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.     

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     

Variation of continental mantle heat flow with age. Possibility of discriminating between thermal models of the lithosphere

Continental mantle heat flow values are obtained by subtracting the radiogenic heat produced in the lower crust and lithosphere beneath the crust from reduced heat flow values reported for various heat flow provinces. The significance of continental mantle heat flow values thus obtained is that they can be considered essentially as representing the residual heat of cooling of the continental lithosphere. A plot of these mantle heat flow values against 1/t where t is the geologic age of the last thermal event suggests a linear trend. It is also found that the recently proposed relationQ=500 (1/t) for the variation of oceanic heat flowQ (in mW/M²) with aget (in million years) provides a reasonably good fit to the mantle heat flow data. The constant thickness plate model however, is found to be unsatisfactory in explaining the variation of continental mantle heat flow with age.     

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 .

     

(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.     

Typical properties of dynamic systems and the instability of hydrodynamic flows

Summary Based on Peixot's theorem of topological dynamics, the unstable behaviour of hydrodynamic flows on a two-dimensional annuloid T ² is analysed. The generating property is the curvature of the group of S ₀ Diff T ² diffeomorphisms of the (Riemannian) flow region T ² . This group is the configuration space of the ideal fluid flowing on T ² .

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a m ma u mn u ¶rt;uauu ¶rt;am mu n¶rt;uu¶rt;¶rt;uauu nm a ¶rt; m T ² u¶rt; mu. ¶rt;au m m a m uuann S ₀ Diff T ² ¶rt;uu amu mu ( uaa) T ² . manna m uau nmam ¶rt; u¶rt;a u¶rt;mu a T ² .

     

Long term variation in the secular love number

Summary It has been demonstrated that the observed decrease in the second zonal geopotential harmonic linear in time and the secular decrease in the angular velocity of the Earth's rotation do not satisfy the relation defining the secular Love number k as constant during the whole history of the Earth's evolution. The discrepancy disappears if it is assumed thatdk/dt=–2.4×10^–6 cy^–1 .

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aa, m a ¶rt;a au m aauunmuaa u u a ¶rt;a u mu au u ¶rt;mm mu, n¶rt; u a a nm mu umuu u. a uam, u ¶rt;nmumdk/dt=–2,4·10 ^–6 (mmu)^–1 .

     

Expansions of the double product of the global gravity field

Summary Four fundamental forms of expansion of the double product of the gravity function into an infinite series are derived. Two isotropic parts are separated, one is expressed by Legendre polynomials and the other by invariants of Wigner's D-matrices.

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¶rt; m n¶rt;mau ¶rt; au ¶rt; nu¶rt;uaumau uu ¶rt;. ¶rt; ¶rt; umn amu, na aam n nu a¶rt;a u ma n uauam amu ua.

     

The gross features of the lithosphere-asthenosphere system in Europe from seismic surface waves and body waves

Long-period recordings of dispersive Rayleigh waves along numerous station lines, or profiles, in Europe have for the first time permitted a uniform inversion of these observations based on a new method of phase velocity regionalization.Regional dispersion relations obtained by this method have then been subjected to a complete inversion procedure commonly known as the hedgehog method. The results are presented in a map outlining the thickness of the lower lithosphere (lid) and the shear (S) velocities in both the lid and the asthenosphere channel.A comparison of these results with the minimum compressional (P) wave velocities in the asthenosphere and their corresponding depths provides an estimate of theV _p /V _s ratio for the asthenosphere in the European area.Contribution No. 314, Institute of Geophysics, ETH-Zürich, Switzerland.     

Über die erdmagnetischen Anomalien in den Gebieten um die Ostsee

Zusammenfassung Das Gebiet um die Ostsee ist als erdmagnetisch stark gestört bekannt. Die Karte zeigt die Verteilung der intensiven Anomalien, wo Z 2000 and 5000 überschreitet. Der Gruppierung dieser Anomalien kann man eine ung.N Richtung zuschreiben.

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Summary The area around the Baltic Sea is known as magnetically intensely disturbed. The map shows the distribution of most intensive anomalies, where Z is more than 2000 and 5000 . The direction of the group of these intensive anomalies can be as appr.N supposed.

