Spherical harmonic analysis and Fourier transformation

Summary The paper deals with the computation of spherical harmonic coefficients from surface measurements of the magnetic or gravity field of the Earth when the measurements are distributed regularly. The Fourier representation of associated Legendre functions which this procedure makes use of, then enables the harmonic analysis to be transformed to Fourier analysis which has better numerical properties.

---

ama na ama uu uu uum n nm uu aum uuaumau n u a, ¶rt;a mu uu an ammu ma. ¶rt;mau n a¶rt; , m unm mm n¶rt;¶rt;, nm nmauu aau naam aau , m a¶rt;am uu uumu mau.

     

Deuteron whistlers in the outer ionosphere

Summary Upgoing and downgoing deuteron whistlers were found on VLF records made by Interkosmos 5, 14 and 19 satellites even at heights below 1000 km. To account for them, a slight admixture ofD ⁺ ions has been introduced into the ionospheric plasma model with the usual content of only three ion speciesH ⁺,He ⁺ andO ⁺. Relations derived for the calculation of characteristic frequencies in a five-component plasma (e,H ⁺,D ⁺,He ⁺,O ⁺) are given as well as the values of characteristic frequencies calculated on this basis. The observed features of upgoing and downgoing deuteron whistlers could be explained by the calculation results, and it is also possible to formulate some conclusions for the purposes of plasma diagnostics.

---

mu um, anmau a ma u u, u a a nmua m 5, 14 u 19 a ma ¶rt;a 1000 . u u a ¶rt;a ¶rt; u na ¶rt;au uH ⁺,He ⁺,O ⁺ aa nuD ⁺ u. m mm ua nma ¶rt;a ¶rt; aamumuu amm ¶rt;a ¶rt;u na. uu aamumuu amm nuu um a¶rt;a mu ¶rt;mu um. a m ¶rt; unam aamumuu ¶rt;mu um ¶rt; u¶rt;au naam na.

     

Study of the velocity conditions in the earth's crust in the regions of the Bohemian massif and the carpathian system along international profiles VI and VII

u¶rt;m n uu ¶rt;u m n u ma n¶rt;aa, nu m¶rt;u u ¶rt;uau. n nuu uu ¶rt;u m n ¶rt;a¶rt; nu NoNo VI, VII. u au u n m a (x, H), ¶rt;auu an¶rt;u ¶rt;u m ¶rt; m¶rt; nu, u mua m nuu (H), aamuu an¶rt;u m a mua ¶rt;¶rt; uu ¶rt;uua u a. u a ¶rt;u m (x, H) amm ¶rt;uuu (u) a m¶rt; nu. m¶rt; u, auuu aau, om aamuam muau an¶rt;u ¶rt;u m, uu , n m u m nu aamuu a nmu, am ma a¶rt;am aa uu ¶rt;u m. aa u a¶rt;u n nu NoNo VI u VII u umuu ¶rt;a. mua m nu (H) num m ¶rt;u amu aua u anam um, ¶rt;a amu ¶rt;aua u ¶rt;- nma (nu No VII). ma ¶rt; ¶rt; aua, maa numa nm m u numa nm ma¶rt;um, a unaa nuu umnmauu a¶rt;uu ¶rt;uau amu aua.     

Approximate solutions of the surface mass loading of a spherical Earth model

Summary Simple linear representation of the components of an approximate plane solution of point mass loading of the Earth's surface in a conveniently chosen coordinate system leads to selection of a 2nd-degree curve which is the best fit of the spherical solution for the given Earth model. The new approximate solution, which, analogously to the plane solution, can be called a parabolic solution, enables the simple input parameters of the plane solution to be used also for substantially larger angular distances. The comparison with the spherical solution is carried out by computing the effects of the M₂-wave of ocean tides. The results of the computations for the tidal station Brussels prove the two solutions to be in sufficient agreement for global problems as well.

---

m nu uau aa nuuum nm u m m au nmu u n¶rt;¶rt; um ¶rt;uam ¶rt;m ma u m mnu, ma auu a n¶rt;¶rt;um u u ¶rt; ¶rt;a ¶rt;u u. nuuum u, m n aauu nm u aam naauu u, nm unam nm ¶rt; ¶rt;a nm u ¶rt;a ¶rt; m u amu. au uu u m uu uu ₂ u nuu. mam uu ¶rt; nuu mauu ¶rt;aam ¶rt;mum au u u ¶rt;a ¶rt;a a¶rt;a.

