Lengths and hazards from channel-fed lava flows on Mauna Loa, Hawai‘i, determined from thermal and downslope modeling with FLOWGO

Using the FLOWGO thermo-rheological model we have determined cooling-limited lengths of channel-fed (i.e. a) lava flows from Mauna Loa. We set up the program to run autonomously, starting lava flows from every 4th line and sample in a 30-m spatial-resolution SRTM DEM within regions corresponding to the NE and SW rift zones and the N flank of the volcano. We consider that each model run represents an effective effusion rate, which for an actual flow coincides with it reaching 90% of its total length. We ran the model at effective effusion rates ranging from 1 to 1,000 m³ s^–1, and determined the cooling-limited channel length for each. Keeping in mind that most flows extend 1–2 km beyond the end of their well-developed channels and that our results are non-probabilistic in that they give all potential vent sites an equal likelihood to erupt, lava coverage results include the following: SW rift zone flows threaten almost all of Mauna Loas SW flanks, even at effective effusion rates as low as 50 m³ s^–1 (the average effective effusion rate for SW rift zone eruptions since 1843 is close to 400 m³ s^–1). N flank eruptions, although rare in the recent geologic record, have the potential to threaten much of the coastline S of Keauhou with effective effusion rates of 50–100 m³ s^–1, and the coast near Anaehoomalu if effective effusion rates are 400–500 m³ s^–1 (the 1859 a flow reached this coast with an effective effusion rate of 400 m³ s^–1). If the NE rift zone continues to be active only at elevations >2,500 m, in order for a channel-fed flow to reach Hilo the effective effusion rate needs to be 400 m³ s^–1 (the 1984 flow by comparison, had an effective effusion rate of 200 m³ s^–1). Hilo could be threatened by NE rift zone channel-fed flows with lower effective effusion rates but only if they issue from vents at 2,000 m or lower. Populated areas on Mauna Loas SE flanks (e.g. Phala), could be threatened by SW rift zone eruptions with effective effusion rates of 100 m³ s^–1.Editorial responsibility: J Donnelly-Nolan     

Amplitude Response of a LCR Gravimeter with Feedback at Periods of Microseisms and Earthquake Waves

The amplitude response of a LCR gravimeter with the SRW-E feedback was determined on a vertical vibrating platform. The ink-pen recorder was connected parallel with the digital voltmeter input to obtain an analog response of the gravimeter to the harmonic motion of the base with a peak-to-peak amplitude of 10 m and periods excited in an interval of 4 - 10 s as by the ground motion of meteorological microseisms, and in the interval 10 -100 s as by surface waves of distant strong earthquakes. In the first interval, an unexpected maximum of the amplitude response was observed with the double amplitude of apparent 6,5 Gal (6.5 × 10 _–8 m/s ² ) at a period of 4.8 s, and a baseline shift with the amplitude of–64Gal was observed at the same period. The value of this direct component cannot be separated from the effect of the Earth's gravity field. In the second interval, the amplitude response of the gravimeter displayed one expected maximum at a period of 40 s with the double amplitude of 8.1Gal. At the usual level of microseisms with a peak-to-peak amplitude of up to 2 m the fluctuation of the gravimeter on the direct baseline shifted by –4.9 Gal was estimated at 1 Gal. With typical Rayleigh surface waves with periods of 20 s and double amplitudes of up to 100 m, the fluctuation reached 67 Gal.     

Stratospheric ozone variability near the IMF sector boundary

Summary We search for the effects of the interplanetary magnetic field (IMF) sector boundary crossing (SBC) in upper stratospheric ozone. The SBUV data (Nimbus-7) at the 10, 3 and 1 hPa levels are analysed for latitudes 45° N and 55° N for winters of the period December 1979 to December 1982. An effect of the IMF SBC wos only found at the 10 hPa level. These first results concerning the IMF SBC effect in upper stratospheric ozone are rather preliminary.

