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1.
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   

2.
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: 1o creusement et comblement en général; 2o creusement et comblement des centres et des cols; 3o mouvement des centres et des cols; 4o instabilité d'un champ moyen; 5o 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.
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: 1o deepening and filling in general; 2o deepening and filling of the centres and cols; 3o motion of the centres and cols; 4o instability of a mean field; 5o 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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3.
Summary Seven optimal networks consisting of 4 to 10 stations are compared for a given region, where velocity-depth profiles and the distribution of seismic intensity are known. Assuming that the standard error of arrival time is t =0.05 s and the standard errors of the parameters of velocity-depth profiles are equal to 5% of their values, the average standard errors of the origin time and focus coordinates are estimated. The application of optimum methods to the planning of seismic networks in the Lublin Coal Basin is presented, and maps of standard errors of origin time , depth and epicenter ( xy ) for the case of an optimum network of 6 seismic stations are given.  相似文献   

4.
Piest  Jürgen 《Ocean Dynamics》1963,16(1):9-14
Zusammenfassung Als Zusammenhang zwischen der kennzeichnenden Wellenperiode und der durchschnittlichen Periode im Seegang wird die Formel angesetzt. Mit Hilfe empirischer Unterlagen wird nachgewiesen, daßc eine Funktion des von D. E. Cartwright und M. S. Longuet-Higgins [1956] eingeführten Spektralparameters ist. Es wird eine vorläufige quantitative Beziehung zwischenc und abgeleitet.
Empirical investigations of the relation between the mean and the significant wave period in the sea
Summary It is supposed that the formula represents the relation between the significant wave period and the mean period in the sea. With the aid of empirical data it is demonstrated thatc is a function of the spectral parameter introduced by D. E. Cartwright and M. S. Longuet-Higgins [1956]. A preliminary quantitative relation betweenc and is derived.
Etudes empiriques de la relation entre la période moyenne et la période significative des vagues dans la houle
Résumé On suppose que la formule représente la relation entre la période significative des vagues et la période moyenne dans la houle. A l'aide des données empiriques on montre quec est une fonction du paramètre spectral , introduit par D. E. Cartwright et M. S. Longuet-Higgins [1956]. Une relation quantitative préliminaire entrec et est dérivée.
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5.
Summary The object of the present paper is to investigate the propagation of surface waves on a non-homogeneous aeolotropic cylindrical shell surrounded by vacuum. The elastic constantsc ij (i, j=1,2...) and density of the material of the shell are assumed to be of the form and respectively, where ij, 0 are constants andk 1,k 2 are any integers.  相似文献   

6.
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   

7.
Krainov  S. R.  Ryzhenko  B. N.  Pavlov  Yu. S. 《Water Resources》2003,30(2):154-176
Synthesis of empirical natural materials and thermodynamic computer modeling of geochemical processes in water–rock systems at different boundary conditions (solid-to-liquid ratio, , T) were used to determine the genetic causes of the inverse geochemical zonality that forms in deep horizons of oil-and-gas bearing structures. The geochemical pattern of inversion water was found to form chiefly because of changes in the Eh–pH-conditions of the original groundwater under the effect of organic components of rocks and because of an increase in temperature to 100°C at low values of solid-to-liquid ratios and at no higher than 10–2 bar.  相似文献   

8.
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.) Rm at proves to be the key measure in determining how far into the subcritical regime the system can advance.  相似文献   

9.
The conditions under which two magmas can become mixed within a rising magma batch are investigated by scaling analyses and fluid-dynamical experiments. The results of scaling analyses show that the fluid behaviours in a squeezed conduit are determined mainly by the dimensionless number where 1 is the viscosity of the fluid, U is the velocity, g is the acceleration due to gravity, is the density difference between the two fluids, and R is the radius of the tube. The parameter I represents a balance between the viscous effects in the uppermost magma which prevent it from being moved off the conduit walls, and the buoyancy forces which tend to keep the interface horizontal. The experiments are carried out using fluid pairs of various density and viscosity contrasts in a squeezed vinyl tube. They show that overturning of the initial density stratification and mixing occur when I>order 10-1; the two fluids remain stratified when I 10-3. Transitional states are observed when 10-3<I<10-1. These results are nearly independent of Reynolds number and viscosity ratio in the range of and Re 1<300. Applying these results to magmas shows that silicic to intermediate magmas overlying mafic magma will be prone to mixing in a rising magma batch. This mechanism can explain some occurrences of small-volume mixed lava flows.  相似文献   

