On some problems of seismic crustal phase

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Distribution of empirical recurrence intervals for segment-rupturing earthquakes on active faults of the Chinese mainland

IntroductionInassessingtheprobabilitiesoftime-dependentandlong-termseismichazardsforsegmentsofactivefaults,itisnecessarytohavetheprobabilitydensity,f(O,fordescribingtherecurrenceintervaldistributionforsegment-rupturingearthquakes.Fromf(nandthefollowingequation,theconditionalprobability,pc,whichincreaseswiththetime,Te,elapsedsincethelatestearthquake,isabletobecalculated(Nishenko,Buland,1987,WorkingGrouponCaliforniaEarthquakeProbabilities,1995;Wen,1995,1998)fwhereATisthetimeintervalforthefor…     

Types of focal mechanism solutions and parameter consistency of the sub-blocks in Sichuan and Yunnan Provinces

Based on P- and S-wave amplitudes and some clear initial P-wave motion data, we calculated focal mechanism solutions of 928 M≥2.5 earthquakes （1994-2005） in four sub-blocks of Sichuan and Yunnan Provinces, namely Sichuan-Qinghai, Yajiang, Central Sichuan and Central Yunnan blocks. Combining these calculation results with those of the focal mechanism solutions of moderately strong earthquakes, we analyzed the stress field characteristics and dislocation types of seismogenic faults that are distributed in the four sub-blocks. The orientation of principal compressive stress for each block is： EW in Sichuan-Qinghai, ESE or SE in Yajiang, Central Sichuan and Central Yunnan blocks. Based on a great deal of focal mechanism data, we designed a program and calculated the directions of the principal stress tensors, σ1, σ2 and σ3, for the four blocks. Meanwhile, we estimated the difference （also referred to as consistency parameter θ^- ） between the force axis direction of focal mechanism solution and the direction of the mean stress tensor of each block. Then we further analyzed the variation of θ^- versus time and the dislocation types of seismogenic faults. Through determination of focal mechanism solutions for each block, we present information on the variation in θ^- value and dislocation types of seismogenic faults.     

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

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     

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

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.     

Background aspects of lake restoration: water balance,heavy metal content,phosphorus homeostasis

Perturbations of the lake water balance, inputs of heavy metals to lakes, and intensifying fertilization of lakes through input and accumulation of phosphorus—these three classes of phenomena are among the more important background processes in lake restoration. Lake restoration consists of a series of measures animed at producing a homeostatic response of a lake system to external perturbations. The success of its implementation is affected by the morphometric and edaphic parameters of different types of lakes. The relationship between the volume (V) and mean-depth of fresh-water lakes indicates a trend of . Glacial lakes occuring on or near crystalline shields have relatively shallow depths, whereas volcanic lakes, rift valley and deep valley lakes have relatively greater depths for the same volume. For saline lakes (21 lakes, V>1 km³) that undergo cycles of expansion and shrinkage, the V to relationship is closer to power 1. Water residence times (τ) of small and big fresh-water lakes show a trend of τ approximately linear in or τ∝V^0.3. Volcanic lakes and Maare have longer residence times in comparison to other lakes of similar volumes. For the major inorganic chemical species and heavy metals, the regulatory upper-limit concentrations in drinking water in the USA and EEC are from several times to more than 100 times higher than their concentrations in a global mean river water. Only three elements (Fe, P, and Al) occur in river water at concentrations approaching such upper-limit recommendations. Rates of accumulation of phosphorus in lake water and sediments, computed as the difference between input and ouflow removal rates for 23 fresh-water lakes, are generally lower for lakes of longer water residence time. The rate of accumulation is a measure of homeostatic response of the lake system to input load: it is equivalent to the rate of all the removal processes needed to maintain phosphorus concentration in lake water at a steady state.     

Piezo-remanent magnetization of lunar rocks

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.

     

Estimate of earthquake hazard in the Vrancea (Romania) region

A maximum likelihood method is used to estimate the earthquake hazard parameters maximum magnitudeM _max, annual activity rate , and theb value of the Gutenberg-Richter equation in the Vrancea (Romania) region. The applied procedure permits the use of mixed catalogs with incomplete historical as well as complete instrumental parts, the consideration of variable detection thresholds, and the incorporation of earthquake magnitude uncertainty.Our imput data, comprises 105 historical earthquakes which occurred between 984 and 1934, and a complete data file containing 1067 earthquakes which occurred during the period 1935–30 August, 1986. The complete part was divided into four subcatalogs according to different thresholds of completeness. Only subcrustal events were considered, and dependent events were removed.The obtained value (=0.65) is at the lower range of the previously reported results, but it appears concurrent with conceptual and observational facts. The same concerns inferred value of _max = 7.8 and activity rate _4.0 = 5.34.     

Ueber Herde elastischer Wellen in isotropen,homogenen Medien

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.

     

Travel times and body wave magnitude

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.     

Frequency-time analysis of geomagnetic beating-type pulsationsPc3

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.     

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

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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Some comparisons between mining-induced and laboratory earthquakes

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.     

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

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.

     

Zur Interpretation von seismischen Refraktionsmessungen

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.

     

The dynamics of magma mixing in a rising magma batch

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.     

Lyapunov exponent and dimension of the strange attractor of elastic frictional system

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Recherches complémentaires sur le bases du calculateur météorologique «Temp»

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.

     

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

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.     

A review on the lithospheric structures in the Tibetan Plateau and constraints for dynamics

In the last decade, several international joint projects were conducted in the Tibetan Plateau by Chinese, American and French geophysicists and geologists. In the present review, the results from vertical reflections, wide-angle reflections and broadband digital seismic recordings are reviewed and compared. Constraints for the dynamics of continent-continent collision from the lithospheric structures, seismicity, focal mechanism and anisotropy are discussed.The velocities ofPn,Sn, , were accurately determined by using their travel times from local events. They evidenced that the uppermost mantle underneath the Tibetan Plateau was similar to that of the ordinary continental mantle.The reflection profile from INDEPTH-I furnishes convincing evidence that the Indian crust penetrates into the Tibetan lower crust. The results from teleseismic waveform inversion reveal that the Moho discontinuity dips northwards, and an offset of Moho occurs near Bangong suture.The fact that materials within the Tibetan Plateau escape laterally has been proposed by several authors. Recent data and studies provide further convincing evidence that eastward mass transfer does occur, and their paths and natures are investigated.Some authors suggested that the large strike slip faults (Kun Lun, Xianshuihe) in the eastern plateau may be related to the lateral extrusion. However, most of the strike slips are left-lateral, and extrusion could not occur without right-lateral strike slips. Recent observations of the focal mechanisms and geological structure indicate that the earthquakes in the Yanshiping-Changdu belt are left-lateral strike slip. It is the southeast zone of the left-lateral slip faults in the eastern Tibetan plateau. Geological and seismological evidence show that the Bencuo-Jiali belt is the only large right-lateral fault in the eastern plateau. It was proposed that the present eastward extrusion occurs between the Yangshiping-Changdu left-lateral strike slip and the Bencuo-Jiali right-lateral strike slip. The other left-lateral strike slips north of the Yangshiping-Changdu belt are considered to be the fossils of the ancient flow paths.