Lagrangian Solution of Dynamo Equations and Path Integrals

We discuss an explicit solution of the Cauchy problem for induction equation and suggest its generalization for equations of ²-dynamo. These solutions are based on concepts of multiplicative, Wiener path, and stochastic integrals. Obtained explicit solution can be useful as a tool in investigations of a dynamo with fluctuating helicity.     

The Karlsruhe Dynamo Experiment. A Mean Field Approach

At the Forschungszentrum Karlsruhe an experiment is in preparation which it is hoped, in view of the geodynamo and other cosmic dynamos, that a homogeneous dynamo will be demonstrated and investigated. This experiment is discussed within the framework of mean-field dynamo theory. Results are presented concerning kinematic cylindrical mean-field dynamo models reflecting some features of the experimental device, as well as results of detailed calculations of the -effect that apply to arbitrarily high magnetic Reynolds numbers. On this basis estimates of the excitation conditions of the dynamo are given and predictions concerning the geometrical structure of the generated magnetic fields are made.     

Origin of the fumarolic fluids of Vulcano Island,Italy and implications for volcanic surveillance

Variations in D and ¹⁸O values with H₂O contents and outlet temperatures indicate that the fumaroles of La Fossa crater have discharged mixtures of magmatic water and marine hydrothermal water, since 1979. The contribution of meteoric water was low in the period 1979–1982 and very low afterwards. The ¹⁸O values of the marine-hydrothermal component of +5 to +7.2 are due to isotopic exchange with the ¹⁸O-rich silicates of the rocks under high-temperature and low-permeability conditions. The ¹⁸O value of the magmatic end-member is generally +3.5 to +4.3, although values as high as +5.5 to +6.5 were reached in the summer of 1988, when magma degassing appears to have extended into the core of the magma body. The D values of the end-member were close to -20, typical of andesitic waters. Both the isotopic values and chemical data strongly support a dry model, consisting of a central magmatic gas column and a surrounding hydrothermal envelope, in which marine hydrothermal brines move along limited fracture zones to undergo total evaporation on approaching the conduits of magmatic fluids. The vents at the eastern and western boundaries of the fumarolic field are fed by fluids whose pressure is governed by the coexistence of vapor, liquid and halite, giving rise to a high risk of phreato magmatic explosions, should magma penetrate into these wet environments. Most La Fossa eruptions were triggered by an initial hydrothermal blast and continued with a series of phreatomagmatic explosions. The fluids discharged by the Forgia Vecchia fumaroles are mixed with meteoric water, which is largely evaporated, although subordinate loss of condensed steam may be responsible for scrubbing most of the acidic gas species. The temperatures and pressures, and the risk of a sudden pressure increase, are low. A boiling hydrothermal aquifer at 230° C is present underneath the Baia di Levante beach. This area has a minor risk of hydrothermal explosions.     

Cenozoic Intraplate Alkaline Volcanism of Western Bohemia

Three independent volcanic suites have been recognised in W Bohemia: (i) the old unimodal alkaline ol. nephelinite-tephrite (29-19 Ma) in the Ohe Rift, (ii) two contemporaneous weakly (trachybasalt/trachyandesite-trachyte/rhyolite; 13-11 Ma) and strongly (ol. nephelinite-tephrite/basanite; 12-8 Ma) alkaline series in the flank of the Cheb-Domalice Graben formed by the Teplá Highland and (iii) the young unimodal ol. melilitite/ol. nephelinite alkaline suite (2.0-0.12 Ma) at the intersection of the above mentioned structures in the Cheb Basin. The magmas of all the suites are mantle-derived and, in the case of the Cheb-Domalice Graben series, associated with the AFC process. Two main fault systems: (i) ENE-WSW and (ii) NNW-SSE are developed in W Bohemia, corresponding to the directions of the two prominent taphrogenic structures. The southwesterly continuation of the Ohe Rift across the Mariánské Lázn Fault is marked by volcanics only.     