10.
Riassunto Data una variabile casuale X che segue la legge normale di probabilitl con valor medio a ed error medio y 1'A. considera un'altra variabile casuale che prende il valore intero r quando r–1/2
Summary Given a random variable X following the normal probability law, with expectation a and standard error p, the author considers another random variable , that takes the entire value r when r–1/2  相似文献   

11.
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   

12.
Résumé On commence par définir le creusement et le comblement d'une fonctionp(, t) du tempst et des points (, ) d'une surface régulière fermée en se donnant, sur cette surface, un vecteur vitesse d'advection ou de transfert tangent à . Le creusement (ou le comblement) est la variation dep sur les particules fictives se déplaçant constamment et partout à la vitesse , A chaque vecteur et pour un mêmep(, ,t) correspond naturellement une fonction creusementC (, ,t) admissible a priori; mais une condition analytique très générale (l'intégrale du creusement sur toute la surface fermée du champ est nulle à chaque instant), à laquelle satisfont les fonctions de perturbation sur les surfaces géopotentielles, permet de restreindre beaucoup la généralité des vecteurs d'advection admissibles a priori et conduit à des vecteurs de la forme: , oùT est un scalaire régulier, () une fonction régulière de la latitude , le vecteur unitaire des verticales ascendantes etR/2 une constante. Ces vecteurs sont donc une généralisation naturelle des vitesses géostrophiques attachées à tout scalaire régulier. Dans le cas oùp(, ,t) est la perturbation de la pression sur la surface du géoïde, le vecteur d'advection par rapport auquel on doit définir le creusement est précisément une vitesse géostrophique: on a alors ()=sin etT un certain champ bien défini de température moyenne.On déduit ensuite une formule générale de géométrie et de cinématique différentielles reliant la vitesse de déplacement d'un centre ou d'un col d'un champp(, ,t) à son champ de creusementC (, ,t) et au vecteur d'advection correspondant. Cette formule peut être transformée et prend la forme d'une relation générale entre le creusement (ou le comblement) d'un centre ou d'un col et la vitesse de son déplacement, sans que le vecteur d'advection intervienne explicitement. On analyse alors les conséquences de ces formules dans les cas suivants: 1o) perturbations circulaires dans le voisinage du centre; 2o) perturbations ayant, dans le voisinage du centre, un axe de symétrie normal ou tangent à la vitesse du centre; 3o) évolution normale des cyclones tropicaux.Finalement, on examine les relations qui existent entre le creusement ou le comblement d'un champ, le vecteur d'advection et la configuration des iso-lignes du champ dans le voisinage d'un centre.Ces considérations permettent d'expliquer plusieurs propriétés bien connues du comportement des perturbations dans différentes régions.
Summary The deepening and filling (development) of a functionp(, ,t) of the timet and the points (, ) of a regular closed surface is first of all defined, in respect to a given advection or transfer velocity field tangent to , as the variation ofp on any fictitious particle moving constantly and everywhere with the velocity . For a givenp(, ,t) and to any there corresponds a well defined development fieldC (, ,t). All theseC fields are a priori admissible, but a very general analytical condition of the perturbation fields in synoptic meteorology (the integral of the development fieldC (, ,t) on any geopotential surface vanishes at any moment), leads to an important restriction to advection vectors of the form: , whereT is any regular scalar, () any regular function of latitude, the unit vector of the ascending verticals andR/2 a constant. These vectors are a natural generalisation of the geostrophic velocities attached to any regular scalar. Whenp(, ,t) is the pressure perturbation at sea level, its development must be defined in respect to a geostrophic advection vector belonging to the above defined class of vectors with ()=sin andT a well defined mean temperature field.A general formula of the differential geometry and kinematics ofp(, ,t) is then derived, giving the velocity of any centre and col of ap(, ,t) as a function of the advection vector and the corresponding development fieldC (, ,t). This formula can be transformed and takes the form of a general relation between the deepening (and filling) of a centre (or a col) of ap(, ,t) and its displament velocity, the advection vector appearing no more explicitly. A detailed analysis of the consequences of these formulae is then given for the following cases: 1o) circular perturbations in the vicinity of a centre; 2o) perturbations having, in the vicinity of a centre, an axis of symmetry normal or tangent to the velocity of the centre; 3o) normal evolution of the tropical cyclones.Finally, the relations between the developmentC (, ,t) of a fieldp(, ,t), the advection velocity vector and the configuration of the iso-lines in the vicinity of a centre are analysed.These theoretical results give a rational explanation of several well known properties of the behaviour of the perturbations in different geographical regions.

