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.     

Zur Interpretation von seismischen Refraktionsmessungen mit abgebrochenen Potenzreihen

Zusammenfassung Es wird die Interpretation der dreigliedrigen Laufzeitfunktion (1) vervollständigt und als Beispiel (P _n () nachJeffreys-Bullen im Bereich von 0° bis 19° behandelt.

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Summary The interpretation of the travel-time function (1) is completed and an example is given.

     

The effect of the number of charges carried by the argon ion on the darkening of ilford Q2 emulsion as ion detectors in mass-spectrometer

Summary The darkening (S) of Illford Q₂ photographic plates as ion detectors in mass spectrometer has been investigated. The dependence of the darkening (S) on the ion density (n=ions/mm²) i.e.S=S(n)E for constant energy (E)=z U ranging from 4U20 Kv of the impinging⁴⁰A⁺¹-,⁴⁰A⁺²- and⁴⁰A⁺³-ions whenS does not exceed the value 0.15 and the second relationn=n(z U) _S for darkening 0.05S0.15 constructed from the above relationS=S(n) _E has been determined. The darkening was found to increase with increasing ion-density which inturn decreases with the ionenergy. For⁴⁰A⁺¹-,⁴⁰A⁺²-, and⁴⁰A⁺³-ion of equal energy and ion-density the darkening effect was independent of the number of the charges carried by the argon ion.     

Tidal currents and residual currents at Norderney,Elbe 1, and Aussen-Eider lightships and their variation under the influence of prevailing winds

Summary Four hourly current-and wind observations during the years 1924–1927 at the German lightvessels Norderney, Elbe 1, and Aussen-Eider were subjected to harmonic analysis with emphasis on the influence of the wind on the residual as well as on the tidal current. The tidal current is strongest at Elbe 1 and weakest at Aussen-Eider. The half-monthly inequality of the current is strongly influenced by a ₂ tidal component. Wind influences the velocity, phase and duration of ebb-and flow current in a systematic way at Norderney and Elbe 1. Deviations from the mean tidal current are caused mainly by the change in wind direction rather than by wind velocity. The mean residual current is weak at the three stations. But wind driven currents have a velocity up to 5 times as great as the mean residual current and reverse their direction with the wind. The annual variation of the mean residual current, however, is caused only to a small part by the annual wind variation.Abbreviations used in this paper Gr. M. Tr. Greenwich moon transit, i.e. Greenwich civil time of the upper or lower transit of the moon through the meridian of Greenwich - C _n computed tidal current at M1/2Hn - C _n ^m computed mean tidal current at M1/2Hn - M _n Moon-half hour mean, i.e. mean of all current velocities observed during M1/2Hn - M.A. Moon age of an observation, true Greenwich time of Gr.M.Tr. directly preceeding the time of observation, expressed in 12 integral numbers, each representing M.A. falling in 12 different hourly intervals - M1/2H Moon-half hour, 1/2 of the interval between one moon transit and the next, i.e. 1/24 of 12h25m - R _n ^o ,R _n ^' ,R _n ^" residual current computed by harmonic analysis ofn M1/2H means of the mean current, the current at weak winds, and the current at strong winds respectively - d.o.f. degrees of freedom - standard deviation ofC _n fromM _n - ^* mean standard deviation ofC _n fromM _n for analysis with weighted means - A _o Standard error of the residual currentA _o - AB standard error of the harmonic coefficientsA ₁,B ₁,A ₂,B ₂,... - S ₂ Phase of the current componentS ₂     

Fundamental geodetic parameters of the earth's figure and the structure of the earth's gravity field derived from satellite data

