Time pattern of large earthquake sequences in Europe in 1976–1979

Summary The time development of three large sequences, Friuli 1976, Thessaloniki 1978 and Monte Negro-Albania 1979, was investigated by analysing the characteristics of the time distribution of magnitudes of the events, M(t), of average magnitudes, (t), and of the number of events, n(t), as well as the strain release curves and the magnitude-frequency relations, N(M). The existence of time gaps and of an anomalous decay of the numbers of shocks before major events, as well as the oscillation of ( const b^–1) may be considered as precursory phenomena. The clustering of events has been tested by the Poisson and negative binomial laws.Communication presented at the XVIIth General Assembly of the European Seismological Commission in Budapest, 21–29 August, 1980 under the title Properties of Seismic Regime and Recent Earthquake Sequences in Europe.     

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.     

“Pandora box” — Matrix in the calculus of observations

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.     

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.

     

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

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.     

Anisotropy of Cs137 gamma-ray absorption in rocks

Summary The anisotropy of the Cs¹³⁷ gamma-ray absorption coefficient has been investigated in layered models and several rock samples. It was found that in contrast to other petrophysical parameters the gamma-ray absorption coefficient is characterized by a relatively small coefficient of anisotropy (3–5%). Therefore, the possible effect of the anisotropy can be neglected in the measurements of for rocks as it is usually below current observational errors.     

Nonlinear Magnetoconvection and the Geostrophic Flow - Subcritical Solutions

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.     

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.

     

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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On some problems of seismic crustal phase

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An analysis of heat-, momentum-transports,and spectra for clear air turbulence in mid-stratosphere

Summary An analysis of the clear air turbulence in the mid-stratosphere indicates that the turbulence is characterized by an anisotropic field of turbulence with an intense lateral component of the turbulence, associated with strong thermally stable stratification. The Richardson number in the region of turbulence is generally smaller than , the Taylor's criterion for a stratified shear flow.The cospectra for the momentum transport by the streamwise, lateral, and vertical components of the velocity show similarity in their distribution, decreasing with increasing wavenumber. The cospectra for the heat transport by the streamwise, lateral, and vertical components of the velocity show similarity in the high and medium wavenumber ranges, but not in the low wavenumber range of the spectra.The power spectra of the temperature and wind speed are very similar, and are approximately proportional to the power of the wavenumber. The power spectra of the streamwise and lateral components of the velocity are approximately proportional to the –2 power of the wavenumber, whereas the spectrum of the vertical component of the velocity is approximately proportional to the –1 power of the wavenumber.sponsored by the National Science Foundation.     

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.     

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.

     

Fermat's Variational Principle for Anisotropic Inhomogeneous Media

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.     

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.     

Rossby-Haurwitz's equation for the conservation of vertical vorticity component in the baroclinic atmosphere

Summary It is shown that the conservation equation of potential vorticity in the barotropic atmosphere holds good, even in the baroclinic atmosphere, if it is permissible to introduce the isentropic and mass-conservation approximations.     

Radiance and color of the sky at twilight: Perturbations caused by stratospheric haze

Layers of stratospheric aerosol with optical thicknesses as small as 10^–4 cause noticeable perturbations in the monochromatic logarithmic brightness gradient,G, and the color ratio,C, of the twilight sky. Modeling of the twilight's radiant properties shows that definite single-valued relationships exist between maxima inC or minima inG and optical thickness, , physical thickness h, and mean altitude, , of stratospheric layers. It is therefore possible to determine , h and and monitor their variations by performing either single wavelength measurements ofG or two-wavelength spectrophotometric measurements ofC. The presence of haze in the lower troposphere and the occurrence of multiple scattering both have relatively minor influences on the recovery of the stratospheric dust properties, provided that 10< <30 km.Formal mathematical inversions of the single-scattering twilight equations are possible in principle, but difficult in practice because of non-linearities. Inversions incorporating an iterative linearization process with constrained smoothing, successfully recovered the features of the haze layer, but tended to oversmooth the vertical profile and underestimate the mean altitude of the haze layer.     