Communication à la 2ème Assemblée de la «Società Italiana di Geofisica e Meteorologia» (Gênes, 23–25 Avril 1954).  相似文献   

13.
aam mam uu mn¶rt;muaamuu n¶rt; u u nua ua —aam auumu m mnam (200–1000°, 2 10–1 a). aa¶rt;u, m um na¶rt;a uu a n¶rt;u auumu mn¶rt;mu m mnam, u¶rt;m auumu ¶rt;a mn¶rt;mu mnam u n¶rt;m mu mnam uma.  相似文献   

14.
Attenuation of P,S, and coda waves in Koyna region,India   总被引：1，自引：0，他引：1  
The attenuation properties of the crust in the Koyna region of the Indian shield have been investigated using 164 seismograms from 37 local earthquakes that occurred in the region. The extended coda normalization method has been used to estimate the quality factors for P waves and S waves , and the single back-scattering model has been used to determine the quality factor for coda waves (Q c). The earthquakes used in the present study have the focal depth in the range of 1–9 km, and the epicentral distance vary from 11 to 55 km. The values of and Q c show a dependence on frequency in the Koyna region. The average frequency dependent relationships (Q = Q 0 f n) estimated for the region are , and . The ratio is found to be greater than one for the frequency range considered here (1.5–18 Hz). This ratio, along with the frequency dependence of quality factors, indicates that scattering is an important factor contributing to the attenuation of body waves in the region. A comparison of Q c and in the present study shows that for frequencies below 4 Hz and for the frequencies greater than 4 Hz. This may be due to the multiple scattering effect of the medium. The outcome of this study is expected to be useful for the estimation of source parameters and near-source simulation of earthquake ground motion, which in turn are required in the seismic hazard assessment of a region.  相似文献   

15.
Estimation of coda wave attenuation in East Central Iran   总被引：1，自引：0，他引：1  
The attenuation of coda waves, Q c , has been estimated in Zarand, Jiroft, and Bam regions of east central Iran using a single back-scattering model of S-coda envelopes. For this purpose, the recordings of 97 earthquakes by three seismic networks and a local strong ground motion network have been used. In this research, the frequency-dependent Q c values are estimated at central frequencies of 1.5, 3, 6, 8, 12, 16, and 24 Hz using different lapse time windows from 20 to 60 s. The frequency-dependent relationships obtained are for Zarand, for Jiroft, and for Bam region. From the strong ground motion data, we obtain the relation . The Q c frequency-dependent relationship for the entire region of east central Iran from all data (both seismograms and accelerograms) is . The average Q c values estimated and their frequency dependent relationships correlate well with a highly heterogeneous and highly tectonically active region. Results also show that the attenuation is higher in Bam region compared to Zarand and Jiroft regions.  相似文献   

16.
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17.
Summary On the basis of the 1966–73 data, the effect of the difference between pro- and anti-sectors of the IMF is found to be negligible in the winter midlatitude (Central Europe) ionosphere contrary to the dominant effect of this difference in the high-latitude ionosphere found earlier.
a ¶rt;a a 1966–73. u¶rt;m u m amu ¶rt; pro- u anti- mau . na a u ¶rt;um (¶rt; na) u, , a naa a, naum um u.
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18.
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   

19.
Marginal instabilities in a horizontal unstably stratified rapidly rotating fluid layer permeated by an azimuthal magnetic field growing linearly with distance from the vertical rotation axis, are investigated in dependence on electromagnetic boundary conditions and Roberts number . Electrical conductivities of perfectly thermally conducting boundaries are either infinite or finite Earthlike ones. Following Soward's (1979) results the case of gives the instabilities of MAC-waves with much greater frequencies than for the case of q 1. Critical frequencies of MAC waves are most sensitive on Roberts number for q 1 and lose this sensitivity for q2. On the other hand the critical Rayleigh numbers are slightly dependent on q 1. Many qualitative differences in the dependences on q do exist for infinitely and finitely conducting boundaries. The former do not allow fast eastward modes for q 1 and the latter, e.g. allow eastward MC-waves with azimuthal wave number m = 1. The MC-waves are almost independent on Roberts number q.  相似文献   

20.
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 fB amounted to 1–5 mHz. A tendency was observed for fB to increase with increasing degree of disturbance of the geomagnetic field.  相似文献   

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