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¶rt;m uu nu mau () nam aum n () a mam. SBUV ¶rt;a (u-7) a nm ¶rt;au 10, 3 u 1a aauum ¶rt; um 45° u 55° . . ua nu¶rt;a ¶rt;a 1979 – ¶rt;a 1982. m uu a¶rt; m a 10a. mu n mam n uuu a mam m n¶rt;aumu.

     

Weighting of vertical angles

Summary According to the results of the adjustments of eight trigonometric and three-dimensional networks, the a priori variance m²() of the measured vertical angle is expressed by the formula: m²() = m²(a) + [C 1/2 m(k)]², where m(a) represents accidental observation errors; the constant C is estimated in the interval 0.5–1.5 according to the number of repreated observations and the variation of their changes with time; is the angle between the normals to the ellipsoid at the initial and final point of the line of sight, and m(k) is the mean square error of the coefficient of refraction which can be estimated for a given network from Tab. 1.Dedicated to 90th Birthday of Professor Frantiek Fiala     

Deuteron whistlers in the outer ionosphere

Summary Upgoing and downgoing deuteron whistlers were found on VLF records made by Interkosmos 5, 14 and 19 satellites even at heights below 1000 km. To account for them, a slight admixture ofD ⁺ ions has been introduced into the ionospheric plasma model with the usual content of only three ion speciesH ⁺,He ⁺ andO ⁺. Relations derived for the calculation of characteristic frequencies in a five-component plasma (e,H ⁺,D ⁺,He ⁺,O ⁺) are given as well as the values of characteristic frequencies calculated on this basis. The observed features of upgoing and downgoing deuteron whistlers could be explained by the calculation results, and it is also possible to formulate some conclusions for the purposes of plasma diagnostics.

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mu um, anmau a ma u u, u a a nmua m 5, 14 u 19 a ma ¶rt;a 1000 . u u a ¶rt;a ¶rt; u na ¶rt;au uH ⁺,He ⁺,O ⁺ aa nuD ⁺ u. m mm ua nma ¶rt;a ¶rt; aamumuu amm ¶rt;a ¶rt;u na. uu aamumuu amm nuu um a¶rt;a mu ¶rt;mu um. a m ¶rt; unam aamumuu ¶rt;mu um ¶rt; u¶rt;au naam na.

     

Scattering attenuation and the fractal geometry of fracture systems

Scattering of seismic waves can be shown to have a frequency dependenceQ ^{–1 3–v} if scattering is produced by arrays of inhomogeneities with a 3D power spectrumW _3D(k) k ^–v. In the earth's crust and upper mantle the total attenuation is often dominated by scattering rather than intrinsic absorption, and is found to be frequency dependent according toQ ^–1 , where –1<–0.5. IfD ₁ is the fractal dimension of the surface of the 3D inhomogeneities measured on a 2D section, then this corresponds respectively to 1.5<D ₁1.75, since it can be shown that =2(D ₁–2). Laboratory results show that such a distribution of inhomogeneities, if due to microcracking, can be produced only at low stress intensities and slow crack velocities controlled by stress corrosion reactions. Thus it is likely that the earth's brittle crust is pervaded by tensile microcracks, at least partially filled by a chemically active fluid, and preferentially aligned parallel to the maximum principal compressive stress. The possibility of stress corrosion implies that microcracks may grow under conditions which are very sensitive to pre-existing heterogeneities in material constants, and hence it may be difficult in practice to separate the relative contribution of crack-induced heterogeneity from more permanent geological heterogeneities.By constrast, shear faults formed by dynamic rupture at critical stress intensities produceD ₁=1, consistent with a dynamic rupture criterion for a power law distribution of fault lengths with negative exponentD. The results presented here suggest empirically thatD ₁-1/2(D+1), thereby providing the basis for a possible framework to unify the interpretation of temporal variations in seismicb-value (b-D/2) and the frequency dependence of scattering attenuation ().This is PRIS contribution 046.     

