Iterative geophysical tomography

Summary The algorithm of iterative geophysical tomography is presented. The medium is approximated smoothly by means of B-splines. The tww-point problem of ray computation is solved with the aid of paraxial approximation. The parameters of the medium are obtained from the iterative algorithm of minimizing the quadratic form. Two numerical 2-D examples are given.

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u¶rt; au umamuuu mauu. ¶rt;a annuuaa n nu nu -na. ma na aa a nu nu naaua annuauu. aam ¶rt; n a umamu aua uuauauu a¶rt;amu . am nu¶rt; ¶rt;a 2-D u nua.

     

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).     

Truncation Error due to Geopotential Model EGM96

The truncation error for the harmonic EGM96 series has been investigated on the basis of 24 242 testing points covering about 70% of the Earth's surface. No degree n of harmonics retained was found at which the series becomes divergent. The EGM96 rms diminishes with increasing n. The truncation error due to EGM96 at the physical Earth's surface has no limiting consequences.     

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.     

Source characteristics of the 1992 Nicaragua tsunami earthquake inferred from teleseismic body waves

We analyzed the broadband body waves of the 1992 Nicaragua earthquake to determine the nature of rupture. The rupture propagation was represented by the distribution of point sources with moment-rate functions at 9 grid points with uniform spacing of 20 km along the fault strike. The moment-rate functions were then parameterized, and the parameters were determined with the least squares method with some constraints. The centroid times of the individual moment-rate functions indicate slow and smooth rupture propagation at a velocity of 1.5 km/s toward NW and 1.0 km/s toward SE. Including a small initial break which precedes the main rupture by about 10 s, we obtained a total source duration of 110 s. The total seismic moment isM _o =3.4×10²⁰ Nm, which is consistent with the value determined from long-period surface waves,M _o =3.7×10²⁰ Nm. The average rise time of dislocation is determined to be 10 s. The major moment release occurred along a fault length of 160 km. With the assumption of a fault widthW=50 km, we obtained the dislocationD=1.3 m. From andD the dislocation velocity isD=D/0.1 m/s, significantly smaller than the typical value for ordinary earthquakes. The stress drop =1.1 MPa is also less than the typical value for subduction zone earthquakes by a factor of 2–3. On the other hand, the apparent stress defined by 2E _s /M _o , where andE _s are respectively the rigidity and the seismic wave energy, is 0.037 MPa, more than an order of magnitude smaller than . The Nicaragua tsunami earthquake is characterized by the following three properties: 1) slow rupture propagation; 2) smooth rupture; 3) slow dislocation motion.     

Deceleration in the Earth's rotation due to the Sun

Summary The estimate of the tidal long-term decrease in the angular velocity of the Earth's rotation due to the Sun is given as –(0.8±0.3)×10 ^–22 rad s ^–2. It was computed on the basis of the observed total long-term decrease in , of the observed tidal deceleration of the Moon and the observed decrease in the second-degree zonal Stokes geopotential harmonic term. Adopting the estimate given, the product of the Love number and the tidal phase lag angle due to the Sun (in degrees) comes out as 0.53±0.20.

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am a z nuuu u z mu au u, az : –(0,8±0,3) 10 ^–22 a¶rt; ^–2 . ¶rt; ua n a¶rt;a u , n a¶rt;a nuu u ¶rt;z ¶rt;uu u n a¶rt;a u mz az znmuaz naama ma. u num n au, m nu¶rt;u ua a a z u ( za¶rt;a) a z nuua a (0,53±0,20).

     

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.     

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     

Radioactivity and geochemistry of granulites and some related rocks from the saxonian granulite complex

Summary The distribution of radioactive(Th, U, K), major and selected trace(Rb, Sr, Ba, Y, Zr, V, Cr, Ni) elements of granulites from the Saxonian Granulite Complex was studied. Similarly to the South Bohemian granulites, the Saxonian granulites can be divided according to the contents of their major and trace elements into two main groups, groupA containing mostly acid and subacid granulites (K ₂ O>2.5%, SiO ₂ >68%), and groupB containing mostly intermediate and basic granulites (K ₂ O<2.5%, SiO ₂ <68%). Statistically significant differences between groupsA andB were found for all major oxides and several trace elements(Rb, V, Cr, Ni). The Saxonian granulites follow the same calc-alkaline trend as the South Bohemian, granulitesA being placed mostly in the rhyolite field and granulitesB mostly in the dacite, andesite and basalt fields of this trend. The investigated granulites are characterized by a considerable scatter ofTh andU contents accompanied by very variableTh/U ratios; theTh andU concentrations of granulitesA are substantially lower than is usual for rocks of corresponding acidity.