     

Friction constitutive law with rate and state dependences

A general formula for the Dieterich-Ruina friction constitutive law with rate and state (n-state variables,n=1, 2,...) dependences has been obtained and discussed under the assumption that the slip acceleration a varies ion a linearly with the slip displacement , namelya = a ₀ + (-₀). Wherea ₀, ₀ are initial constants, is the acceleration rate and constant.a ₀ and may be arbitrary constants (positive, negative or zero).The extreme value of frictional resistance and the existence condition of the extreme value, which are very important and govern to some degree the motion process of a frictionally slipping mechanical system, have been analyzed. A critical value _c which is the measure of the velocity weakening and velocity strengthening of the mechanical system, and its properties and the relationship to the extreme problem have been studied. Again, according to the critical value _c, the concepts of light or strong velocity weakening (or strengthening) are introduced.A possibly new phenomenon that frictional resistance may vary in some kind of decayed oscillation is found. Finally, the condition for the smallest frictional resistance for a slipping mechanical system with nonuniform acceleration has been obtained.     

Solar activity variations and climatic changes

Summary For the last two millenia it has been possible to determine the secular variation of solar activity from naked-eye sunspots, aurorae and radiocarbon variations. The results of the analysis of old East Asian observations of comets, which reflect the night cloudiness variation, do not agree with the former findings that the long-term climatic changes derived from comets depend on solar activity. The distinct anticorrelation between the Chinese records of comets and naked-eye sunspots is found only for the period from the 3rd to 6th century A.D., but in other centuries any correlation can hardly be seen. East Asian cometary observations give evidence of climatic changes in different parts of this large geographic region.Secular variations of the River Nile levels, regularly measured from the 7th to 15th century A.D., clearly correlate with the solar variations, which suggests evidence for solar influence on the climatic changes in the East African tropics. The decline of the Kingdoms in ancient Egypt and the occurrence of the Intermediate Periods are generally explained by very low Nile floods and prolonged droughts followed by severe famines and the destruction of the political structure. But the radiocarbon data show that at least the First and Second Intermediate Periods coincide with the secular maxima of solar activity and the Middle Kingdom with the minimum. This contradicts the positive correlation found from the eight centuries of measurements of River Nile levels made by Arabs. It seems that the influence of solar activity on the secular climatic changes has an episodic character.

---

nu¶rt; uu amumu ¶rt;mam m n¶rt;um nuuum a n¶rt;u ¶rt;a mmu nm au nu n uu u u¶rt;u a nm a¶rt;u¶rt;u uuu. ¶rt; amm nu n uu uu n mmu .. um a m uu ¶rt;a umumuaum n. ¶rt;m auau nu m amum ua a uu amumu a am — am, maau ¶rt;nu¶rt; uamuu uu. ¶rt;a, mam aaua ¶rt;u a¶rt;u m u n a a m am muu ¶rt;au. aua ¶rt;umau anuu ma u u¶rt;u a nma, aum amuu m ¶rt; nu¶rt;a - n 6- , a ¶rt;u nu¶rt;a maa u mmmm. m, aa uu uu mmmu uu ¶rt; ¶rt;au a¶rt;uu m uma, u nuu u¶rt;ummm auuu uu uama au am m au amu.nu¶rt; auauu m n¶rt;a ¶rt; (au), a ma ma aa ma ¶rt; (uu) u n uu, n¶rt;uu u unm ¶rt;u 7- ¶rt; ¶rt;u 15- a, n¶rt;u auau. m u¶rt;ummm uuu a a uamuu uu m-auau mnua. a u u numu aumu ¶rt;unmu am m au ua nuaa. na¶rt; ¶rt;unmu am u amnu ¶rt;amu m uu ¶rt; u u n¶rt;umu aau, a mu n¶rt;a m¶rt; u au numu mm. ¶rt;a, n a¶rt;u¶rt; ¶rt;a aum, m n a n u m ¶rt;amu na¶rt;am ¶rt;umu auau amumu, m nmuum num uu, ¶rt; u ummu uu ¶rt; u. am, m uu amumu a uu uama um aa nu¶rt;u aam.

     

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.

---

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.