Die anlagerungsgechwindigkeit der elektrisch geladenen und neutralen Emanationsfolgeprodukte an das atmosphärische Aerosol

Zusammenfassung Die Anlagerungsgeschwindigkeiten der elektrisch geladenen und neutralen²¹²Pb (ThB)-Atome an das atmosphärische Aerosol wurden experimentell bestimmt. Bei einer mittleren Aerosolkonzentration von 5·10⁴ Teilchen/cm³ wurden die Anlagerungshalbwertszeiten _a = 29 für positive und _a ⁰ = 46 für neutrale Radon-Folgeprodukte erhalten. Ausserdem konnte gezeigt werden, dass bis zu 40% der Teilchen des atmosphärischen Aerosols dem RadienbereichR10^–6cm angehören, und dass dieser Teilchenanteil die Grösse der Anlagerungshalbwertszeiten nur geringfügig (2–4%) beeinflusst, d.h. der Anteil der angelagerten Radionuklide ist in diesem Teilchenradienbereich vernachlässigbar. Zum Schluss wurde mit Hilfe der gemessenen Anlagerungskonstanten der prozentuale Anteil der unangelagerten²²²Rn- und²²⁰Rn-Folgeprodukte in der Atmosphäre berechnet.

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Summary The velocities of attachment of neutral and charged radon-220 daughters to the natural atmospheric aerosol were measured. The half-lives of attachment _a = 29 for positive and _a ⁰ = 46 for neutral radon decay peoducts were found with an average aerosol concentration of 5·10⁴ particles/cm³. It is also shown that about 40% of the atmospheric particles have radiiR10^–6 cm and that these particles have only a small influence (2–4%) on the values of the half-lives of attachment; therefore, in this range of particle radii the number of the attached radioactive atoms can be neglected. Finally the percentage of the unattached²²²Rn and²²⁰Rn-decay products in the atmosphere was computed.

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Résumé Les vitesses de l'agglomération des descendats neutres et électriquement chargés de²²⁰Rn atomes à l'aérosol atmosphérique sont mésurées. Les périodes de l'agglomération _a = 29 pour les descendants positives et _a ⁰ = 46 pour le neutres, étaient établis à une concentration d'aérosol moyenne de 5·10⁴ particules/cm³. De plus on pouvait montrer, que jusqu'à 40% des particules de l'aérosol atmosphérique ont un rayonR10^–6cm et que cette part des particules n'a que une petite influence sur la valeur des périodes d'agglomération (2–4%), c'est-à-dire que le nombre des descendants agglomérés à cet domaine des rayons est négligeable. Finalement le pourcentage des particules non-agglomérés a eté calculé au moyen des paramètres de l'agglomération mésurées.

     

Echo-resonance and hydraulic perturbations in magma cavities: application to the volcanic tremor of Etna (Italy) in relation to its eruptive activity

A study is presented of spectral features of volcanic tremor recorded at Mount Etna (Sicily, Italy) following the methods of analysis suggested by the resonant scattering formalism of Gaunaurd and Überall (1978, 1979a, 1979b) and the model for hydraulic origin of Seidl et al. (1981). The periods investigated include summit and flank eruptions that occurred between 1984 and 1993. Recordings from a permanent station located near the top of the volcano were used, and the temporal patterns associated with (a) the average spacing ( ) between consecutive spectral peaks in the frequency range 1–6 Hz, (b) the spectral shape and (c) the overall spectral amplitude were analyzed. values are thought to depend on the physical properties of magma, such as its density, which, in turn, is controlled by the degree of gas exsolution. Variations in the spectral shape are tentatively attributed to changes in the geometrical scattering from the boundary of resonant conduits and magma batches. Finally, the overall amplitude at the station should essentially reflect the state of turbulence of magma within the superficial ascending path. A limit in the application of the resonant scattering formalism to the study of volcanic tremor is given by the fact that the fundamental modes and integer harmonics are difficult to identify in the frequency spectra, as tremor sources are likely within cavities of very complex geometry, rather than in spherical or cylindrical chambers, as expected by theory. This study gives evidence of some correlations between the analyzed temporal patterns and the major events in the volcanic activity, related to both lava flow and explosions at the summit vents. In particular, relatively high values of have been attained during the SE crater eruption of 1984, the complex eruptive phases of September–October 1989 and the 1991–1993 flank eruption, suggesting the presence of a relatively dense magma for all of these events. Conversely, very low values have been recorded in coincidence with the December 1985 activity and the paroxysmal explosions at the summit craters of early 1990, which are interpreted here as fed by fluid-vesiculated magma. Appreciable modifications in the spectral shape have been observed in relation to changes of the volcanic activity that probably preceded the opening and disactivation of shallow dykes or magma batches. Finally, the overall amplitude seems to be a sensitive indicator of the state of gas turbulence within the shallow conduits, as is suggested by the high values attained during phases of intense volcanic activity.