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¶rt;a an¶rt;u a¶rt;uamu(Th, U, K) u ua ¶rt;u(Rb, Sr, Ba, Y, Zr, V, Cr, Ni) m aum n¶rt;a aaum na. naa, m u¶rt;aum n uu aam n aaum u ¶rt;u am aua, u u uu. aum n u uu ma a¶rt;um ¶rt; ¶rt;nn; nnA nua¶rt;ama a au¶rt; u au¶rt;aum (K ₂ O>2,5%, Si O ₂ >68%), nnB ¶rt;u u aum (K ₂ O<2,5%, SiO ₂ <68%). ¶rt; muunnau mm mamumuu m au ¶rt; a u u ¶rt; m ¶rt;u m(Rb, V, Cr, Ni). auaum n¶rt;¶rt;m um- m¶rt; a u -uaum;aumA a¶rt;ma a uum n, uaumB a a ¶rt;aum, a¶rt;um u aam n m m¶rt;a. ¶rt;aum — u unnA — aamum uu ¶rt;au da¶rt;uamu mTh uU.

     

Lengths and hazards from channel-fed lava flows on Mauna Loa, Hawai‘i, determined from thermal and downslope modeling with FLOWGO

Using the FLOWGO thermo-rheological model we have determined cooling-limited lengths of channel-fed (i.e. a) lava flows from Mauna Loa. We set up the program to run autonomously, starting lava flows from every 4th line and sample in a 30-m spatial-resolution SRTM DEM within regions corresponding to the NE and SW rift zones and the N flank of the volcano. We consider that each model run represents an effective effusion rate, which for an actual flow coincides with it reaching 90% of its total length. We ran the model at effective effusion rates ranging from 1 to 1,000 m³ s^–1, and determined the cooling-limited channel length for each. Keeping in mind that most flows extend 1–2 km beyond the end of their well-developed channels and that our results are non-probabilistic in that they give all potential vent sites an equal likelihood to erupt, lava coverage results include the following: SW rift zone flows threaten almost all of Mauna Loas SW flanks, even at effective effusion rates as low as 50 m³ s^–1 (the average effective effusion rate for SW rift zone eruptions since 1843 is close to 400 m³ s^–1). N flank eruptions, although rare in the recent geologic record, have the potential to threaten much of the coastline S of Keauhou with effective effusion rates of 50–100 m³ s^–1, and the coast near Anaehoomalu if effective effusion rates are 400–500 m³ s^–1 (the 1859 a flow reached this coast with an effective effusion rate of 400 m³ s^–1). If the NE rift zone continues to be active only at elevations >2,500 m, in order for a channel-fed flow to reach Hilo the effective effusion rate needs to be 400 m³ s^–1 (the 1984 flow by comparison, had an effective effusion rate of 200 m³ s^–1). Hilo could be threatened by NE rift zone channel-fed flows with lower effective effusion rates but only if they issue from vents at 2,000 m or lower. Populated areas on Mauna Loas SE flanks (e.g. Phala), could be threatened by SW rift zone eruptions with effective effusion rates of 100 m³ s^–1.Editorial responsibility: J Donnelly-Nolan     

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.

     

Großkreisdifferenzgleichen

Summary Echo soundings of the U.S. Cruiser Milwaukee in the Puerto Rico Trough in 1939 are briefly discussed, and two depths of 30246 feet or 9219 m, found at 19° 36 N, 68° 20.5 W and at 19° 35N, 68° 8.75W, are stated to be the greatest depths which are known so far in the Atlantic Ocean.     

On the problem of standardization of the magnitude-frequency relation

au u uu mu a amu am a¶rt; mum ma¶rt;amuauau nmm m a, ¶rt;a m u ¶rt;u naam — aum¶rt; a, nu¶rt; a¶rt;u uu na¶rt;u am — nu muaua muam ¶rt; m ¶rt;a. ¶rt;aa n ma¶rt;amuauu nm naam ¶rt;u munaua nmmu ¶rt;.     