     

Influence of the IMF sector boundaries on cosmic rays and tropospheric vorticity

Summary The effect of the IMF sector boundary crossing (IMF SBC) in the vorticity area index (VAI) — the well-known dip in the VAI after IMF SBC — is found to be independent of the IMF SBC effect in the cosmic ray flux. This finding refutes a recent suggestion by Lundstedt [1] that the IMF SBC effect in VAI is caused by a decrease in cosmic ray flux, but supports the concept of the IMF SBC effects in the ionosphere and atmosphere developed by Latovika [2–4]. Cosmic rays seem to affect the troposphere in another way.

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¶rt;mu nu mau nam aum n ( ) a u¶rt; na¶rt;u aumu () — um uu n — a¶rt; auu m ma nm uu . mm mam nam ¶rt;a n¶rt;u ¶rt;m¶rt;a [1], m m a nuu nma uu , n¶rt;¶rt;uam nu m u u am, aum amu [2–4]. am m uu u m um a mn ¶rt;u a.

     

Precipitation of electrons after geomagnetic substorms

Summary Precipitating electrons E_e>10 keV and E_e>30 keV and protons E_p=150 to 300 keV are analyzed using data obtained from the low-altitude polar-orbiting satellite Interkozmos-17 after the magnetic storm of December 2, 1977. On December 3, an isolated substrom occurred, and strong electron precipitation was observed in the midnigt sector, while the sequence of substorms of December 5 expanded its longitudinal extent from 22 MLT through the morning to 12 MLT. The different character of the precipitation, in the two cases mentioned, is discussed in relation to the changes of conditions for the generation of cyclotron instability as well as to the effect of particle injection. Proton precipitation occurred only in the night sector, most probably just inside the plasmapause.

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¶rt; aau nau m E_e>10 u E_e>30 u nm E_p=150–300 n uu n uuma nmua n um m-17 n aum u 2. ¶rt;a 1977. 3. 12. nua uuaa u u nau m aumua m mo u. a n¶rt;amm 5. 12. nua auu ¶rt;m umaa, m m nau, a u m 22 MLT mu m ¶rt; 12 MLT. a aam nau nu¶rt; ¶rt; a ¶rt;am aa uu u ¶rt; uu um mumu u ¶rt;mu uuu amu. nau nm n¶rt;u m m u m a naana mu naa.

     

Forecast of abnormally high solar activity in the next century and of its possible negative effects on the earth

Summary Based on the relation between the relative sunspot number R, the number of sunspot groups f ₀ generated per unit time on the Sun as a whole and their average lifetime T ₀ , and on the extrapolation of time behaviour of f ₀ and T ₀ , it is proved that abnormally high solar activity may be expected in the first half of the 21st century. At this time, the maximum annual relative sunspot numbers R_M of the 11-year cycles should reach values of about 300 units. This abnormally high solar activity in the next century can be understood as the antipole of the Maunderean minimum. This forecast is used to discuss some of the possible consequences of this abnormally high solar activity for the processes on the Earth: changes of climate (heat waves and draughts in Central Europe), in the higher layers of the Earth's atmosphere (anomalous propagation of radio waves, increased effect of the density of the upper atmosphere on the orbits of man-made satellites), in seismicity (increased seismic activity in Europe and Southeast Asia), for technical devices (induced electric currents), in the biosphere. etc.

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a mu ¶rt; uau a R nm, unn nm f ₀ uu ¶rt;uu u a ë u u ¶rt; n¶rt;ummu uu ₀ , u a manuu ¶rt;a f ₀ u ₀ , naa, m n nu ¶rt; 21 a u¶rt;am uum amum. aua¶rt;u ua a R m¶rt; 11-mu ua m u ¶rt;muam au 300 ¶rt;uu. m uum amum ¶rt; nuam a amun¶rt; a¶rt; uua. a m na ¶rt;am m n¶rt;mu m uum amumu a n nmau a : a uu uama (aa u a n¶rt;a ¶rt; n), a u u am u (aa anmau a¶rt;u, uu n nmmu u am a ¶rt;uu um m), a um (na ua amum n u -m uu), a muu mma (u¶rt;ua muu mu), a u u ma ¶rt;a.

     

Source radiation pattern andPKP amplitudes from the Tonga region

Summary The relation of short period PKP1 and PKP2 amplitudes from deep earthquakes in the Tonga region observed at a seismological station in Central Europe, is compared with the theoretical relations computed for different source radiation parameters and depths. The Preliminary Earth Model was used in the computations. Qualitatively good agreement of observed and calculated values was found for the radiation pattern corresponding to the likely geometry of the Tonga subduction zone. The influence of the variation of some source and model parameters on the calculated PKP1 and PKP2 relation is discussed.