Summary Using the geocentric constant GM=398 601.3 × 10 ⁹ m ³s ^–2 , the known value of the angular velocity of the Earth's rotation , Stokes' constants J _n ^(k) and S _n ^(k) upto n=21 (zonal), n=16 (tesseral and sectorial) [2], the geocentric co-ordinates and heights above sea-level of SAO satellite stations [2], the following will be derived: the potential on the geoid W_o, the scale factor for lengths R_o=GM/W_o, the radius-vector of the surface W=W_o, the parameters of the best-fitting Earth tri-axial ellipsoid, and the components of the deflections of the vertical with respect to the geocentric rotational IAG ellipsoid (Lucerne 1967), as well as to the best-fitting geocentric tri-axial ellipsoid. Some of the differences in the structure of the gravity field over the Northern and Southern Hemispheres will be given, and the mean values of gravity over the equatorial zone, determined from the dynamics of satellite orbits, on the one hand, and from terrestrial gravity data, on the other, will be compared.Presented at the Fifteenth IUGG General Assembly, Moscow, July 30 — August 14, 1971.     

Cyclic variations of the initial height of the sporadicE-layer at middle geographical latitudes

Summary The variations of the initialh E _s height are investigated in the solar cycle 1957–1968, deriving the regressive dependency:h E _s =121.4–6·10^–2 R referring to the median monthly values at a solar zenith angle =75°. The similar variations ofh E _s (R) during the day and night are interpreted as a domination of the sporadic layer formation from a redistribution of the day-time ionization and secondary participation of nightly ionizing sources. The analogous cyclich E _s andh E variations confirm this conclusion while the seasonal variations in the state of the sporadic layer show outlined dynamical effects. The comparatively not big cyclic variation in the spatial state of theE-region are considered to confirm the predominating ionizing action of the ultraviolet range (933–1038 Å) in the lower part of theE-region, while the soft X-radiation influences mainly the near maximum part of this region.     

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.     

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}      

Planar charged-particle trajectories in multipole magnetic fields

This paper provides a complete generalization of the classic result that the radius of curvature () of a charged-particle trajectory confined to the equatorial plane of a magnetic dipole is directly proportional to the cube of the particles equatorial distance () from the dipole (i.e. ³). Comparable results are derived for the radii of curvature of all possible planar chargedparticle trajectories in an individual static magnetic multipole of arbitrary order m and degree n. Such trajectories arise wherever there exists a plane (or planes) such that the multipole magnetic field is locally perpendicular to this plane (or planes), everywhere apart from possibly at a set of magnetic neutral lines. Therefore planar trajectories exist in the equatorial plane of an axisymmetric (m = 0), or zonal, magnetic multipole, provided n is odd: the radius of curvature varies directly as ⁿ⁼². This result reduces to the classic one in the case of a zonal magnetic dipole (n = 1). Planar trajectories exist in 2m meridional planes in the case of the general tesseral (0 < m < n) magnetic multipole. These meridional planes are defined by the 2m roots of the equation cos[m()–_n^m)] = 0, where _n^m = (1/m) arctan (h_n^m/g_n^m); g_n^m and h_n^m denote the spherical harmonic coefficients. Equatorial planar trajectories also exist if (n – m) is odd. The polar axis ( = O,) of a tesseral magnetic multipole is a magnetic neutral line if m > I. A further 2_m(n – m) neutral lines exist at the intersections of the 2_m meridional planes with the (n – m) cones defined by the (n – m) roots of the equation P_n^m(cos ) = 0 in the range 0 < 9 < , where P_n^m(cos ) denotes the associated Legendre function. If (n – m) is odd, one of these cones coincides with the equator and the magnetic field is then perpendicular to the equator everywhere apart from the 2m equatorial neutral lines. The radius of curvature of an equatorial trajectory is directly proportional to ⁿ⁼² and inversely proportional to cos[m(–)]. Since this last expression vanishes at the 2m equatorial neutral ines, the radius of curvature becomes infinitely large as the particle approaches any one of these neutral lines. The radius of curvature of a meridional trajectory is directly proportional to rⁿ⁺², where r denotes radial distance from the multiple, and inversely proportional to P_n^m(cos )/sin . Hence the radius of curvature becomes infinitely large if the particle approaches the polar magnetic neutral ine (m > 1) or any one of the 2m(n – m) neutral ines located at the intersections of the 2m meridional planes with the (n – m) cones. Illustrative particle trajectories, derived by stepwise numerical integration of the exact equations of particle motion, are pressented for low-degree (n 3) magnetic multipoles. These computed particle trajectories clearly demonstrate the non-adiabatic scattering of charged particles at magnetic neutral lines. Brief comments are made on the different regions of phase space defined by regular and irregular trajectories.Also Visiting Reader in Physics, University of Sussex, Falmer, Brighton, BN1 9QH, UK     

