Asymptotic Rayleigh instantaneous unit hydrograph     

B. M. Troutman  M. R. Karlinger 《Stochastic Environmental Research and Risk Assessment (SERRA)》1988,2(1):73-78

The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude,N, tends asymptotically, asN grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, , where is a mean link wave travel time.  相似文献   

Sull'approssimazione numerica di una variabile casuale normale,con applicaztone agli errori d'osservazione     

Prof. Dr. Beniamino Gulotta 《Pure and Applied Geophysics》1950,18(1):64-77

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   

An algorithm for the optimum distribution of a regional seismic network — II. An analysis of the accuracy of location of local earthquakes depending on the number of seismic stations     

Andrzej Kijko 《Pure and Applied Geophysics》1977,115(4):1011-1021

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   

Empirische Untersuchung zur Frage der Beziehung zwischen durchschnittlicher und kennzeichnender Wellenperiode im Seegang     

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.

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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.

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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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Relations entre le creusement et le comblement des perturbations et leur déplacement     

Gião  Antonio 《Pure and Applied Geophysics》1954,28(1):171-189

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: 1^o) perturbations circulaires dans le voisinage du centre; 2^o) perturbations ayant, dans le voisinage du centre, un axe de symétrie normal ou tangent à la vitesse du centre; 3^o) 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.

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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: 1^o) circular perturbations in the vicinity of a centre; 2^o) perturbations having, in the vicinity of a centre, an axis of symmetry normal or tangent to the velocity of the centre; 3^o) 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.

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

Ueber Herde elastischer Wellen in isotropen,homogenen Medien     

Fritz Gassmann 《Pure and Applied Geophysics》1958,40(1):55-77

Zusammenfassung 1) Es werden Multipollösungen der skalaren Wellengleichung ² f/t ² – c² div gradf=0 betrachtet. Einerseits kann man solche Lösungen direkt durch Kugelfunktionenn-ter Ordnung ausdrücken, anderseits aus der Einpollösungf=1/p F(t–p/c) durch Differentiation nachn Richtungen erhalten. Es wird der Zusammenhang zwischen den Ergebnissen der beiden Verfahren gezeigt. — 2) Für die Energiedichte und den Energiefluss durch Kugelflächen bei kleinen elastischen Verschiebungen werden Ausdrücke in Kugelkoordinaten angegeben. — 3) Für die Wellengleichung grad div –b ² rot rot werden rotationsfreie Multipollösungen angegeben und Ausdrücke für Energiedichte und Energiefluss hergeleitet. — 4) Das gleiche wird für divergenzfreie Multipollösungen durchgeführt. — 5) Es werden Multipole betrachtet, die weder rotationsfrei noch divergenzfrei sind. Als Spezialfälle werden Multipole mit zeitlich begrenzter und solche mit periodischer Erregung gezeigt, ferner Lösungen der Wellengleichung, die sowohl rotationsfrei wie divergenzfrei sind. — 6) Es wird gezeigt, wie man die elastischen Wellen, die im Sinne vonStokes von einem Herdgebiet endlicher Ausdehnung ausgehen, näherungsweise durch elastische Multipole darstellen kann. — 7) Es wird angedeutet, wie man durch Messung von Komponenten von oder u.s.w. in Punkten im Innern des Mediums die Erregung und Energie von elastischen Multipolen bestimmen kann. Ferner wird auf den Fall hingewiesen, wo ein rotationsfreier Einpol sich im Innern eines Halbraumes befindet und die Messungen an seiner Oberfläche ausgeführt werden.

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Summary (On foci of elastic waves in isotropic homogeneous media) — 1) Multiplets as solutions of the scalar wave equation ² f/t ² – c² div gradf=0 are considered. Such solutions can be obtained either directly by aid of spherical harmonics of ordern, or by differentiating the single polef=1/p F(t–p/c) with respect ton directions. The relations between the results of those two procedures are shown. — 2) In the case of small elastic displacements , the density of energy and the flow of energy through spherical surfaces are expressed by spherical coordinates. — 3) Multiplets which satisfy the equation of motion =a ² grad div b ² curl curl and the equation curl = 0 are given, and expressions for the density and flow of energy are found. — 4) The same is done with multiplets satisfying the equation of motion and the equation div = 0. — 5) General multiplets which satisfy the equation of motion are treated. As special cases, multiplets with excitation of finite length and multiplets with periodic excitation are considered, furthermore solutions of the equation of motion and of the equations curl = 0 and div = 0 are given. — 6) It is shown how elastic waves whose origin is a region of finite extension in the sense given byStokes, can be approximated by elastic multiplets. — 7) Some indications are given on the problem of how to find the functions of excitation and the energy of an elastic multiplet by measuring components of or etc., at points in the interior of the medium. The same problem is considered in the case of the single elastic pole. = grad 1/p F (t–p/a), if the measurements are made at the surface of an elastic half space.