Differences between Mean Sea Levels for the Pacific,Atlantic and Indian Oceans From Topex/Poseidon Altimetry

Geopotential values W of the mean equipotential surfaces representing the mean ocean topography were computed on the basis of four years (1993 - 1996) TOPEX/POSEIDON altimeter data: W = 62 636 854.10m ² s ^–2 for the Pacific (P), W = 62 636 858.20m ² s ^–2 for the Atlantic (A), W = 62 636 856.28m ²s^–2 for the Indian (I) Oceans. The corresponding mean separations between the ocean levels were obtained as follows: A – P = – 42 cm, I– P = – 22 cm, I – A = 20 cm, the rms errors came out at about 0.3 cm. No sea surface topography model was used in the solution.     

Scientific objectives of the Solar Mesosphere Explorer mission

The 1981–82 Solar Mesosphere Explorer (SME) mission is described. The SME experiment will provide a comprehensive study of mesospheric ozone and the processes which form and destroy it. Five instruments will be carried on the spinning spacecraft to measure the ozone density and its altitude distribution from 30 to 80 km, monitor the incoming solar ultraviolet radiation, and measure other atmospheric constituent which affect ozone. The polar-orbiting spacecraft will be placed into a 3pm-3 am Sun-synchronous orbit. The atmospheric measurements will scan the Earth's limb and measure: (1) the mesospheric and stratospheric ozone density distribution by inversion of Rayleigh-scattered ultraviolet limb radiance, and the thermal emission from ozone at 9.6 m; (2) the water vapor density distribution by inversion of thermal emission at 6.3 m; (3) the ozone photolysis rate by inversion of the O₂(¹g) 1.27 m limb radiance; (4) the temperature profile by a combination of narrow-band and wide-band measurements of the 15 m thermal emission by CO₂; and, (5) theNO₂ density distribution by inversion of Rayleighscattered limb radiance at 0.439 m. The solar ultraviolet monitor will measure both the 0.2–0.31 m spectral region and the Lyman-alpha (0.1216 m) contribution to the solar irradiance. This combination of measurements will provide a rigorous test of the photochemical equilibrium theory of the mesospheric oxygen-hydrogen system, will determine what changes occur in the ozone distribution as a result of changes in the incoming solar radiation, and will detect changes that may occur as a result of meteorological disturbances.     

La risoluzione dell'equazione di Laplace nel campo esterno a uno sferoide

Riassunto L'Autore dimostra che, nel sistema di coordinate polari , , , si possono determinare un numeros di funzioni della sola variabile :Q ₁,Q ₃, ....Q _2s–1 tali che la sommatoria delleQ _2i–1/^2i–1 rappresenti il potenzialeV di un geoide di rotazione. La condizione di armonicità determina ciascunaQ (che si riduce a un polinomio nelle potenze di sen ) a meno di una costante arbitraria; si dispone pertanto dis costanti che servono per soddisfare la natura dellaV sulla superficie del geoide. Come esempio l'Autore ha determinato la gravità sul geoide sferico, confermando i risultati delSomigliana, e su uno sferoide generico dove ha ritrovato la relazione diClairaut.

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Summary The Author proofs that, in the system of polar coordinates , , , it is possible to determine a numbers of functions only of the variable :Q ₁,Q ₃ ....Q _2s–1 in such a way as to make the summatory of theQ _2i–1/^2i–1 represent the potential function of a rotational geoid. The condition of harmonicity determines, saving an arbitrary constant, each of theQ which is reduced to a polynom developed by the sin powers; therefore one disposes of a number of constants to make use for satisfing theV on the geoid. To illustrate his theory the Author determines the gravity on the spherical geoid, thus confirmingSomigliana's formulas and on a spheroidal on which he pointed outClairaut's relations.

     

Cs137 gamma-ray absorption in eclogites

Summary The coefficient of the gamma-ray absorption _Cs ¹³⁷ investigated in eclogites of the Bohemian Massif varies with fresh samples from0.2477 cm ^–1 to 0.2804 cm ^–1 . Symplectite is the main factor decreasing the value of down to0.242 cm ^–1 . On the contrary, the coefficient increases with the increasing content of clinopyroxene and especially of garnet. The linear dependence of the coefficient on the density may be expressed by the equation =0.0682+0.028.     