Application of A. C. demagnetization to investigate the stability of rock magnetization caused by lightning currents

Summary An apparatus is described which enables progressive demagnetization of rock specimens under alternating fields in order to remove the unstable components of magnetization while retaining a measurable fraction of the stable component.The apparatus is utilized to study the stability of magnetization created in rock specimens by artificial lightning currents. It is shown that the remanent magnetization due to strong lightning currents could be fairly stable and in certain cases peak a. c. fields of intensity as high as 1700 Oe may fail to destroy completely the effect of this hard component.Possible means for avoiding the magnetic noise effect of lightning on paleomagnetic investigations are discussed.

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Zusammenfassung Es wird eine Apparatur beschrieben die es ermöglicht, Gesteinsproben mit Hilfe von Wechselfeldern schrittweise zu Entmagnetisieren. Dabei werden die unstabilen Komponenten der Magnetisierung entfernt, während ein Teil der stabilen Magnetisierung erhalten bleibt.Die Apparatur wurde verwendet, um die Stabilität der in den Gesteinsproben durch künstliche Beblitzung erzeugten Magnetisierung zu untersuchen. Es wird gezeigt, dass die durch starke Blitze erzeugte remanente Magnetisierung recht stabil sein kann und dass es in gewissen Fällen selbst Wechselfeldern mit Feldstärken bis zu 1700 Oe nicht gelingt, diese harte Magnetisierung zum Verschwinden zu bringen.Möglichkeiten, um den störenden Einfluss der Blitze bei päleomagnetischen Untersuchungen zu vermeiden, werden besprochen.

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Part II of the dissertation Theoretical study of the magnetic attraction due to rock bodies and experimental investigation of the stability of rock magnetism submitted to the Swiss Federal Institute of Technology (ETH), Zurch, for the degree of Doctor of Natural Sciences.     

Dependence of the effective attachment coefficient of small ions upon the size of condensation nuclei

Summary To clarify the ionization equilibrium near the ground, simultaneous measurements of the rate of ion pair production (q), the concentrations of small ions (n) and condensation nuclei (Z), and the diffusion coefficient of condensation nuclei (D) were carried out at several stations in the central area of Japan. The total rate of ion pair production (q) was estimated fromq=q(Rn)+q(Tn)+q()+q(+CR). The value ofq was estimated as 10J to 20J. The mean life () and the effective attachment coefficient () of small ions were also estimated at each station. Correlations amongn, Z, q, andD were also studied. If we take the variation ofD into consideration, the correlation was expressed by the simple formula;q=n Z. The dependence of upon size of nuclei (2r) were also measured, and was found to correlate well withD orr.     

Crystallization of Mount St. Helens 1980–1986 dacite: A quantitative textural approach