---

---

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

Results of concentration and mobility measurements of positively and negatively charged particles taken by a rocket-borne parachuted aspiration (Gerdien) probe in the height region from 72 to 39 km

Summary With a self-neutralizing, rocket-borne parachute aspiration probe concentration and mobility measurements of positively and negatively charged carriers were made between 72 and 40 km over Sardinia. Between 72 km and 60 km a heavy and a light group of positively charged particles were found. The heavy group was more abundant than the hight group in the greater heights. For the negatively charged particles only one mobility group was found which roughly corresponded to the mobility of the light group of the positively charged carriers. The probe was designed so that no electrons could enter the analyzer section of the aspiration system. By this the electron concentration was given by the difference in concentration between the positively and negatively charged particles.This paper was read byH. Dolezalek, in an abbreviated form supplied by the authors.     

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.

---

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.

     

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.     

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.

---

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.

     

Effects of the interplanetary magnetic field sector structure in the winter ionosphere

Summary The ionospheric effects of the interplanetary magnetic field (IMF) sector boundary crossings are studied for the winters of 1963–69. They are considerably stronger for proton than for non-proton sector boundaries. There are two different types of effects. The geomagnetic type is a disturbance, observed in geomagnetic activity, the night-time ionosphere and the day-time F2 region near the geomagnetic equator. The effect in the ionosphere is interpreted in terms of the IMF sector boundary crossing related changes in geomagnetic activity. The tropospheric type is aquietening, observed in tropospheric vorticity and in the day-time mid-and low-latitude ionosphere (except the geomagnetic equator region). The mechanism of this effect remains unexplained.

---

¶rt;m u m nu mau nam aum n () ¶rt; u 1963–69. u m u ¶rt; nm ¶rt; a mau. mm ¶rt;a m¶rt; muna m. aum m u, a¶rt;a aum amumu, u u ¶rt; F2 amu uuaum ama. mu u m ¶rt;mu uu aum amumu, m a nu mau . n mun m nu, a¶rt; aumu mn u ¶rt; ¶rt;- u uum u (a uu amuaum ama). au m ma um.

     

Changes of stability of remanent magnetization with the concentration of vacancies in titanomagnetites

¶rt;am uu mm ¶rt;m a mam aaum aam u uu nu au anuu. mam naam, m m ¶rt;m m ¶rt;u u a am, m uu a m nmua a u ¶rt;uu ¶rt;uau. na mau aau mu muu mumaamuma uuam mauom mam aaumu.     

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.

---

¶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.

     

Energy regimes in the Earth's magnetosphere

Summary The dynamics of the main processes of energy accumulation and dissipation in the Earth's magnetosphere at various geomagnetic disturbance levels is examined. The results of the relevant calculations are tabulated. The relationships between the energy parameters of the solar wind and the Earth's magnetosphere are analyzed. Some conclusions concerning the field-aligned currents in polar caps, the Joule dissipation of energy and the energy injection into the ring current, the energy releases in the upper ionosphere, etc., are drawn.

---

ama ¶rt;uaua n anu u ¶rt;uunauu uu aum u nu au aum mu. mam uu n¶rt;ma maua. auum au ¶rt; muuu aamumuau ma u aum u. u¶rt;m m au n¶rt; ma n an, uu ¶rt; ¶rt;uunauu, uu uuu m, uu, ¶rt; u, u m. ¶rt;.

     

The Earth's structure in the region of the crimea according to the Rayleigh waves observations

Summary The Earth's crust and mantle structure in the region Crimea are investigated on the surface waves observations. For this investigation the long-period seismographs have been installed for the triangle of the seismic stations Simferopol, Alushta, Theodosiya. The phase velocities dispersion has been determined on the base of surface waves for the 8 earthquakes. The observed dispersion curves agree with the theoretical ones for the Earth's model with the crust's thickness of 36–40 km and with (in the mantle) the low velocity layer (V _s =4.3 km/sec at the depth of about 120 km). . , , . 8 . 36–40 . (V _s=4.3 /) 120 .Presented to the IASPEI General Assembly, Madrid, 1969.     

Asymmetry in a nearly symmetric dynamo

mam u¶rt;m uu aumuu a m n uamu ¶rt;u nmu umu ¶rt;ua a maum ¶rt;a amu u. a um naa nu nu naama umuu , au a um aumu m n aau umuu mau aum n. aam, m mum au ¶rt;-amu a ma mu aum u u n a aumu m n.     

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.     

Heat flow variations in the presence of an irregular contact of different rock type

Summary The effect of an irregular contact of two different rock types on the surface heat flow was analysed for the Zlatý Kopec region in northwest Bohemia. The 2-D geothermal model of subsurface structures was compiled according to measured values of the thermal conductivity and heat sources and by using isobaths map of the metamorphite-granite boundary. The heat flow was computed numerically from the temperature distribution obtained as a finite-difference solution of the heat conduction equation. It was found that the heat flow variation, corresponding to the most probable model, amounts approximately to the half of the actually observed changes. The surface heat flow is affected strongly by the thermal conductivity contrast between the overlying metamorphites and underlying granites and, on the contrary, it is little sensitive to the heat production difference between both rock types. It seems, therefore, that, despite the big heat production contrast observed, the main source of the heat flow variability are thermal conductivity inhomogeneities.