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“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   

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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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   

Propagation of surface waves on the surface of a non-homogeneous aeolotropic cylindrical shell     

B. G. Verma  Vinod Kumar Srivastava 《Pure and Applied Geophysics》1973,110(1):1939-1945

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   

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   

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   

Strong Potential Magnetic Field Influence on Slightly Differentially Rotating Spherical Shell   总被引：1，自引：0，他引：1  

Starchenko  S. V. 《Studia Geophysica et Geodaetica》1998,42(3):314-319

An electrically conducting viscous fluid-filled spherical shell is permeated by an axisymmetric strong potential magnetic field with large Elssaser number ² 1. We describe analytically the steady flow driven by a slightly faster rotation of the conducting inner boundary of the shell. The main flow is controlled by Ekman-Hartmann boundary layers with a small thickness /, where ² is the Ekman number. Asymptotics based on small ^–1 1 reveal the nature of a free shear layer O((/)^1/2) and a super-rotation that allows a part of the fluid to rotate faster than the inner sphere. The free shear is following an imposed field line that is tangent to the inner or outer sphere. Meridional flux is concentrated in the shear and boundary layers. Fluid tends to rotate with the inner sphere and to expel azimuthal magnetic field from an -region restricted by the free shear in the spherical shell. For an imposed axial uniform magnetic field, this -region is outside the cylinder tangent to the inner sphere and rotates with the outer sphere. Weak differential rotation O(/) is inside the cylinder, while almost all difference in rotation rates between spheres is accommodated in the thin O((/)^1/2) free shear. For an imposed dipole magnet, the region has a shape of a lobe touching the outer equator. Inside a super-rotation exists; this is the common case for such when the source of the imposed field is inside.  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   

Integral Equations for Kinematic Dynamo Models     

Dobler  W.  Rädler  K.-H. 《Studia Geophysica et Geodaetica》1998,42(3):302-308

A new technique for the treatment of the kinematic dynamo problem is presented. The method is applicable when the dynamo is surrounded by a medium of finite conductivity and is based on a reformulation of the induction equation and boundary conditions at infinity into an integral equation. We show that the integral operator involved here is compact in the case of homogeneous conductivity, which is important for both mathematical and numerical treatment. A lower bound for the norm of then yields a necessary condition for the generation of magnetic fields by kinematic dynamos. Numerical results are presented for some simple ²-dynamo models. The far-field asymptotics for stationary and time-dependent field modes are discussed.  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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Some comparisons between mining-induced and laboratory earthquakes   总被引：3，自引：0，他引：3  

A. McGarr 《Pure and Applied Geophysics》1994,142(3-4):467-489

Although laboratory stick-slip friction experiments have long been regarded as analogs to natural crustal earthquakes, the potential use of laboratory results for understanding the earthquake source mechanism has not been fully exploited because of essential difficulties in relating seismographic data to measurements made in the controlled laboratory environment. Mining-induced earthquakes, however, provide a means of calibrating the seismic data in terms of laboratory results because, in contrast to natural earthquakes, the causative forces as well as the hypocentral conditions are known. A comparison of stick-slip friction events in a large granite sample with mining-induced earthquakes in South Africa and Canada indicates both similarities and differences between the two phenomena. The physics of unstable fault slip appears to be largely the same for both types of events. For example, both laboratory and mining-induced earthquakes have very low seismic efficiencies where _a is the apparent stress and is the average stress acting on the fault plane to cause slip; nearly all of the energy released by faulting is consumed in overcoming friction. In more detail, the mining-induced earthquakes differ from the laboratory events in the behavior of as a function of seismic momentM ₀. Whereas for the laboratory events 0.06 independent ofM ₀, depends quite strongly onM ₀ for each set of induced earthquakes, with 0.06 serving, apparently, as an upper bound. It seems most likely that this observed scaling difference is due to variations in slip distribution over the fault plane. In the laboratory, a stick-slip event entails homogeneous slip over a fault of fixed area. For each set of induced earthquakes, the fault area appears to be approximately fixed but the slip is inhomogeneous due presumably to barriers (zones of no slip) distributed over the fault plane; at constant , larger events correspond to larger _a as a consequence of fewer barriers to slip. If the inequality _a / 0.06 has general validity, then measurements of _a =µE _a /M ₀, where is the modulus of rigidity andE _a is the seismically-radiated energy, can be used to infer the absolute level of deviatoric stress at the hypocenter.  相似文献   

The dynamics of magma mixing in a rising magma batch     

Takehiro Koyaguchi  Stephen Blake 《Bulletin of Volcanology》1989,52(2):127-137

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