Das Spektrum der internen Bewegungsvorgänge der westlichen Ostsee im Periodenbereich von 0,3 bis 60 Minuten     

Eckard Hollan 《Ocean Dynamics》1966,19(5):193-218

Zusammenfassung Für ein Beobachtungsbeispiel (Stromgeschwindigkeit, Dichte) aus der Kieler Bucht wird eine Deutung ausgeprägter Maxima der zugehörigen Spektren zwischen 0,3 und 60 Minuten durch interne Wellen gegeben. Mit einer beobachteten Periode von zwei Minuten durchgeführte Rechnungen ergeben eine starke Abhängigkeit der Wellenlänge von der mittleren Strömung . Im Falle erhält man bei 23,5 m Wassertiefe eine Wellenlänge von etwa 70 m, im Falle von etwa 85 m. Die berechneten Schwingungen stellen uneigentliche interne Wellen dar (W. Krauß [1966]). Die Interpretation durch eine Grenzflächenwelle führt auf eine Wellenlänge von 86 m, die nur geringfügig von denen der internen Wellen 1. Ordnung in stetig sich ändernder Strömung abweicht.In einer theoretischen Untersuchung werden kleinräumige Anfangsstörungen (z. B. momentane Druckänderungen an der Meeresoberfläche) als mögliche Ursache für die Entstehung kurzperiodischer interner Wellen erkannt. Es zeigt sich, daß kurzzeitig wirksame Anfangsbeschleunigungen in ihrem Einwirkungsbereich stehende, allmählich abklingende interne Wellen erzeugen, während in der Umgebung gleichzeitig fortschreitende Wellen entstehen, deren Amplituden mit wachsender Entfernung vom Erregungsgebiet abnehmen. Die Perioden der Schwingungen haben größere Werte als die zu einer exponentiellen Schichtung gehörige Väisäläperiode und verändern sich in Abhängigkeit von der Größe des Anregungsgebietes wie die zellularer Stabilitätsschwingungen.

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The powerspectrum of internal motions in the western baltic between the periods 0.3 and 60 minutes. Part 1: Interpretation of the wavelike component of the internal unrest in the sea

Summary The powerspectra of the internal unrest in the sea show marked peaks in the range of periods between 0.3 and 60 minutes. An interpretation of these phenomena is given in terms of internal waves for a specific example obtained from short periodic current and density variations in the Kieler Bucht. The numerical calculations for an observed period of two minutes show an important influence of the vertical distribution of the current on the wavelength. In the case of the wavelength amounts to about 70 m, where as in the case of the length is about 85 m, assuming a depth of the sea of 23.5 m. The computed oscillations represent improper internal waves (W. Krauß [1966]). Interpretation by internal boundary waves yields a wavelength of 86 m, which is slightly different only from those of the first mode of internal waves in the case of continuously varying .By a theoretical investigation it is shown that short periodic internal waves may be caused by local initial perturbations (for instance by sudden variations of pressure at the surface). The solution of the problem describes slowly decreasing standing internal waves, which are generated within the area upon which short-dated initial accelerations have acted. At the same time a train of progressive waves is developed in the environment travelling away from the centre of the excitation. The amplitudes of these waves diminish with increasing distance from the origin. The periods of the computed oscillations yield higher values than the Väisäläperiod belonging to an exponential stratification. The variability in these periods is caused by variations in depth, by variations in stability, and by changes in the horizontal dimensions of the area of initial perturbation. This dependence is similar to that of cellular oscillations of stability.

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Spectre des oscillations internes de la mer Baltique Ouest pour des périodes comprises entre 0,3 et 60 minutes. 1ère Partie: Interprétation des éléments ondulatoires de mouvement

Résumé Pour un cas d'observation (vitesse de courant, densité) en baie de Kiel, des maximums bien marqués des spectres correspondants entre 0,3 et 60 minutes s'expliquent par des ondes internes. Des calculs effectués avec une période de deux minutes montrent que la longueur d'onde dépend beaucoup du courant moyen, . Pour , par 23,5 m de profondeur, on obtient une longueur d'onde environ 70 m; pour , une longueur d'environ 85 m. Les oscillations calculées représentent des ondes internes qui ne sont pas des ondes propres. L'interprétation par une onde de surface limite conduit à une longueur d'onde de 86 m très peu différente de celles des ondes internes du premier ordre dans un courant constamment variable.Une étude théorique montre que des perturbations initiales peu étendues (par exemple variations momentanées de la pression à la surface de la mer) peuvent être à l'origine d'ondes internes à courte période. Il apparaît que des accélérations initiales, agissant brièvement, font naître dans leur zone d'action des ondes internes stationnaires qui s'amortissent peu à peu, tandis qu'en même temps aux alentours se produisent des ondes progressives dont l'amplitude décroît à mesure qu'elles s'éloignent de la région où elles ont pris naissance. Les périodes des oscillations ont des valeurs plus grandes que celle de la période de Väisälä rapportée à une stratification exponentielle, et elles varient suivant la grandeur de la zone où elles ont pris naissance comme les oscillations de stabilité cellulaire.