Quantitative measurements of crystal size distributions (CSDs) have been used to obtain kinetic information on crystallization of industrial compounds (Randolph and Larson 1971) and more recently on Hawaiian basalts (Cashman and Marsh 1988). The technique is based on a population balance resulting in a differential equation relating the population densityn of crystals to crystal sizeL, i.e., at steady staten =n ^o exp(–L/itG), wheren ^o is nucleation density,G is the average crystal growth rate, is the average growth time, and the nucleation rateJ =n ^o G. CSD (Inn vsL) plots of plagioclase phenocrysts in 12 samples of Mount St. Helens blast dacite and 14 samples of dacite from the 1980–1986 Mount St. Helens dome are similar and averageG = 9.6 (± 1.1) × 10^–3 cm andn ^o = 1–2 × 10⁶ cm^–4. Reproducibility of the measurements was tested by measuring CSDs of 12 sections cut from a single sample in three mutually perpendicular directions; precision of the size distributions is good in terms of relative, but not necessarily absolute values (± 10%). Growth and nucleation rates for plagioclase have been calculated from these measurements using time brackets of = 30–150 years; growth ratesG are 3–10 × 10^–12cm/s, and nucleation ratesJ are 5–21 × 10^–6/cm³ s.G andJ for Fe-Ti oxides calculated from CSD data areG = 2–13 ± 10^–13 cm/sec andJ = 7–33 × 10^–5/cm³ s, respectively. The higher nucleation rate and lower growth rate of oxides resulted in a smaller average crystal size than for plagioclase. Sizes of plagioclase microlites (<0.01 mm) in the blast dacite groundmass have been measured from backscatter SEM photographs. Nucleation of these microlites was probably triggered by intrusion of material into the cone of Mount St. Helens in spring 1980. This residence time of 52 days gives minimum crystallization estimates ofG = 1–3 × 10^–11 cm/s andJ = 9–16 × 1O³/cm³ s. The skeletal form of the microlites provides evidence for nucleation and growth at high values of undercooling (T) relative to the phenocrysts. A comparison of nucleation and growth rates for the two crystal populations (phenocrysts vs microlites) suggests that while growth rate seems to be only slightly affected by changes inT, nucleation rate is a very strong function of undercooling. A comparison of plagioclase nucleation and growth rates measured in the Mount St. Helens dacite and in basalt from Makaopuhi lava lake in Hawaii suggests that plagioclase nucleation rates are not as dependent on composition. Groundmass textures suggest that plagioclase microphenocrysts crystallized at depth rather than in the conduit, in the dome, or after extrusion onto the surface. Most of this crystallization appears to be in the form of crystal growth (coarsening) of groundmass microphenocrysts at small degrees of undercooling rather than extensive nucleation of new crystals. This continuous crystallization in a shallow magmatic reservoir may provide the overpressurization needed to drive the continuing periodic domebuilding extrusions, which have been the pattern of activity at Mount St. Helens since December 1980.     

Anisotropic magnetic susceptibility of rocks under mechanical stresses

Summary The magnetic susceptibility of a rock under a uniaxial compression () decreases along the axis of compression and increases along the direction perpendicular to the axis, with an increase of . Thus, the magnetic susceptibility of a compressed rock becomes anisotropic.The decrease of longitudinal susceptibility,K (), and the increase of transverse susceptibility,K (), are theoretically derived from a model of rock which assumes the uniaxial anisotropy and the isotropic magnetostriction of magnetic minerals in rocks and a random orientation of the minerals. Results show thatK () decreases toward zero whereasK () increases and approaches a finite asymptotic value with an increase of , and –(/)K () is twice as large as /K () for small values of . These results are in good agreement with experimental data.

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Zusammenfassung Die magnetische Suszeptibilität eines Steines unter zunehmender uniachsigen Druckspannung () nimmt ab längs der Achse der Druckspannung und nimmt zu längs der Richtung senkrecht der Achse. Somit wird die magnetische Suszeptibilität des gedrückten Steines anisotrop.Die Abnahme der longitudinalen Suszeptibilität,K (), und die Zunahme der transversalen Suszeptibilität,K (), werden theoretisch von einem Modell eines Steines hergeleitet, das die uniachsige Anisotropie, die isotrope Magnetostriktion, und eine nichtbevorzugte Orientierung der magnetischen Minerals im Stein annimmt. Die Ergebnisse zeigen, dass mit einer Zunahme des ,K () gegen Null abnimmt, währendK () zunimmt und sich einem begrenzten asymtotitschen Wert nähert und, dass für kleine Werte des , –(/)K () zweimal so gross wie /K () ist. Diese Ergebnisse stimmen gut mit den Versuchangaben überein.

