Basaltic thermals and Subplinian plumes: Constraints from acoustic measurements at Shishaldin volcano, Alaska

The 1999 basaltic eruption of Shishaldin volcano (Alaska, USA) included both Strombolian and Subplinian activity, as well as a “pre-Subplinian” phase interpreted as the local coalescence within a long foam in the conduit. Although few visual observations were made of the eruption, a great deal of information regarding gas velocity, gas flux at the vent and plume height may be inferred by using acoustic recordings of the eruption. By relating acoustic power to gas velocity, a time series of gas velocity is calculated for the Subplinian and pre-Subplinian phases. These time series show trends in gas velocity that are interpreted as plumes or, for those signals lasting only a short time, thermals. The Subplinian phase is shown to be composed of a thermal followed by five plumes with a total expelled gas volume of .The initiation of the Subplinian activity is probably related to the arrival of a large overpressurised bubble close to the top of the magma column. A gradual increase in low-frequency (0.01–0.5 Hz) signal prior to this “trigger bubble” may be due to the rise of the bubble in the conduit. This delay corresponds to a reservoir located at ≈3.9 km below the surface, in good agreement with studies on other volcanoes.The presence of two thermal phases is also identified in the middle of the pre-Subplinian phase with a total gas release of and . Gas velocity at the vent is found to be and for the Subplinian plumes and the pre-Subplinian thermals respectively.The agreement is very good between estimates of the gas flux from modelling the plume height and those obtained from acoustic measurements, leading to a new method by which eruption physical parameters may be quantified. Furthermore, direct measurements of gas velocity can be used for better estimates of the flux released during the eruption.     

Geochemical monitoring of the 2002–2003 eruption at Stromboli volcano (Italy): precursory changes in the carbon and helium isotopic composition of fumarole gases and thermal waters

Significant changes in the helium and carbon isotopic composition of shallow thermal waters vs. gas and a crater fumarolic gas have been recorded at Stromboli prior and during the 2002–2003 eruption. The³He/⁴He ratios corrected for air contamination (Rc/Ra), and δ¹³C of fumarolic gases gradually increased from May to November 2002 before the eruption onset. These variations imply early degassing of a gas-rich magma at depth that likely fed both the intense Strombolian activity and small lava overflows recorded during that period. The lava effusion of late December 2002 was shortly preceded by a marked Rc/Ra decrease both in water and fumarolic gases. Comparison of He/CO₂ and CH₄/CO₂ ratios in dissolved gas and with values rules out the Rc/Ra decrease due to an increasing input of radiogenic⁴He. The Rc/Ra decrease is attributed to the He isotope fractionation during rapid magma ascent and degassing. A new uprising of ³He-rich magma probably occurred in January to February 2003, when Rc/Ra ratios displayed the highest values in dissolved gases ever measured before (4.56 Rc/Ra). The increase in He/CO₂ and CH₄/CO₂ ratios and decrease in δ¹³C of dissolved CO₂ was recorded after the 5 April 2003 explosive paroxysm, likely caused by enhanced gas-water interaction inducing CO₂ dissolution. No anomalous Rc/Ra values were recorded in the same period, when usual Strombolian activity gradually resumed.Editorial responsibility: H Shinohara     

Attenuation of P,S, and coda waves in Koyna region,India

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

Airborne Gradiometry Error Analysis

Gravity gradiometry is one of the older methods of determining the Earth’s local gravitational field, but lies in the shadow of more conventional static and moving-base gravimeter-based systems. While the static torsion balance appears to have been relegated to the museum, support for the airborne and space-borne differential accelerometer (gradiometer) continues so as to overcome limitations in spatial resolution and accuracy inherent in ordinary moving-base gravimetry. One airborne system exists, building on 30 year old technology concepts, and new technologies (e.g., cold-atom interferometry) promise significant improvements. Concomitant advances are required to measure accurately the angular velocity and angular acceleration of the platform, which inseparably combine (in an absolute sense) with the Earth’s gravitational gradients. A numerical analysis of instrument errors, with simulated aircraft dynamics, shows that navigation-grade gyros are just sufficient to account for these effects in gradiometers with 1E/ sensitivity. More accurate instruments, with 0.1 E/ sensitivity, require commensurate sensitivity in the gyros, of the order of 0.01°/h/ = 1.5\times10^{−4 °} \ for typical survey aircraft dynamics. On the other hand, typical orientation errors in the platform, which are problematic for vector gravimetry, are much less of a concern in gradiometry. They couple to the gradient signals and affect only the very low frequencies of the total gradient error.     

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.     

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     

“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.     

Calculating the azimuth of mountain waves, using the effect of tilted fine-scale stable layers on VHF radar echoes

A simple method is described, based on standard VHF wind-profiler data, where imbalances of echo power between four off-vertical radar beams, caused by mountain waves, can be used to calculate the orientation of the wave pattern. It is shown that the mountain wave azimuth (direction of the horizontal component of the wavevector), is given by the vector are radar echo powers, measured in dB, in beams pointed away from vertical by the same angle towards north, south, east and west respectively, and W is the vertical wind velocity. The method is applied to Aberystwyth MST radar data, and the calculated wave vector usually, but not always, points into the low-level wind direction. The mean vertical wind at Aberystwyth, which may also be affected by tilted aspect-sensitive layers, is investigated briefly using the entire radar output 1990–1997. The mean vertical-wind profile is inconsistent with existing theories, but a new mountain-wave interpretation is proposed.     

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.     

