5.5 to +6.5 were reached in the summer of 1988, when magma degassing appears to have extended into the core of the magma body. The D values of the end-member were close to -20, typical of andesitic waters. Both the isotopic values and chemical data strongly support a dry model, consisting of a central magmatic gas column and a surrounding hydrothermal envelope, in which marine hydrothermal brines move along limited fracture zones to undergo total evaporation on approaching the conduits of magmatic fluids. The vents at the eastern and western boundaries of the fumarolic field are fed by fluids whose pressure is governed by the coexistence of vapor, liquid and halite, giving rise to a high risk of phreato magmatic explosions, should magma penetrate into these wet environments. Most La Fossa eruptions were triggered by an initial hydrothermal blast and continued with a series of phreatomagmatic explosions. The fluids discharged by the Forgia Vecchia fumaroles are mixed with meteoric water, which is largely evaporated, although subordinate loss of condensed steam may be responsible for scrubbing most of the acidic gas species. The temperatures and pressures, and the risk of a sudden pressure increase, are low. A boiling hydrothermal aquifer at 230° C is present underneath the Baia di Levante beach. This area has a minor risk of hydrothermal explosions.     

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      

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.     

Addition of magmatic volatiles into the hot spring waters of loowit canyon,Mount St. Helens,Washington, USA

Geochemical studies on cold meteoric waters, post-1980 hot spring waters, fumarole emissions from the dacite dome, and volcanic rocks at Mount St. Helens (MSH) from 1985 to 1989 show that magmatic volatiles are involved in the formation of a new hydrothermal system. Hot spring waters are enriched in ¹⁸O by as much as 2 and display enrichments in D relative to cold waters. A well-defined isotopic trend is displayed by the isotopic composition of a>400°C fumarole condensate collected from the central crater in 1980 (-33 D, +6 ¹⁸O), of condensate samples collected on the dome, and of cold meteoric and hot spring waters. The trend indicates that mixing occurs between local meteoric water and magmatic water degassing from the dacite dome. Between 30 and 70% magmatic water is present in the dome fumarole discharges and 10% magnatic water has been added to the waters of the hydrothermal system. Relations between Cl, SO₄ and HCO₃ indicate that the hot spring waters are immature volcanic waters formed by reaction of rocks with waters generated by absorption of acidic volcanic fluids. In addition, the B/Cl ratios of the spring waters are similar to the B/Cl ratios of the fumarole condensates (0.02), values of ¹³C in the HCO₃ of the hot springs (-9.5 to-13.5) are similar to the magmatic value at MSH (-10.5), and the ³He/⁴He ratio, relative to air, in a hot spring water is 5.7, suggesting a magmatic origin for this component.managed by Martin Marietta Energy Systems, Inc., under contract DE-AC05-84OR21400 with the US Department of Energy     

Tensional crack development in physical models with inhomogeneities under load

Summary The paper deals with a study of the mean stress field (_M) and its gradient (_M/x) in uniaxially loaded two-dimensional models of small thickness with respect to other dimensions, in which two inhomogeneities, e.g., a circular opening and a linear slit have been made. Particular attention was paid to the stress field development in the treated models durin gthe change of the mutual geometric configuration of both the inhomogeneities in question. The problem was analysed theoretically by means of Muskhelishvili's potentials of the two-dimensional theory of elasticity. To compare the results of calculations, the schlieren method was used to visualize and record the studied gradients of stress fields in physical models. The results of the calculations were calibrated by laboratory tests. In this way the individual model situations were classified from the point of view of their resistance to the applied load.     

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.

     

Derived geometrical constants of the geodetic reference system 1980

Summary A large number of the users of the geomtrical constants of the reference ellipsoid know only the IAG resolutions and not the related special publications; consequently, the numerical values of the derived geometrical constants may be interpreted differently. Some values of possible differences (max. 32 mm) are given, and it is proposed that the GRS-80 geometrical constants be defined by the values of a and f ^–1 with unlimited accuracy in the next IAG resolution.

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¶rt;a um nam zmuuu nmu n-unu¶rt;a am m uu ¶rt;a¶rt; auauu n z¶rt;uu, a nua nuauu; nm m num a mau u au nu¶rt; zmuu nm. mam nu¶rt;m m au am (a. 32 ) u n¶rt;azam n¶rt; uu n¶rt;m muu nm GRS-80 uuau a, f ^–1 zau mm.

     

Fast computation of ray synthetic seismograms in vertically inhomogeneous media

Summary A procedure of fast computation of body-wave ray synthetic seismograms in vertically inhomogeneous media is suggested. The procedure uses a special approximation of the velocitydepth distribution which guarantees continuity of the first and second derivatives of velocity and does not generate false low-velocity layers (oscillations in the velocity-depth function). The ZESY82 program package, which is based on the suggested procedure, is described. The point source with an arbitrary radiation pattern may be situated at any points of the model, the receivers are situated regularly or irregularly along any profile on the Earth's surface, containing the epicentre. Numerical examples of the synthetic record sections for a model of the Earth's crust and the uppermost mantle are given.

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¶rt;aam m¶rt; m ama ummuu a mua ¶rt;¶rt; ¶rt;, u¶rt; u nua annuauu m aa, ma nuam nm mu u n u m nu¶rt; u nu¶rt;um aau um nu mu. am nua aumn na ZESY82, a a m m¶rt;. umu aamumu uu an m ¶rt;u; nuuu ¶rt; m an¶rt; ¶rt; nu, ¶rt;a num. u¶rt; nu ummuu a ¶rt; ¶rt; ¶rt;u u amuu.