     

Multifractal measures,especially for the geophysicist

This text is addressed to both the beginner and the seasoned professional, geology being used as the main but not the sole illustration. The goal is to present an alternative approach to multifractals, extending and streamlining the original approach inMandelbrot (1974). The generalization from fractalsets to multifractalmeasures involves the passage from geometric objects that are characterized primarily by one number, namely a fractal dimension, to geometric objects that are characterized primarily by a function. The best is to choose the function (), which is a limit probability distribution that has been plotted suitably, on double logarithmic scales. The quantity is called Hölder exponent. In terms of the alternative functionf() used in the approach of Frisch-Parisi and of Halseyet al., one has ()=f()–E for measures supported by the Euclidean space of dimensionE. Whenf()0,f() is a fractal dimension. However, one may havef()<0, in which case is called latent. One may even have <0, in which case is called virtual. These anomalies' implications are explored, and experiments are suggested. Of central concern in this paper is the study of low-dimensional cuts through high-dimensional multifractals. This introduces a quantityD _q, which is shown forq>1 to be a critical dimension for the cuts. An enhanced multifractal diagram is drawn, includingf(), a function called (q) andD _q.This text incorporatesand supersedes Mandelbrot (1988). A more detailed treatment, in preparation, will incorporateMandelbrot (1989).     

Correlation of wind direction observations and other surface elements

Summary Many tabulations of climatological data present the distribution of specified elements with wind direction. It is shown that statistical characteristics expressing the relationship between cloud cover or visibility andwind direction can be computed with meaningful meteorological interpretation. The U.S. Navy Summaries of Monthly Aerological Records (SMAR) are used. Several distribution characteristics are suggested and the method of computing is discussed with samples given.The linear correlation coefficientr _yx between cloud cover or visibility classes and wind directions seems to be a fairly good characteristic but because of the nonlinearity of the relationship, the correlation ratio _yx is more efficient.Climatological features may also be studied by the linear correlation coefficientR _yx, which expresses the unweighted relation between cloud cover (visibility) classes and wind direction. The mathematical formulation of the relationship by polynomials indicates that higher order terms affect the functional connection.

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Zusammenfassung In vielen klimatologischen Tabellierungen werden Häufigkeitsverteilungen verschiedener meteorologischer Elemente in Abhängigkeit von Windrichtung geben. In diesem Artikel wird zegeigt, dass statistische Parameter berechnet werden können, welche die Beziehung zwischenWindrichtung und Himmelsbedeckung beziehungsweise Sichtweite mit sinnvoller meteorologischer Interpretation ausdrücken. Die Studien wurden an Monatszusammenfassungen aerologischer Daten (SMAR) des Marinewetterdienstes der U.S. durchgeführt. Mehrere statistischen Parameter werden vorgeschlagen und die Berechnungsweise mit Beispielen erläutert.Der lineare Korrelationskoeffizientr _xy, der die Windrichtungshäufigkeit in Abhängigkeit von Klassen der Himmelbedeckung bzw. der Sichtweite ausdrückt, erscheint brauchbar, wenn auch nicht zuviel erwartet werden darf, weil die Beziehung vielfach nichtlinear ist. Daher ist das Korrelationsverhältnis _yx mehr zu empfehlen.Klimatologische Zusammenhänge können auch mit Hilfe des KoeffizientenR _xy ausgedrückt werden. Dieser stellt den linearen Anteil einer Polynomreihe zwischen Klassenwerten der Himmelbedeckung (bzw. Sichtweite) dar, ohne den einzelnen Klassen ein Gewicht ihrer Häufigkeit entsprechend zu geben. Bei der vollen Berechnung der Beziehung durch Polynome kann man den nichtlinearen Anteil erkennen.Das spezielle Ergebnis der vorliegenden Arbeit ist, dass die Darstellung der Sichtweite oder Himmelsbedeckung bei Windrichtungsklassen wenig klimatologischen Effekt offenbart, da die Form der Verteilungsfunktion von Sichtweite und Himmelbedekkung dominiert und klimatologische Effekte in den Hintergrund treten lässt.