Planar charged-particle trajectories in multipole magnetic fields

This paper provides a complete generalization of the classic result that the radius of curvature () of a charged-particle trajectory confined to the equatorial plane of a magnetic dipole is directly proportional to the cube of the particles equatorial distance () from the dipole (i.e. ³). Comparable results are derived for the radii of curvature of all possible planar chargedparticle trajectories in an individual static magnetic multipole of arbitrary order m and degree n. Such trajectories arise wherever there exists a plane (or planes) such that the multipole magnetic field is locally perpendicular to this plane (or planes), everywhere apart from possibly at a set of magnetic neutral lines. Therefore planar trajectories exist in the equatorial plane of an axisymmetric (m = 0), or zonal, magnetic multipole, provided n is odd: the radius of curvature varies directly as ⁿ⁼². This result reduces to the classic one in the case of a zonal magnetic dipole (n = 1). Planar trajectories exist in 2m meridional planes in the case of the general tesseral (0 < m < n) magnetic multipole. These meridional planes are defined by the 2m roots of the equation cos[m()–_n^m)] = 0, where _n^m = (1/m) arctan (h_n^m/g_n^m); g_n^m and h_n^m denote the spherical harmonic coefficients. Equatorial planar trajectories also exist if (n – m) is odd. The polar axis ( = O,) of a tesseral magnetic multipole is a magnetic neutral line if m > I. A further 2_m(n – m) neutral lines exist at the intersections of the 2_m meridional planes with the (n – m) cones defined by the (n – m) roots of the equation P_n^m(cos ) = 0 in the range 0 < 9 < , where P_n^m(cos ) denotes the associated Legendre function. If (n – m) is odd, one of these cones coincides with the equator and the magnetic field is then perpendicular to the equator everywhere apart from the 2m equatorial neutral lines. The radius of curvature of an equatorial trajectory is directly proportional to ⁿ⁼² and inversely proportional to cos[m(–)]. Since this last expression vanishes at the 2m equatorial neutral ines, the radius of curvature becomes infinitely large as the particle approaches any one of these neutral lines. The radius of curvature of a meridional trajectory is directly proportional to rⁿ⁺², where r denotes radial distance from the multiple, and inversely proportional to P_n^m(cos )/sin . Hence the radius of curvature becomes infinitely large if the particle approaches the polar magnetic neutral ine (m > 1) or any one of the 2m(n – m) neutral ines located at the intersections of the 2m meridional planes with the (n – m) cones. Illustrative particle trajectories, derived by stepwise numerical integration of the exact equations of particle motion, are pressented for low-degree (n 3) magnetic multipoles. These computed particle trajectories clearly demonstrate the non-adiabatic scattering of charged particles at magnetic neutral lines. Brief comments are made on the different regions of phase space defined by regular and irregular trajectories.Also Visiting Reader in Physics, University of Sussex, Falmer, Brighton, BN1 9QH, UK     

Amplitudes of explosion-generated seismic waves

Summary Records of underwater explosions in Iceland in 1959 and 1960, mainly performed for crustal studies, have been investigated with regard to amplitudes. The amplitudes ofP2 in the 1959 explosions and of the first arrivingP waves in the 1960 explosions were found to be proportional to the first power of the charge weight, whereas amplitudes ofP1 andS1 in the 1959 explosions were proportional to the 3/4-power of the charge up to 200 kg, but increased much slower for larger charges. The influence of water depth of shot point on the charge weights, required to obtain a certain amplitude, has been determined and it was found that the logarithm of the charge weight has a linear relation to water depth down to about 8 meters. The amplitudes of first arrivingP waves decrease as the inverse 2.2-power of the distance up to about 30 km. For greater distances an exponential decrease of the form (const./) exp (–) is valid. ForP2 waves with a frequency of 10 cps we found =0.027±0.003 km^–1 for a profile across central Iceland and =0.009±0.004 km^–1 for a profile in the western part of Iceland.