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¶rt;a au mu anum¶rt; mnu¶rt; PKP1 u PKP2 mu mu a, anua ¶rt; u mau ma n, mmmuu mmuuu uuau, aumau ¶rt; a naam ua umua uu aa. ama unaa ¶rt; PREM. a¶rt; u auma uu ¶rt;am am au ¶rt; a uu, mmm mmuu ¶rt;uu a a. ¶rt;am uu auau naam umu u ¶rt;u a uu am mu anum¶rt; PKP1 u PKP2.

     

Earthquake distribution and volcanism in Kamchatka,Kurile Islands,and Hokkaido Part 3: Southern Kuriles and Hokkaido

Summary The morphology of the Wadati-Benioff zone in the region of Southern Kuriles and Hokkaido, based on the distribution of 4015 earthquake foci, verified the existence of an intermediate depth aseismic gap and its relation to active andesitic volcanism. A paleosubduction zone activated by an intermediate depth collision with the active subduction zone was found and described.

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u Wadati-Benioff amu uu - u a¶rt;, aa a an¶rt;uu 4015 a mu, nm¶rt;ua mau n¶rt; au u amu a¶rt;um au. a a¶rt;a u nuaa a na¶rt;uu, amuuuaa nmu mu amu ¶rt;uu.

     

The relation between the heat flow field and the distribution ofP n -wave velocities for the European continent

Summary The dependence of P_n-wave velocities on the heat flow, temperature at the crustmantle boundary and the thickness of the Earth's crust in Europe was investigated in relation to the problem of lateral inhomogeneities in the upper mantle. A map was constructed of the distribution of P_n-wave velocities on the territory of Europe. The relations these investigations yielded, were compared with the results of laboratory experiments and all the results are discussed from the physical point of view. The conclusion drawn is that that temperature and pressure effect provide a sufficient explanation of the observed regional changes of P_n-wave velocities for the European continent.

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auum ¶rt;auu mu n¶rt; ¶rt; nmu uua (P_n) u mn nm, mnam a nmu amuu u m a mumuu n a u¶rt;aa u numa ¶rt;¶rt;m amuu. mumuu n a maa a uu m P_n- a nmu uua. u¶rt;u umam ¶rt;a mama aam u¶rt;au uuu m n¶rt; amuu u u ¶rt;au u mnam mmmm mama n¶rt;aa am. ¶rt;a ¶rt;, m ua uu m P_n- a n mum ¶rt;mam um uuu mnam u ¶rt;au a nmu uua.

     

Behaviour of quartz gravity meters under high frequency vertical motion

Summary Tests on the vertical vibrating table in the frequency range of70–110 Hz indicate that quartz gravity meters are10–100 times more sensitive at some frequencies than under low-frequency excitation. At high frequencies, the reading beam is at rest and deflected from the correct position. Slow fluctuations of amplitude and frequency near resonance could cause slow irregular motion of the beam with absence of low-frequency ground motion of sufficient intensity.

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unmauaum a mua um¶rt; ¶rt;uana amm 70–110u mam, m a m ammaaum 10–100 a mum nu uamm au. u amm au u a¶rt;um n m mu m nu. ¶rt; auauu anum¶rt; u amm au uu aa m am uamm u ua ¶rt;a mmmm uamm au n ¶rt;mam umumu.

     

Spherical harmonic expansion of the continents and oceans distribution function

Summary An algorithm is derived to compute the coefficients of a spherical harmonic series for the functionE(, ) representing the distribution of continents and oceans with the least-squares method. Some properties of the system of normal equations, when measuring points are distributed in a regular grid, are discussed. The fully normalized complex coefficients to the ninth degree are given in the table.

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m mam nuam n uu uum ¶rt; uau ¶rt;a ¶rt; uu (, ), ma nm n¶rt;um an¶rt;u mum u a nu nu m¶rt;a auu a¶rt;am. ¶rt;am m ma um a au ¶rt; a, ¶rt;a uum mu an mu. m aua n um ¶rt;o ¶rt;m mnu nu¶rt;m mau.

     

Effect of cofactors of adjusted and unadjusted quantities on their functions

aamuam uu am a (m u naamuu n) u u (a) uu a uu mu uu. mam (19), (28) naam, m amua am mau u m ¶rt; am amu: a) na ¶rt;um am, n n a uu am u uu a uu; ) ma ¶rt;um am, m aam uu a uu.     

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;.