The gross features of the lithosphere-asthenosphere system in Europe from seismic surface waves and body waves

Long-period recordings of dispersive Rayleigh waves along numerous station lines, or profiles, in Europe have for the first time permitted a uniform inversion of these observations based on a new method of phase velocity regionalization.Regional dispersion relations obtained by this method have then been subjected to a complete inversion procedure commonly known as the hedgehog method. The results are presented in a map outlining the thickness of the lower lithosphere (lid) and the shear (S) velocities in both the lid and the asthenosphere channel.A comparison of these results with the minimum compressional (P) wave velocities in the asthenosphere and their corresponding depths provides an estimate of theV _p /V _s ratio for the asthenosphere in the European area.Contribution No. 314, Institute of Geophysics, ETH-Zürich, Switzerland.     

Mean Field Dynamos with Algebraic and Dynamic α-Quenchings

Calculations for mean field dynamo models (in both full spheres and spherical shells), with both algebraic and dynamic -quenchings, show qualitative as well as quantitative differences and similarities in the dynamical behaviour of these models. We summarise and enhance recent results with extra examples. Overall, the effect of using a dynamic appears to be complicated and is affected by the region of parameter space examined.     

Channel overflows of the Pōhue Bay flow,Mauna Loa,Hawai'i: examples of the contrast between surface and interior lava

A number of overflows from a large lava channel and tube system on the southwest rift zone of Mauna Loa were studied. Initial overflows were very low viscosity gas-rich phoehoe evidenced by flow-unit aspect ratios and vesicle sizes and contents. Calculated volumetric flow-rates in the channel range between 80 and 890 m³/s, and those of the overflows between 35 and 110 m³/s. After traveling tens to hundreds of meters the tops of these sheet-like overflows were disrupted into a surface composed of clinker and phoehoe fragments. After these 'a' overflows came to rest, lava from the interiors was able to break out on to the surface as phoehoe. The surface structure of a lava flow records the interaction between the differential shear rate (usually correlated with the volumetric flow-rate) and viscosity-induced resistance to flow. However, the interior of a flow, being better insulated, may react differently or record a later set of emplacement conditions. Clefts of toothpaste lava occurring within fields of clinker on proximal-type 'a' flows also record different shear rates during different times of flow emplacement. The interplay between viscosity and shear rate determines the final morphological lava type, and although no specific portion of lava ever makes a transition from 'a' back to phoehoe, parts of a flow can appear to do so.     

Tilt Observations in the Normal Mode Frequency Band at the Geodynamic Observatory Cueva de los Verdes,Lanzarote

We have conducted observations with the aid of a seismo-tiltmeter station, which is based on the Ostrovsky pendulum and installed at the Geodynamic Observatory Cueva de los Verdes at Lanzarote Island since 1995. In this station the signal is separated into two frequency bands – tidal tilts (from 0 to 5 mHz) and ground oscillations in the frequency range of free Earths normal modes (from 0.2 to 5 mHz). The later band, called accelerometer channel, has additional amplification. We analyzed the background records in the frequency range of Earths free oscillations from August 2000 to September 2001, as well as, Earths normal modes after strong earthquakes. We found several distinctive persistent peaks in the spectra of background oscillations. Both amplitudes of distinguished peaks and noises have seasonal variations. We found that spectra of background oscillations are different in the frequency interval between 1.4 and 2.5 mHz for North- South and East-West components.     

Hawaiian magma-reservoir processes as inferred from the petrology of gabbro xenoliths in basalt,Kahoolawe Island

Gabbro xenoliths in a tholeiitic lava of Kahoolawe Island, Hawaii, a 1.3–1.4 Ma shield volcano, are 1–3 cm in size and comprised of plagioclase, clinopyroxene, and orthopyroxene. Gabbro textures — while intergranular and in part subophitic-are open due to 28–48 vol.% of vesicular basalt occupying xenolith space. Vesicles in and around the xenoliths are lined or filled with rhyolitic glass (segregation vesicles). The host is evolved tholeiite (MgO 6.1 wt%) with phenocrysts, microphenocrysts, and glomerocrysts of olivine, clinopyroxene, orthopyroxene, and plagioclase, and megacrysts (1 cm) of plagioclase. The Sr-isotope ratio of one xenolith is 0.70489; the host basalt ratio is 0.70460. Xenolith isotope composition, grain resorption, and clinopyroxene (Fs_12.5–15Wo_38–35.5), orthopyroxene (Fs_19.5–24Wo_4.1), and plagioclase (An_68–65Or_0.8–1.2) compositions suggest that these gabbros crystallized from Kahoolawe tholeiitic magma of essentially the same composition as the host basalt, but pre-dating the magma represented by the host. Based on the absence of intergranular Fe–Ti oxide phases from the pl+cpx+opx assemblages, and the open, vuggy textures, we envision crystallization on a reservoir roof at temperatures >1100°C. Entrainment of gabbro assemblages and plagioclase megacrysts from a roof mush/suspension zone occurred during convection associated with replenishment of the magma reservoir. These open-textured gabbro xenoliths are therefore not fragments of preexisting coarse-grained bodies such as sills or segregation veins. Rhyolitic glass in vesicles represents a gas-effervescence filtration process that forced fractionated residual liquids from the groundmass into voids associated with the xenoliths.Sirrine Environmental Consultants, Fremont, CA 94538     