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Zusammenfassung In den Jahren 1959 und 1960 wurden auf Island Unterwasser-Explosionen ausgelöst, deren Hauptziel Untersuchung der Erdkruste waren. Die Aufzeichnungen der Explosionen werden hier in Hinsicht auf die Amplituden der Wellen untersucht. DieP2-Amplituden in den Explosionen von 1959 und die Amplituden der zuerst ankommendenP-Wellen in den Explosionen von 1960 waren proportional der ersten Potenz des Ladungsgewichtes, während diePl-undSl-Amplituden in den Explosionen von 1959 proportional der 3/4-Potenz des Ladungsgewichtes bis 200 kg waren. Für höhere Ladungsgewichte wuchsen die Amplituden langsamer an. Es wurde der Einfluss der Tiefe des Schusspunktes unterhalb des Wasserspiegels auf das für eine gewisse Amplitude benötigte Ladungsgewicht bestimmt. Es ergab sich dabei, dass der Logarithmus des Ladungsgewichtes in einer linearen Beziehung zur Tiefe, bis etwa 8 m, steht. Die Amplituden der zuerst ankommendenP-Wellen sind umgekehrt proportional der 2.2-Potenz der Entfernung, bis etwa 30 km. Für grössere Entfernungen ist die Abnahme der Amplituden exponential und kann durch (Konst./) exp (–) dargestellt werden. FürP2 mit einer Frequenz von 10 cps haben wir =0.027±0.003 km^–1 für ein Profil in Zentral-Island und =0.009 ± 0.004 km^–1 für ein Profil in West-Island gefunden.

     

On the determination of the European gravimetric geoid

Summary The method of the automated computation of the gravimetric deflections of the vertical and of the geoidal heights for the European region is described. The work was carried out during the period 1986–1988 by the Topographic Service of the Czechoslovak Army. The computation applies to 20 sheets of the international map 1:1 000 000 (total area of =16^c, =30^c - see Fig. 1). The mean values of the free-air anomalies for each surface element =5, =7.5, approximately 9 × 9 km, were used with radius of integration of 300 km.     

Fracture surface energy of olivine

A relatively simple indentation technique for the rapid measurement of fracture surface energy, , of small samples is described. The reliability of this technique is assessed by testing soda-lime glass for which there are good independent fracture mechanics determinations of fracture surface energy. The indentation technique gives a value for of 4.33 J m^–2 which compares favourably with the accepted value of 3.8 J m^–2. Fracture surface energies of the {010} and {001} cleavage planes of single crystal olivine (modal composition Fo₈₈Fa₁₂) are then determined and compared with theoretical estimates of the thermodynamic surface energy, , calculated from atomistic parameters ( is equal to in the absence of dissipative processes during crack extension). The experimental values for _{010} and _{001} are respectively 0.98 J m^–2 and 1.26 J m^–2. The calculated values of _{010} and _{001} are respectively in the range from 0.37 J m^–2 to 8.63 J m^–2 and 12.06 J m^–2. The particular advantages of the indentation technique for the study of the fracture surface energies of geological materials are outlined.     

Geographical and vertical variation of the earth's seismicity

Information concerning a total number of 13700 instrumentally recorded earthquakes is used to study the geographical and the vertical distribution of the Earth's seismicity. From these earthquakes, which form four complete samples of data (M 7.0, 1894–1992; M 6.5, 1930–1992; M 6.0, 1953–1992; M 5.5, 1966–1992), 11511 are shallow (h 60 km), 2085 are of intermediate focal depth (61 h 300 km) and 564 are deep focus earthquakes (301 h 720 km). The parameters a and b of the frequency-magnitude relationship were calculated in a grid of equally spaced points at 1° by using the data of earthquakes located inside circles centered at each point. The radius of the circles increased from 30 km with a step of 10 km until the information for the earthquakes located inside the circle fulfil three criteria which concern the size of the sample used to compute these parameters at each point of the grid. The results are given in a qualitative way (epicenter maps) as well as in a quantitative way (mean return periods).     