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Molecular refraction in the Earth's mantle     

Sŀawomir Maj 《Pure and Applied Geophysics》1982,120(3):538-547

The Drude law (molecular refraction) for the temperature radiation in a monoatomic model of the Earth's mantle is derived. The considerations are based on the Lorentz electron theory of solids. The characteristic frequency (or eigenfrequency) of independent electron oscillators (in energy units, ) is identified with the band gapE _G of a solid. The only assumption is that solid material related to the Earth's mantle has the mean atomic weight A21 g/mole, and its energy gap (E _G) is about 9 eV. In this case the value of molecular refraction (in cm³/g) is (n ²–1)/=0.5160.52, where andn are the density and the refractive index at wavelength _D=0.5893 m (sodium light), respectively. The average molecular refraction of important silicate and oxide minerals with A21, obtained byAnderson andSchreiber (1965) from laboratory data, is , where denotes the mean arithmetic value calculated from three principal refractive indices of crystal. For the rock-forming minerals with 19A<24 g/mole the new relation was found byAnderson (1975).  相似文献   

Piezo-remanent magnetization of lunar rocks     

Takesi Nagata 《Pure and Applied Geophysics》1973,110(1):2022-2030

Summary Characteristics of the piezo-remanent magnetization (PRM) of lunar rocks are particularly interesting in comparison with the PRM of terrestrial rocks, because ferromagnetic constituents in lunar materials are metallic iron grains whose average magnetostriction coefficient is negative. Experimentally observed characteristics of the PRM of lunar rocks are substantially the same as those of the PRM of terrestrial rocks and magnetites, in which is positive. These experimental results indicate that the acquisition mechanism of PRM is due to a non-linear superposition of the magnetoelastic pressure upon the magnetostatic pressure on both sides of the 90° domain walls in ferromagnetic particles, as suggested by Nagata and Carleton.

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Zusammenfassung Die Eigenschaften der piezo-remanenten Magnetisierung (PRM) der Mondgesteine sind besonders interessant im Vergleich mit der PRM der Erdgesteine, weil die ferromagnetischen Bestandteile der Mondmaterien die metallischen Eisenkörnchen sind, derer durchschnittliche Magnetostriktion-Koeffizient negativ ist. Die experimentelle gemessenen Eigenschaften von PRM der Mondgesteine sind wesentlich dieselbe der Erdgesteine und Magnetite, derer positive ist. Solche experimentaren Ergebnisse zeigen an, dass die Erwerbung von PRM durch eine nonlineare Übereinanderwirkung des magnetoelastischen Druckes und des magnetostatischen Druckes gegen die beiden Seiten der 90° Gebietwände der ferromagnetischen Teilchen ist, wie Nagata und Carleton vorgeschlagen haben.

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Frequency-time analysis of geomagnetic beating-type pulsationsPc3     

Karel Prikner  Jaroslav Střeštík  Karel Dobeš  Reviewer M. Hvoždara 《Studia Geophysica et Geodaetica》1974,18(3):266-273

Summary The mechanism of beating of Pc3 type pulsations is studied. Using the method of numerical computation of a sonagram (the method of frequency-time analysis) a set of samples of pulsations from the Budkov Observatory is treated (1968–1969) mostly at K-indices equal to 2–3. By comparing f–t diagrams with the spectra of the samples an attempt has been made at interpreting the beating as a superposition of the frequency components, contained in the pulsation signal. In most observed cases it is possible to determine two close frequencies, the difference of which is on the average =5.4 mHz. The average carrier frequency of the samples was =37.6 mHz, and the average frequency of the beating =2.7 mHz. The interval of observed values of f_B amounted to 1–5 mHz. A tendency was observed for f_B to increase with increasing degree of disturbance of the geomagnetic field.  相似文献   

Zur Interpretation von seismischen Refraktionsmessungen     

Priv.-Doz. Max Weber 《Pure and Applied Geophysics》1955,30(1):27-32

Zusammenfassung Unter der Voraussetzung, dass die Frontgeschwindigkeitc eine stetige und monoton wachsende Funktion von der Tiefez ist, wird dargelegt, wie man aus einer gemessenen Laufzeitkurve () die zuc inverse Funktionz=z (c) auf einfache Weise berechnen kann. Weiter wird die Eindringtiefez _m in Funktion von ermittelt und abschliessend ein Beispiel gegeben.