Community preparedness for lava flows from Mauna Loa and Hualālai volcanoes,Kona, Hawai‘i

Lava flows from Mauna Loa and Huallai volcanoes are a major volcanic hazard that could impact the western portion of the island of Hawaii (e.g., Kona). The most recent eruptions of these two volcanoes to affect Kona occurred in a.d. 1950 and ca. 1800, respectively. In contrast, in eastern Hawaii, eruptions of neighboring Klauea volcano have occurred frequently since 1955, and therefore have been the focus for hazard mitigation. Official preparedness and response measures are therefore modeled on typical eruptions of Klauea.The combinations of short-lived precursory activity (e.g., volcanic tremor) at Mauna Loa, the potential for fast-moving lava flows, and the proximity of Kona communities to potential vents represent significant emergency management concerns in Kona. Less is known about past eruptions of Huallai, but similar concerns exist. Future lava flows present an increased threat to personal safety because of the short times that may be available for responding.Mitigation must address not only the specific characteristics of volcanic hazards in Kona, but also the manner in which the hazards relate to the communities likely to be affected. This paper describes the first steps in developing effective mitigation plans: measuring the current state of peoples knowledge of eruption parameters and the implications for their safety. We present results of a questionnaire survey administered to 462 high school students and adults in Kona. The rationale for this study was the long lapsed time since the last Kona eruption, and the high population growth and expansion of infrastructure over this time interval. Anticipated future growth in social and economic infrastructure in this area provides additional justification for this work.The residents of Kona have received little or no specific information about how to react to future volcanic eruptions or warnings, and short-term preparedness levels are low. Respondents appear uncertain about how to respond to threatening lava flows and overestimate the minimum time available to react, suggesting that personal risk levels are unnecessarily high. A successful volcanic warning plan in Kona must be tailored to meet the unique situation there.     

Critical remarks on the use of medieval eclipse records for the determination of long-term changes in the Earth's rotation

The use of some Arabic medieval solar and lunar eclipse records for the determination of secular changes in the Earth's rotation is critically reviewed. The published results derived from these data suggest a non-uniform decrease in the Earth's rotation rate over the last 27 cy. There is, however, up to this day no sound physical explanation for the deduced non-tidal oscillations, with an apparent period of about 1500 yr and a semi-amplitude of some 4 ms in the l.o.d., which overlayed to a constant secular tidal change in the Earth's rotation rate produce a net non-uniform deceleration of the Earth's rotation. In this paper we discuss a set of observations, which were executed by professional Arabic astronomers. We show by our analysis the way in which the non-uniform deceleration of the Earth's rotation was constructed. A correct reading of the Arabic medieval observations shows that they do not contradict a secular constant decrease in the Earth's rotation rate of nearly -4.6 10-22 rad s-2. This value is in accordance with other similar ones derived from ancient eclipse records and from satellite tracking data.     

Ductile creep and compaction: A mechanism for transiently increasing fluid pressure in mostly sealed fault zones

A simple cyclic process is proposed to explain why major strike-slip fault zones, including the San Andreas, are weak. Field and laboratory studies suggest that the fluid within fault zones is often mostly sealed from that in the surrounding country rock. Ductile creep driven by the difference between fluid pressure and lithostatic pressure within a fault zone leads to compaction that increases fluid pressure. The increased fluid pressure allows frictional failure in earthquakes at shear tractions far below those required when fluid pressure is hydrostatic. The frictional slip associated with earthquakes creates porosity in the fault zone. The cycle adjusts so that no net porosity is created (if the fault zone remains constant width). The fluid pressure within the fault zone reaches long-term dynamic equilibrium with the (hydrostatic) pressure in the country rock. One-dimensional models of this process lead to repeatable and predictable earthquake cycles. However, even modest complexity, such as two parallel fault splays with different pressure histories, will lead to complicated earthquake cycles. Two-dimensional calculations allowed computation of stress and fluid pressure as a function of depth but had complicated behavior with the unacceptable feature that numerical nodes failed one at a time rather than in large earthquakes. A possible way to remove this unphysical feature from the models would be to include a failure law in which the coefficient of friction increases at first with frictional slip, stabilizing the fault, and then decreases with further slip, destabilizing it.     