---

¶rt;am uu mama ¶rt; m¶rt; mun n¶rt; a nm mn nm ¶rt; amu am n ana¶rt; uu. a u au mnn¶rt;mu u mnauu u n amu aauauaum — mauu n¶rt; a maa ¶rt;a ¶rt; nunm mm. n nm auma n -am u au mnn¶rt;mu. mam ¶rt;m, m auau mn nma ma a m ¶rt;u, n¶rt;mam nuuum nu a¶rt;a uu. a nm m u um aua mnn¶rt;mu ¶rt; aauu mauuu n¶rt;au u uaauaum, u am, nm a mum auu mnauu ¶rt; muu n¶rt;au. aum, m, m a a¶rt;a au mnauu,a umu auau mn nma m ¶rt;¶rt;mu uma mnn¶rt;mu.

     

Elektronenproduktion,Rekombination, Elektronendichte und Absorption in der ionosphärischenD-Region und ihre jahreszeitlichen Variationen

Zusammenfassung Es wird die Gleichung für die Elektronenproduktionq(z) abgeleitet, die die meteorologischen Elemente der Mesosphäre berücksichtigt. Nach Angaben über die mit Satelliten und Raketen gemessene Röntgenstrahlung mit 8 Å wird das Differentialspektrum des ionisierenden Energieflusses für eine mittlere Sonnenaktivität konstruiert. Auf dieser Grundlage und nach der bekannten Intensität der Strahlung Ly- sowie nach Angaben über dieElektronenproduktion der kosmischen Strahlung werden die Profileq _Rö(z),q _Ly-(z) undq _CR(z) für mittlere geographische Breiten und Standardatmosphäre entwickelt. Nach eingehender Analyse der vollständigen Gleichung für den effektiven Rekombinationskoeffizienten wird für die Verhältnisse in der tiefen Ionosphäre der Beitrag jeder einzelnen Komponente der Gleichung bestimmt. ist eine recht veränderliche Grösse, die von den aeronomischen und meteorologischen Verhältnissen und der Sonnenzenitdistanz abhängt. Aus den fürq(z) und (z) erhaltenen Angaben werden zwei ElektronendichteprofileN(z) für =30° und 75° erhalten. Das ProfilN(z) bei =30° wird mit dem gemittelten Profil einer umfangreichen Gruppe experimentell gefundener VerteilungenN(z) verglichen; das Profil bei =75° wird durch Messung der deviativen und nondeviativen Absorption für eine längere Zeitperiode überprüft. In beiden Fällen hat sich die Richtigkeit der theoretisch erhaltenen Profile bestätigt. Die jahreszeitlichen Variationen der nondeviativen Absorption in derD-Region sind ausschliesslich durch die Variationen der meteorologischen Parameter im Bereich der Mesopause bei konstantem Energiefluss der ionisierenden Strahlung bedingt.

---

Summary An equation about the electron production is deduced in which the meteorological elements of the mesosphere are taken into account. The differential spectrum of the ionizing energy flux with 3 Å for average solar activity is constructed on evidence from rocket and satelitc measurements. The profilesq _Rö(z),q _Ly-(z) andq _CR(z) for mean geographical latitudes and standard atmosphere are plotted on that basis as well as on data fot the known intensity of the Ly- emission and the electron production of the cosmic rays. An exhaustive analysis is made of the full equation for the effective recombination coefficient and the contribution of all its components at lower ionosphere conditions is determined. is a rather variable quantity, dependent on the aeronomical and meteorological condition of the area under consideration, as well as on the solar zenith angle. Two profiles for the electron concentrationN(z) at =30° and 75° are drawn on the basis of data forq(z) and (z). The profileN(z) at =30° is compared with the averaged profile of a large group experimentally obtained distributionsN(z); the profile at =75° is checked by measurements of the deviative and nondeviative absorption taken for a lengthy period. Both checks are in good agreement with the theoretically obtained profiles. The seasonal variations of the nondeviative absorption in theD region could be completely explained with the variations of the meteorological parameters in the mesopause area at constant energy flux of the ionizing radiation.