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Summary Based on a recorded travel-time curve (), a simple direct method is developed for calculating the functionz=z (c), under the asumption that the wave velocityc is a regularly monotone increasing function of the depthz. Finally a rumerical example is given.

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On a certain doubt L. Euler had with respect to determining the rotation of the earth and of celestial bodies     

Mariya I. Yurkina 《Studia Geophysica et Geodaetica》1995,39(1):11-18

Summary The application of Euler's postulate , which determines rotation (here denotes the derivative of the angular momentum with respect to time, L the resultant torque of exterior forces relative to the centre of inertia), to a celestial body, which is not spherically symmetric, had aroused doubts in Euler himself because of the displacement of the resultant attractive force of other celestial bodies from the said centre. As Minding had noted, it is more logical to compute the resultant torque relative to a point at which the torque has a minimum. This point should be named the attrahentis centrum after Euler. Newton was aware of this displacement of the resultant force and had mentioned it in the Principia. A review of Euler's works connected with this subject is given.  相似文献   

Seismic crustal study of the Oslo Rift     

Johannes Tryti  Markvard A. Sellevoll 《Pure and Applied Geophysics》1977,115(4):1061-1085

A seismic refraction investigation across the southern part of the Oslo Rift has been made, based on quarry blasts at three localities. The study shows a three-layered crust with the followingP-wave velocities: . the upper mantleP-wave celocity, is 8.07 km/s. The velocity-depth relationship for the uppermost crust, obtained by solving the Wiechert-Herglotz integral equation numerically, shows a continuously decreasing velocity gradient in the region of the Oslo Rift which approaches zero at a depth of 9 km, the corresponding increase in theP-wave velocity being from 5.55 km/s to 6.34 km/s. The interface separating the subsurface layer ( =6.60 km/s) from the uppermost layer , interpreted as the Conrad discontinuity, is essentially horizontal in the investigated part of the Oslo Rift at a depth of approximately 15 km. A deep crustal layer with aP-wave velocity of 7.10 km/s appears to be related to the rift, though the top of this layer extends somewhat eastwards beneath the Precambrian rocks from the southern part of the rift at a depth of approximately 20 km. The Moho discontinuity is elevated beneath the Oslo Region compared with the surrounding area. A broad regional gravity high of about 45 mgal is observed along the entire rift zone. It is suggested that this anomaly is caused by the elevation of the sub-Conrad and Moho discontinuities during the rifting processes.  相似文献   

Nonlinear Magnetoconvection and the Geostrophic Flow - Subcritical Solutions     

Walker  M. R. 《Studia Geophysica et Geodaetica》1998,42(3):272-279

The magnetoconvection problem under the magnetostrophic approximation is investigated as the nonlinear regime is entered. The model consists of a fluid filled sphere, internally heated, and rapidly rotating in the presence of a prescribed, axisymmetric, toroidal magnetic field. For simplicity only a dipole parity and a single azimuthal wavenumber (m = 2) is considered here. The leading order nonlinearity at small amplitude is the geostrophic flow U _g which is introduced to the previously linear model (Walker and Barenghi, 1997a, b). Walker and Barenghi (1997c) considered parameter space above critical and found that U _g acts as an equilibration mechanism for moderately supercritical solutions. However, for solutions well above critical a Taylor state is approached and the system can no longer equilibrate. More importantly though, in the context of this paper, is that subcritical solutions were found. Here subcritical solutions are considered in more detail. It was found that, at is strongly dependent on . ( is the critical value of the modified Rayleigh number is a measure of the maximum amplitude of the generated geostrophic flow while , the Elsasser number, defines the strength of the prescribed toroidal field.) R_m at proves to be the key measure in determining how far into the subcritical regime the system can advance.  相似文献   

Recherches complémentaires sur le bases du calculateur météorologique «Temp»     

Ing. Antonio Gião  Mr. F. -H. Raymond 《Pure and Applied Geophysics》1954,27(1):121-155