Spatial Structure and Long-Term Variations of The Ground-Level Temperature Variance

The global distribution of the ground-level temperature variance and its long-term variations have been investigated on the basis of the monthly mean temperature anomalies, obtained from ground-based and sea-borne meteorological observations from 1896 to 1990. Particular characteristics of the large-scale structure of the temperature variance have been found. There are three pronounced maxima in the global distribution of the temperature variance: in Central Siberia (60°75°N and 70° 120°E), North America (60°75°N and –170°–120°E) and the Antarctica (50°65°S and –60°10°E, where and are the geographic latitude and longitude, respectively) and there are two minima: over the Atlantic and Pacific Ocean areas. The minimum over the Pacific is not as pronounced, as over the Atlantic. The spatial pattern of the ground-level temperature variance is, on the whole, stable, the positions of the zones of extrema remaining practically unchanged over a long time interval. These results indirectly corroborate the mechanism of solar impact on the properties of the low atmosphere by the modulation of the flux of galactic cosmic rays. The mechanism accounts for the spatial distribution of the temperature variance as a result of combined effect of solar activity and ocean. Long-term variations of the Siberian maximum of the ground-level temperature variance agree with the changing duration of the sunspot cycle, in contrast to the North American maximum.     

On the further generalization of trochoidal frontal waves

Summary A non-linear model of trochoidal waves is presented which represents a geometrical and kinematical generalization of Gerstner's waves and of the results of[2–4].

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¶rt;aam ¶rt; mu¶rt;a , ma m u ma u am[2–4] mu umuu u uamu mm ¶rt;u.

     

Power-law Distributions of Offspring and Generation Numbers in Branching Models of Earthquake Triggering

We consider a general stochastic branching process,which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We apply our results to a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model. The ETAS model assumes that each earthquake can trigger other earthquakes (aftershocks). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (fertility), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime in which the distribution of fertilities is characterized by a power law ~1/¹⁺. For earthquakes we expect such a power-distribution of fertilities with =b/ based on the Gutenberg-Richter magnitude distribution ~ 10^–bm and on the increase ~ 10^–m of the number of aftershocks with the mainshock magnitude m. We derive the asymptotic distributions p_r(r) and p_g(g) of the total number r of offsprings and of the total number g of generations until extinction following a mainshock. In the regime < 2 for which the distribution of fertilities has an infinite variance, we find This should be compared with the distributions obtained for standard branching processes with finite variance. These predictions are checked by numerical simulations. Our results apply directly to the ETAS model whose preferred values =0.8–1 and b=1 puts it in the regime where the distribution of fertilities has an infinite variance. More generally, our results apply to any stochastic branching process with a power-law distribution of offsprings per mother     

Radioactive and trace element distribution in basaltic rocks of Lower Silesia

Summary The distribution of radioactive(Th, U, K) and selected trace(Rb, Sr, Ba, Y, Zr, V, Cr, Ni) elements in volcanic rocks from the Opole and Jawor regions of the Lower Silesia has been studied. The behaviour of these elements in the studied rocks indicates that the Lower Silesian volcanic rocks are characterized by less differentiated type than other volcanic rocks of the Bohemian Massif, the Opole rock types probably having a less differentiated character than the Jawor rock types.

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¶rt;a an¶rt;u a¶rt;uamu(Th, U, K) u m ¶rt;u(Rb, Sr, Ba, Y, Zr, V, Cr, Ni) m auu n¶rt;a am n u u uuu. a n mam n¶rt;num, m aum u uuu n¶rt;mam ¶rt; aamuu n¶rt; u ¶rt;uuau, aum u ana¶rt; uu. au a n¶rt;num, m auu n¶rt; amu n ¶rt;uuau ma ua n¶rt; u amu .

     

Magnetic interpretation of dyke anomalies using derivatives

The horizontal and vertical derivative profiles of magnetic anomalies of dykes show some interesting properties. The points of zero derivatives and the points where the derivatives are equal are conjugate point pairs. A method of interpretation of dyke anomalies is suggested, which utilizes the distances between these points.Notation F Magnetic anomaly in total intensity - Z Depth to top of the dyke - 2T Width of the dyke - Geological dip of the dyke - I Effective intensity of magnetisation in the plane of profile - Dip of effective magnetisation vector in the plane of profile - Strike angle of the dyke - i Magnetic dip - Q – - Q _f –+arctan (sin coti) - I _f