Accuracy of integral migration transformation in dependence on space-time sampling

Summary The accuracy of wave field extrapolation is studied with respect to the discretization of field data and integral extrapolator. Assuming a far-field approximation of the Rayleigh-Sommerfeld solution for a two-dimensional scalar wave equation, the minimum and the maximum transmitted frequency are expressed as functions of the sampling intervals t, x, and the half-width x₀ and angle _a of the migration aperture. The theoretical limitation of the transmitted frequency band is tested on numerical examples.

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aamuam mm manuu auumu m ¶rt;umuauu n u uma manu nama. ¶rt; u uma u -¶rt;a ¶rt; ¶rt; a au, ¶rt; nuuuu ¶rt;a n mu ¶rt; uua u aua n¶rt;aa amm a uu m a -nmam ¶rt;umuauu t u , nuu ₀ u a _a uau anm. mu n¶rt;u amm ¶rt;uanaa mmua a u nua.

     

Variations of the geomagnetic field at the time of reversals

Summary Paleomagnetic investigations of sediments from the Early Quaternary enabled the variations of the geomagnetic field during reversals to be studied. Regularities in the motion of the virtual geomagnetic N paleopole and the related changes in the intensity of the geomagnetic field were determined. The initial phase of the reversal, which took place in the Eastern Hemisphere, is accompanied by an increase in the intensity of the geomagnetic field. A strong decrease occurred at the time the N paleopole was moving around30°N geographic latitude. After the irreversible reversal had been concluded, the intensity of the geomagnetic field stabilized at values corresponding to the field intensity prior to the reversal. The reversible reversal is accompanied by an repeated increase in the itensity of the geomagnetic field.

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au naaum ¶rt;a n n uu a¶rt; n¶rt; mmu nu¶rt;a nu n¶rt;um auuu aum n u m u1,1–0,7×10 ⁶ m. u a mu uuuaum n u uma ¶rt;au nmu n. u u¶rt;a uu a uuu naanmuaum n.

     

Eine Simulierung orographischer Effekte durch Quellsingularitäten zur Fixierung stromaufwärts gelegener Randwerte

Zusammenfassung Ein zweidimensionales, linearisiertes Strömungsmodell für orographisch induzierte Effekte wird vorgestellt: Unter Voraussetzung von Pseudo-Instationärität lassen sich in einem schwach-geschichteten, reibungsfreien Medium mittlerer Größenordnung dynamisch-thermodynamische Störungen parameterisieren. Beim Überströmen eines Hindernisses, das durch effektiven QuellflußQ simuliert wird, kann man für normierte Stromlinien eine inhomogene Helmholtz-Gleichung ableiten, deren vier Randbedingungen durch das Eingreifen zweier Zusatzterme, welche das instationäre Verhalten beschreiben, modifiziert werden. Man wählt im folgenden den Quellfluß derartig, sodaß vonQ ein aufz=0 aufliegender, endlich ausgedehnter Rücken (mit dem ungefähren Querschnitt eines Halbzylinders) beschrieben wird.Näherungslösungen für den stromaufwärts liegenden Teil eines Rechteckbereiches nach Erreichen eines stationären Strömungszustandes sind mit den Methoden von Laplace-Fourier bestimmbar. Die numerische Größenabschätzung dieser kolumnaren Wellen zeigt, daß die im Windfeld orographisch induzierten Scherungszonen noch in beträchtlicher Entfernung stromaufwärts eines endlichen Hindernisses auftreten. Ihre Größenordnung gleicht jener von Scherungen, welche aus Effekten des thermischen Windes entstehen können. Die horizontale Perturbation der Geschwindigkeit ist bloß um eine Größenordnung kleiner als die Fließgeschwindigkeit des Grundstromes.Die Vorteile des neuen Ansatzes werden diskutiert: Quellsingularitäten sind besser als die üblichen analytischen Darstellungen der Topographie geeignet, die mitunter über weite Distanzen laufenden Störwellen niedrigster Frequenzen mit kolumnarem Charakter zu erfassen.Im Anhang findet man die Verallgemeinerung auf ein analoges dreidimensionales Modell: Ein System zweier partieller Differentialgleichungen führt zu Pseudo-Stromlinien des dreidimensionalen Raumes.