Résumé La formule de base, traduisant une propriété analytique d'une classe très générale de fonctions, est un corollaire du théorème fondamental démontré dans un mémoire précédent, d'après lequel, étant donnés une fonction continue,p(, ,t) des points (, ) d'une surface régulière fermée et du temps et le champ d'un vecteur vitesse de transfert ou d'advection tangent à et ayant des lignes de flux fermées et régulières, il existe un opérateur spatial, linéaire, non singulierA tel que la fonctionA(p+Const.) soit purement advective par rapport a (sans creusement ni comblement). Ce théorème peut être exprimé par l'équation , où est un opérateur spatial, linéaire et non singulier, fonction deA.La détermination de peut être faite, soit en comparant deux formes différentes de la solution générale de l'équation en , soit en utilisant un raisonnement a priori très simple. On arrive ainsi au résultat pour un certain scalaireu(, ).Dans le cas oùp(, ,t) est la perturbation de la pression sur la surface du géoïde l'équation résulte aussi, comme nous l'avons montré dans le mémoire précédent, de notre théorie hydrodynamique des perturbations. On montre ici que la même équation peut encore être déduite de l'équation de continuité associée à la condition d'équilibre quasi statique selon la verticale.Comme applications de la formule de base (solution générale de l'équation enM), on étudie les problèmes suivants: 1^o creusement et comblement en général; 2^o creusement et comblement des centres et des cols; 3^o mouvement des centres et des cols; 4^o instabilité d'un champ moyen; 5^o propriétés spatiales des champsp(, ,t) et des vecteurs d'advection analytiques.Après une discussion des erreurs de la prévision d'un champp(, ,t) par la formule de base, du fait des erreurs des observations et du fonctionnement du calculateur, on examine quelques particularités du transfert ou advection d'un champf ₀(, ) par le vecteur . Enfin, le dernier chapitre du mémoire donne des éclaircissements complémentaires sur la structure du calculateur électronique «Temp» (qui effectue automatiquement les opérations mathématiques de la formule de base) et expose l'état actuel de sa construction.

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Summary The basic formula, expressing an analytical property of a very general class of functions, is a corollary of the fundamental theorem, proved in a previous paper, according to which, given a functionp(, ,t) of the points (, ) of a closed regular surface and of the time, and a transfer or advection velocity vector tangent to and having regular closed streamlines, there is a spatial, linear, non singular operatorA such thatA(p+const.) is a purely advective function in respect to (no deepening). This theorem can be expressed by the equation where is a spatial, linear, non singular operator depending onA.The determination of can be attained, either by the comparison of two different forms of the general solution of the -equation, or by a simple a priori reasonning. The conclusion is thus reached that for a certain scalaru(, ).Whenp(, ,t) is the pressure perturbation at sea level, it was shown, in the preceding paper, that the equation can also be derived from our hydrodynamical perturbation theory. We now show that for this particular case, the same equation is also a consequence of the equation of continuity together with the condition of quasi statical vertical equilibrium.The following problems are then analysed by means of the basic formula: 1^o deepening and filling in general; 2^o deepening and filling of the centres and cols; 3^o motion of the centres and cols; 4^o instability of a mean field; 5^o spatial properties of the analytical fields and advection vectors .The errors in the forecast of a field,p(, ,t) by means of the basic formula, due to the observational and computational errors, are discussed, and some peculiarities of the transfer or advection of a fieldf ₀(, ) by are examined. Finally, complementary points are disclosed on the structure of the electronic computer «Temp» which performs automatically the mathematical operations of the basic formula, and a brief report is given of the present state of its construction.

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Travel times and body wave magnitude     

Seweryn J. Duda 《Pure and Applied Geophysics》1971,87(1):13-37

Summary Presently used -charts for magnitude determinations have been obtained principally on the base of direct observations of ground motion amplitudes, and periods, of several components of seismic waves (such as PZ, PH, SH), as function of epicentral distance. However, observations alone can serve for the definition of a magnitude scale for events with only one particular focal depth. In order to make the magnitude concept applicable to all focal depths, it must be decided when two events with different focal depths should be assigned the same magnitude. Any respective decision, which will assure consistent magnitudes, must be based on the velocity vs. depth, and eventually the anelasticity vs. depth profiles of the Earth.It is concluded that in magnitude studies the anelasticity is of minor importance. Thus, after the amplitudes are compensated for the radiation pattern at the focus, the observed variation of amplitudes along the surface of the Earth, as function of epicentral distance, is practically due only to the velocity heterogeneity inside the Earth. Assuming a dependence of the velocity on the distance from the center of the Earth (no lateral velocity heterogeneities are permitted), a set of new -charts is obtained, independent of direct amplitude observations, for PZ-, PH-, and SH-waves. A refinement in the magnitude definition warrants the magnitude figures obtained with the new -charts to be uniform with regard to focal depths. Examples show the new -charts to decrease the scatter of magnitude determinations between stations.Since the efficiency in generating longitudinal and transverse waves is most probably not the same for all events, separate P-wave and S-wave magnitudes are advocated.  相似文献   