     

A further investigation of wind generated waves

Summary Sixty-four wave records taken by the O. W. S. Weather Explorer are investigated and Fourier analysed. The relation between the wind speed and the equivalent heightH, and the frequency of maximum amplitude on the spectrum,f ₀, do not differ greatly from those previously obtained in 1955. The wave spectrum, however, can now be shown to be reducible to the same form for all wind speeds for large fetch,H _f ² /H ² being a function of (f-f ₀) only. The same function applies for shorter values of fetch, only, then, the relation is betweenH _f ² /yH ² andy (f-f ₀), wherey is the ratio of the values ofH and 1/f ₀ at the short fetch to those for the same wind speed at infinite fetch.Agreement can be found with a previous result by R. W. Burling [1955] under certain conditions. For a fetch of 4 miles, agreement to the same order is obtained with the values of mean square slope found by C. S. Cox and W. H. Munk [1954].It has not been possible to find agreement with the results of Project SWOP (J. Chase, L. J. Cote, W. Marks and others [1957]).

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Eine weitere Untersuchung windbedingter Wellen

Zusammenfassung Vierundsechzig Wellenregistrierungen wurden an Bord des O. W. S. Weather Explorer aufgezeichnet und nach der Fourier-Methode analysiert. An dem Verhältnis zwischen der Windgeschwindigkeit und der äquivalenten HöheH sowie der Frequenz der maximalen Amplitude auf dem Wellenspektrumf ₀ wurde im Vergleich zu dem im Jahre 1955 festgestellten Verhältnis nur sehr wenig geändert. Bei großem Fetch kann jedoch das Wellenspektrum als auf die gleiche Form für alle Windgeschwin-digkeiten zurückführbar dargestellt werden, daH _f ² /H ² nur eine Funktion von (f-f ₀) ist. Die gleiche Funktion gilt auch für geringere Fetchlängen, nur ist dann die Beziehung zwischenH _f ² /yH ² undy(f-f ₀), wobeiy das Verhältnis der WerteH und 1/f ₀ bei kurzem Fetch zu den Werten gleicher Windgeschwindigkeit bei unendlichem Fetch darstellt.Unter bestimmten Bedingungen kann eine Übereinstimmung mit einem früheren Ergebnis von R. W. Burling [1955] erreicht werden. Bei einem Fetch von 4 sm erhält man mit dem Quadrat des mittleren Gefälles nach C. S. Cox und W. H. Munk [1954] eine Übereinstimmung gleicher Größenordnung.Eine Übereinstimmung mit den Ergebnissen des Projektes SWOP (J. Chase, L. J. Cote, W. Marks u. a. [1957]) ließ sich nicht erzielen.

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Une autre étude des vagues engendrées par le vent

Résumé Soixante-quatre enregistrements de vagues obtenus par le navire météorologique «Weather Explorer» seront analysés d'après la méthode de Fourier. Le rapport entre la vitesse de vent, la hauteur équivalenteH et la fréquence de l'amplitude maximale sur le spectre d'onde n'a pas beaucoup changé lorsqu'on le compare au rapport constaté en 1955.H _f ² /H ² n'étant qu'une fonction de (f-f ₀), on peut représenter le spectre d'ondes comme d'être réductible à la même forme, à laquelle toutes les vitesses de vent peuvent être référées en présence d'un grand «fetch». La même fonction s'applique à une longueur inférieure de fetch, mais dans ce cas la relation se fait entreH _f ² /yH ² ety(f-f ₀);y étant le rapport des valeursH et 1/f ₀ en présence d'un court fetch à des valeurs d'égale vitesse de vent en présence d'un fetch infini.Dans certaines conditions, l'accord se laisse atteindre avec des résultats récents de R. W. Burling [1955]. Lorsque le fetch a 4 milles marins de longueur, l'accord se fait dans le même ordre de grandeur à l'aide des valeurs du carré de la pente moyenne d'après C. S. Cox et W. H. Munk [1954].Il n'était pas possible d'obtenir un accord avec les résultats du projet SWOP (J. Chase, L. J. Cote, W. Marks et d'autres [1957]).