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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The Geochemical Prerequisites for the Formation of High-Carbonate Inversion Groundwater with Reduced Dissolved Solids Content in Deep Horizons of Oil-and-Gas Bearing Structures

Synthesis of empirical natural materials and thermodynamic computer modeling of geochemical processes in water–rock systems at different boundary conditions (solid-to-liquid ratio, , T) were used to determine the genetic causes of the inverse geochemical zonality that forms in deep horizons of oil-and-gas bearing structures. The geochemical pattern of inversion water was found to form chiefly because of changes in the Eh–pH-conditions of the original groundwater under the effect of organic components of rocks and because of an increase in temperature to 100°C at low values of solid-to-liquid ratios and at no higher than 10^–2 bar.     

Estimation of coda wave attenuation in East Central Iran

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

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.     

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.     

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.

     

Magnesium Ammonium Phosphate Production from Wastewater through Box–Behnken Design and Its Effect on Nutrient Element Uptake in Plants

This study examined ${\rm NH}_{{\rm 4}}^{{\rm + }} $ , ${\rm PO}_{{\rm 4}}^{{\rm 3}- } $ recovery and the concentration of residual ions from anaerobic effluent of the potato processing industry through magnesium ammonium phosphate (MAP) precipitation using a Box–Behnken design. The regression model was statistically significant in terms of ${\rm NH}_{{\rm 4}}^{{\rm + }} $ and ${\rm PO}_{{\rm 4}}^{{\rm 3}- } $ removal efficiency and residual ion concentrations. Optimum ${\rm NH}_{{\rm 4}}^{{\rm + }} $ and ${\rm PO}_{{\rm 4}}^{{\rm 3}- } $ removal was obtained at pH 9.50 and at Mg²⁺/${\rm NH}_{{\rm 4}}^{{\rm + }} $ /${\rm PO}_{{\rm 4}}^{{\rm 3}- } $ molar ratio of 1.8:1:1.8. Under these conditions, Mg, Ca, K, Fe, and Cl concentrations required for plant growth significantly decreased with MAP precipitation, which was supported by EDX analysis of dry MAP precipitate. The fertilizer effect of MAP on the growth of corn and tomato plants was compared with chemical fertilizers through pot trials. Nutrient element uptake levels of plants were examined in different fertilizer sources. While Mg, Fe, Cu, Mn, and Zn nutrient element uptake levels were sufficient in MAP pots, Ca uptake exceeded sufficient level. Average levels of N, P, K, Mg, Cu, and Mn of corn plant were higher in MAP than other pots. The average N, P, and Mg levels of tomato plant in MAP pots were higher than other pots. N/K ratio, which is important in tomato plants, was better optimized in MAP pots. Only Ni, Cr, and Pb heavy metals were found in plants.     

A model for the simulation of turbulent and eddy diffusion processes at heights of 0–65 km

A generalized turbulent diffusion model has been developed which evaluates the time rate of growth of a simulated cloud of particles released into a turbulent (i.e. diffusive) atmosphere. The general model, in the form of second-order differential equations, computes the three-dimensional size of the cloud as a function of time. Parameters which influence the cloud growth, and which are accounted for in the model equations, are: (1) length scales and velocity magnitudes of the diffusive field, (2) rate of viscous dissipation , (3) vertical stability as characterized by the relative adiabatic lapse rate (1/T)(g/C _p +T/z), and (4) vertical shear in the mean horizontal winds , and , for a given height and of spatial extent equal to that of the diffusing cloud. Sample results for near ground level and for upper stratospheric heights are given. For the atmospheric boundary layer case, the diffusive field is microscale turbulence. In the upper stratospheric case it is considered to be a field of highly interactive and dispersive gravity waves.     

Generous statistical tests

A common statistical problem is deciding which of two possible sources, A and B, of a contaminant is most likely the actual source. The situation considered here, based on an actual problem of polychlorinated biphenyl contamination discussed below, is one in which the data strongly supports the hypothesis that source A is responsible. The problem approach here is twofold: One, accurately estimating this extreme probability. Two, since the statistics involved will be used in a legal setting, estimating the extreme probability in such a way as to be as generous as is possible toward the defendant’s claim that the other site B could be responsible; thereby leaving little room for argument when this assertion is shown to be highly unlikely. The statistical testing for this problem is modeled by random variables {X _i } and the corresponding sample mean the problem considered is providing a bound ɛ for which for a given number a ₀. Under the hypothesis that the random variables {X _i } satisfy E(X _i ) ≤ μ, for some 0  < μ < 1, statistical tests are given, described as “generous”, because ɛ is maximized. The intent is to be able to reject the hypothesis that a ₀ is a value of the sample mean while eliminating any possible objections to the model distributions chosen for the {X _i } by choosing those distributions which maximize the value of ɛ for the test used.     

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.

     

High-order <Emphasis Type="Italic">h</Emphasis>-adaptive discontinuous Galerkin methods for ocean modelling

In this paper, we present an h-adaptive discontinuous Galerkin formulation of the shallow water equations. For a discontinuous Galerkin scheme using polynomials up to order , the spatial error of discretization of the method can be shown to be of the order of , where is the mesh spacing. It can be shown by rigorous error analysis that the discontinuous Galerkin method discretization error can be related to the amplitude of the inter-element jumps. Therefore, we use the information contained in jumps to build error metrics and size field. Results are presented for ocean modelling problems. A first experiment shows that the theoretical convergence rate is reached with the discontinuous Galerkin high-order h-adaptive method applied to the Stommel wind-driven gyre. A second experiment shows the propagation of an anticyclonic eddy in the Gulf of Mexico. An erratum to this article can be found at