Fermat's Variational Principle for Anisotropic Inhomogeneous Media     

Červený  V. 《Studia Geophysica et Geodaetica》2002,46(3):567-588

Fermat's variational principle states that the signal propagates from point S to R along a curve which renders Fermat's functional (l) stationary. Fermat's functional (l) depends on curves l which connect points S and R, and represents the travel times from S to R along l. In seismology, it is mostly expressed by the integral (l) = (x ^k,x ^k ')du, taken along curve l, where (x ^k,x ^k ') is the relevant Lagrangian, x ^k are coordinates, u is a parameter used to specify the position of points along l, and x ^k ' = dx ^k÷du. If Lagrangian (x ^k,x ^k ') is a homogeneous function of the first degree in x ^k ', Fermat's principle is valid for arbitrary monotonic parameter u. We than speak of the first-degree Lagrangian ⁽¹⁾(x ^k,x ^k '). It is shown that the conventional Legendre transform cannot be applied to the first-degree Lagrangian ⁽¹⁾(x ^k,x ^k ') to derive the relevant Hamiltonian ⁽¹⁾(x ^k,p _k), and Hamiltonian ray equations. The reason is that the Hessian determinant of the transform vanishes identically for first-degree Lagrangians ⁽¹⁾(x ^k,x ^k '). The Lagrangians must be modified so that the Hessian determinant is different from zero. A modification to overcome this difficulty is proposed in this article, and is based on second-degree Lagrangians ⁽²⁾. Parameter u along the curves is taken to correspond to travel time , and the second-degree Lagrangian ⁽²⁾(x ^k, ^k ) is then introduced by the relation ⁽²⁾(x ^k, ^k ) = [⁽¹⁾(x ^k, ^k )]², with ^k = dx ^k÷d. The second-degree Lagrangian ⁽²⁾(x ^k, ^k ) yields the same Euler/Lagrange equations for rays as the first-degree Lagrangian ⁽¹⁾(x ^k, ^k ). The relevant Hessian determinant, however, does not vanish identically. Consequently, the Legendre transform can then be used to compute Hamiltonian ⁽²⁾(x ^k,p _k) from Lagrangian ⁽²⁾(x ^k, ^k ), and vice versa, and the Hamiltonian canonical equations can be derived from the Euler-Lagrange equations. Both ⁽²⁾(x ^k, ^k ) and ⁽²⁾(x ^k,p _k) can be expressed in terms of the wave propagation metric tensor g _ij(x ^k, ^k ), which depends not only on position x ^k, but also on the direction of vector ^k . It is defined in a Finsler space, in which the distance is measured by the travel time. It is shown that the standard form of the Hamiltonian, derived from the elastodynamic equation and representing the eikonal equation, which has been broadly used in the seismic ray method, corresponds to the second-degree Lagrangian ⁽²⁾(x ^k, ^k ), not to the first-degree Lagrangian ⁽¹⁾(x ^k, ^k ). It is also shown that relations ⁽²⁾(x ^k, ^k ) = ; and ⁽²⁾(x ^k,p _k) = are valid at any point of the ray and that they represent the group velocity surface and the slowness surface, respectively. All procedures and derived equations are valid for general anisotropic inhomogeneous media, and for general curvilinear coordinates x ⁱ. To make certain procedures and equations more transparent and objective, the simpler cases of isotropic and ellipsoidally anisotropic media are briefly discussed as special cases.  相似文献   

“Pandora box” — Matrix in the calculus of observations     

Lubomír Kubáček  Lea Bartalošová  Ján Pecár  Reviewer F. Charamza 《Studia Geophysica et Geodaetica》1977,21(3-4):227-235

Summary If the condition R(A)=k(n), whereA is the design matrix of the type n × k and k the number of parameters to be determined, is not satisfied, or if the covariance matrixH is singular, it is possible to determine the adjusted value of the unbiased estimable function of the parameters f(), its dispersion D( (x)) and ² as the unbiased estimate of the value of ² by means of an arbitrary g-inversion of the matrix . The matrix , because of its remarkable properties, is called the Pandora Box matrix. The paper gives the proofs of these properties and the manner in which they can be employed in the calculus of observations.  相似文献   

A new dissipation model based on memory mechanism   总被引：5，自引：0，他引：5  

M. Caputo  F. Mainardi 《Pure and Applied Geophysics》1971,91(1):134-147

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