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Form-drag instability in a barotropic and a baroclinic atmosphere

We discuss the form-drag instability for a quasi-geostrophic channel flow. We first study the characteristics of this instability in a barotropic flow, considering in detail the influence of the meridional scale and discussing which structure of the perturbation zonal flow must be chosen in order to describe properly this instability.We then consider a continuous quasi-geostrophic channel model in which the topography enters only through the bottom boundary condition, and we discuss how in this case the effects of the form-drag are felt by the mean zonal flow through the ageostrophic mean meridional circulation. Because the meridional structure of the perturbation zonal flow cannot simply be extended from the barotropic to the continuous case, we show how to modify it properly.We then study the baroclinic model in the particular case of constant (in the vertical) basic-state zonal flow and show how this case closely resembles the barotropic, demonstrating the barotropic nature of the form-drag instability.Symbols _t is the partial derivative with respect tot. - _x is the partial derivative with respect tox. - _y is the partial derivative with respect toy. - represents the geostrophic stream function. - u is the eastward component of the geostrophic wind. - v is the northward component of the geostrophic wind. - u _a is the eastward component of the ageostrophic wind. - v _a is the northward component of the ageostrophic wind. - w is the vertical component of the wind. - f is the Coriolis parameter=2 sin f _o+y. - f _o is the Coriolis parameter evaluated at mid-latitude. - N is the Brunt-Vaisala frequency. - [A] is the zonal (x) average ofA at constantp andy. - <A> is the horizontal (x andy) average ofA at constantp     

The temporal series of the New Guinea 29 April 1996 aftershock sequence

The aim of our search is the analysis of aftershock temporal series following a mainshock with magnitude M ≥ 7.0. Investigating aftershock behavior may find the key to explain better the mechanism of seismicity as a whole.In particular, the purpose of this work is to highlight some methodological aspects related to the observation of possible anomalies in the temporal decay. The data concerning the temporal series, checked according to completeness criteria, come from the NEIC-USGS data bank. Here we carefully analyze the New Guinea 29 April 1996 seismic sequence.The observed temporal series of the shocks per day can be considered as a sum of a deterministic contribution (the aftershock decay power law, n(t) = K·(t + c)^−p + K₁) and of a stochastic contribution (the random fluctuations around a mean value represented by the above mentioned power law). If the decay can be modeled as a non-stationary Poissonian process where the intensity function is equal to n(t) = K·(t + c)^−p + K₁, the number of aftershocks in a small time interval Δt is the mean value n(t)·Δt, with a standard deviation .     

Variations of theD-region aeronomical parameters under non-equilibrium conditions

Summary In this paper an attempt is made to define the time variations of theD-region main aeronomical parameters under non-equilibrium conditions by using experimental data by the A3 method, phase-height method and satellite data for the short-wave X-radiation. The SID effect of day-time and time variations of 21 August 1969 electron concentrationN(t) and recombination coefficient (t) are investigated. It is shown that during SID effect (t) increases.

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Résumé Dans le présent travail on a procédé à une expérience pour déterminer les variations temporelles des principaux paramètres aéronomiques en utilisant des données expérimentales par la méthode A3 de mesure de l'absorption ionosphérique, la méthode phase-altitude et des données satellites aux rayons X durs. On a examiné les variations diurnes et les variations temporelles lors de SID effet durant le 21 Août 1969, de la densité électroniqueN(t) et du coefficient de récombinaison (t). On a montré que lors de SID effet (t) s'accroît.

     

A multivariate gamma distribution arising from a Markov model

A Markov chain{X _t }, which has been useful for modelling in hydrology, can be specified by the Laplace transform (LT) of the conditional p.d.f. ofX _t+1 givenX _t =x _t , which is assumed to be of the exponential formH()exp{-G()x _t }. For appropriate choice ofH andG the marginal distribution ofX _t is the (univariate) gamma distribution. In this case, the joint p.d.f. ofX _t +1,...,X _t+n and its LT, are obtained, and this is extended to a seasonal version of the chain. A simple method of generating observations from these multivariate gamma distributions is noted, and the joint LT is applied to the problem of determining moments of weighted sums of such variables.