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Source disturbances simulating orographical effects: The determination of upstream boundary values

Summary As outlined in an Appendix a system of partial differential equations is derived for the stream surfaces of a flow of a stratified fluid over an obstacle for the so-called pseudo-instationary case of an inviscid linearized model for mesoscale motions in three dimensions.The solution for the two-dimensional case, which is the basic part of this paper, results in a Helmholtz Equation, the four boundary conditions of which are partially modified by two additional terms characterizing the instationarity of the problem. The orographic effects are parameterized by the effective source singularity. (The latter corresponds roughly to a mountain range with a semi-circular cross-sectional profile).For the upstream part of a rectangular range steady-state solutions in the limit of long time are obtained by the methods of Laplace-Fourier. The numerical calculation shows, that a system of orographically caused shear-layers (columnar waves) exists. The wind shears induced are of the order of shears due to thermal wind effects, though quite apart from these effects. The perturbations of horizontal velocity are only one order of magnitude smaller than the velocity of the fluid-flow itself.The results show that source singularities are good means to represent topographical effects: Especially they may explain more precisely upstream influences due to horizontally propagating waves having near-zero frequencies than the usual analytical formulations of orography can do it.Finally the theoretical results are compared with some data-sets taken from fluid-tank experiments and from observations from instrumented aircraft.

     

Fluid infiltration into fault zones: Chemical,isotopic, and mechanical effects

Fluid infiltration into fault zones and their deeper-level counterparts, brittle-ductile shear zones, is examined in diverse tectonic environments. In the 2.7 Ga Abitibi greenstone belt, major tectonic discontinuities, with lateral extents of hundreds of kilometres initiated as listric normal faults accommodating rift extension and acted as sites for komatiite extrusion and locally intense metasomatism. During reverse motion on the structures, accommodating shortening of the belt, these transcrustal faults were utilised as a conduit for the ascent of trondhjemitic magmas from the base of the crust and of alkaline magmas from the asthenosphere and for the discharge of thousands of cubic kilometres of hydrothermal fluids. Such fluids were characterised by ¹⁸O=+6±2, D=–50±20, ¹³C=–4±4, and temperatures of 270 to 450°C, probably derived from devolatilisation of crustal rocks undergoing prograde metamorphism. Hydrothermal fluids were more radiogenic (⁸⁷Sr/⁸⁶Sr=0.7010 to 0.7040) and possessed higher than did contemporaneous mantle, komatiites or tholeiites, and thus carried a contribution from older sialic basement. A provinciality of⁸⁷Sr/⁸⁶Sr and ¹³C is evident, signifying that fault plumbing sampled lower crust which was heterogeneous at the scale of tens of kilometres. Mineralised faults possess enrichments of large ion lithophile (LIL), LIL elements, including K, Rb, Ba, Cs, B, and CO₂, and rare elements, such as Au, Ag, As, Sb, Se, Te, Bi, and W. Fluids were characterised by X_{CO 2}0.1, neutral to slightly acidic pH, low salinity 3 wt-%, K/Na=0.1, they carried minor CH₄, CO, and N₂, and they underwent transient effervescence of CO₂ during decompression. Clastic sediments occupy graben developed at fault flexures. The⁴⁰Ar/³⁹Ar release spectra indicate that fault rocks experienced episodic disturbance on time scales of hundreds of millions of years.At the Grenville front, translation was accommodated along two mylonite zones and an intervening boundary fault. The high-temperature (580°C) and low-temperature (430 to 490°C) mylonite zones, formed in the presence of deep-level crust-equilibrated fluids of metamorphic origin. Late brittle faults contain quartz veins precipitated from fluids with extemely negative ¹⁸O (–14 per mil) at 200 to 300°C. The water may have been derived from downward penetration into fault zones of precipitation of low¹⁸O on a mountain range induced by continental collision, with uplift accommodated at deep levels by the mylonite zones coupled with rebound on the boundary faults.Archean gneisses overlie Proterozoic sediments along thrust surfaces at Lagoa Real, Brazil; the gneisses are transected by brittle-ductile shear zones locally occupied by uranium deposits. Following deformation at 500 to 540°C, in the presence of metamorphic fluids and under conditions of low water-to-rock ratio, shear zones underwent local intense oxidation and desilication. All minerals undergo a shift of –10 per mil, indicating discharge of meteoric-water-recharged formation brines in the underlying Proterozoic sediments up through the Archean gneisses, during overthrusting; 1000 km³ of solutions passed through these structures. The shear zones and Proterozoic sediments are less radiogenic (⁸⁷Sr/⁸⁶Sr=0.720) than contemporaneous Archean gneisses (0.900), corroborating the transport of fluids and solutes through the structure from a large external reservoir.Major crustal detachment faults of Tertiary age in the Picacho Cordilleran metamorphic core complex of Arizona show an upward transition from undeformed granitic basement through mylonitic to brecciated and hydrothermally altered counterparts. The highest tectonic levels are allochthonous, oxidatively altered Miocene volcanics. This transition is accompanied by an increase of 12 per mil in ¹⁸O, from +7 to +19, and a 400°C decrease in temperature. Lower tectonic levels acted as aquifers for the expulsion of large volumes of higher-temperature reduced metamorphic fluids and/or evolved formation brines. The Miocene allochthon was influenced by a lower-temperature reservoir inducing oxidative potassic alteration; mixing occurred between cool downward-penetrating thermal waters and the hot, deeper aqueous reservoir.In general, flow regimes in these fault and shear zones follow a sequence, from conditions of high temperature and pressure with locally derived fluids at low water-to-rock ratios, during initiation of the structures, to high fluxes of reduced formation or metamorphic fluids along conduits as the structures propagate and intersect hydrothermal reservoirs. Later in the tectonic evolution and at shallower crustal levels there was incursion of oxidising fluids from near-surface reservoirs into the faults. In general, magmatism, tectonics, and fluid motion are intimately related.     

On the possibility of long-range forecasts of geomagnetic activity

Summary The relation between geomagnetic activity and solar activity is studied in long intervals and in individual 11-year cycles, characterized by certain basic parameters, in connection with investigating the prognostic significance of long-term fluctuations of geomagnetic activity [1, 2]. A number of properties as well as sufficiently close relations with a prognostic significance have been found, such as the secular variation of geomagnetic activity, the 22-year cycle of change in the form of the behaviour of geomagnetic activity in 11-year cycles, long-term concurrence of solar and geomagnetic activity and its changes within the 11-year cycle, relations between solar and geomagnetic parameters characterizing the 11-year cycle.

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a auu uu u ¶rt; uaum amum ¶rt;u nma u u m¶rt; 11-mu ua am mu ¶rt; ¶rt;m nuauaum amumu.

     

Analytical continuation of the gravity field for a two-dimensional body using an infinite series

Summary A procedure is derived which enables the analytical continuation of a two-dimensional gravity field to be expressed in the form of an infinite series. For this purpose, an apparatus is used which represents the two-dimensional analogy of Bicadze-type integrals.

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nuaa m¶rt;ua na aum aaumu n¶rt;u ¶rt;aumau n u¶rt; ¶rt;a. nm annaam n¶rt;mau ¶rt; aau uma muna ua¶rt;.

     

The periodicity of aurorae in the years 1001–1900

Summary The sequence of aurorae, observed at latitudes up to 55° between the years 1001 and 1900 was processed by methods of spectral analysis. The same methods were applied to parts of various duration of this interval. The periods predominant in the time series under investigation were determined. In all the selected parts of the interval, these periods are always located within the same frequency band. Their position is related to the periods corresponding to mutual conjunctions of the large planets.

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¶rt; n uu, a¶rt;au a uma ¶rt; 55° nu¶rt; 1001–1900, ama nu nu m¶rt; nma aaua. a n¶rt; ¶rt; am a ¶rt;u m umaa. u n¶rt; na¶rt;au nu¶rt; u¶rt;a ¶rt;a. mu nu¶rt; ¶rt; a am umaa ¶rt;a a¶rt;m ¶rt;ua ¶rt;uaan amm. nu mum nu¶rt;au, mmmuu au u u nam.