A statistical study of the upstream intermediate ion boundary in the Earth’s foreshock

A statistical investigation of the location of onset of intermediate and gyrating ion populations in the Earths foreshock is presented based on Fixed Voltage Analyzer data from ISEE 1. This study reveals the existence of a spatial boundary for intermediate and gyrating ion populations that coincides with the reported ULF wave boundary. This boundary position in the Earths foreshock depends strongly upon the magnetic cone angle _BX and appears well defined for relatively large cone angles, though not for small cone angles. As reported in a previous study of the ULF wave boundary, the position of the intermediate-gyrating ion boundary is not compatible with a fixed growth rate of the waves resulting from the interaction between a uniform beam and the ambient plasma. The present work examines the momentum associated with protons which travel along this boundary, and we show that the variation of the boundary position (or equivalently, the associated particle momentum) with the cone angle is related to classical acceleration mechanisms at the bow shock surface. The same functional behavior as a function of the cone angle is obtained for the momentum predicted by an acceleration model and for the particle momentum associated with the boundary. However, the model predicts systematically larger values of the momentum than the observation related values by a constant amount; we suggest that this difference may be due to some momentum exchange between the incident solar-wind population and the backstreaming particles through a wave-particle interaction resulting from a beam plasma instability.     

A Local Least-Squares Modification of Stokes’ Formula

The combination of Stokes formula and an Earth Gravity Model (EGM) for geoid determination has become a standard procedure. However, the way of modifying Stokes formula vary from author to author, and numerous methods of modification exist. Most methods are deterministic, with the primary goal of reducing the truncation bias committed by limiting the area of Stokes integration around the computation point, but there are also some stochastic methods with the explicit goal to reduce the global mean square error of the geoid height estimator stemming from the truncation bias as well as the random errors of the EGM and the gravity data. The latter estimators are thus, at least from a theoretical point of view, optimal in a global mean sense, but in a local sense they may be far from optimality.Here we take advantage of the error variance-covariance matrices of the EGM and the terrestrial gravity data to derive the modification parameters of Stokes kernel in a local least-squares sense. The solution is given for the unbiased type of modification of Stokes formula of Sjöberg (1991).     

Velocity analysis from large offset seismic records

One of the most important problems in applied geophysics is to extract velocities of compressional and shear waves, using the observed data collected at the Earth's surface or in boreholes. Unfortunately, in a typical seismic experiment, we do not have enough information to uniquely recover seismic velocities as functions ofx, y, andz. Thus, in the paper, a simplified model of the Earth (a stack of horizontal homogeneous layers) is considered and a critical discussion of modern techniques for processing reflection arrivals is presented.     

On strong ground motion synthesis with k −2 slip distributions

This study deals with the methodical aspects of k ^–2(Bernard et al., 1996) kinematic strong motions modelling: (1) it is shown how to incorporate the k-dependent rise time for 2D fault geometry in the strong motion synthesis according to the representation theorem, (2) it is suggested how to produce realistic k ^–2 slip models including asperity(ies), (3) modifications are introduced concerning the typeof used slip velocity function and the corner wave number in the slip distribution. High frequency effects of these generalized models are discussed.It is shown that, assuming the rise time proportional to the spatial slip wavelength at high wave numbers, the spectral decay of displacement at frequencies higher than the corner frequency is given just by the decay ofthe slip distribution spectrum, regardless of the type of slip velocity function. It is shown numerically that this model provides -squared source spectrum even in a vicinity of a 2D normal fault buried in 1D structure, which is an agreement with previous studies.     

The relation between intensity and magnitude for Italian earthquakes

This paper describes the problems concerning the relation between intensity and magnitude, which are substantially different quantities by nature. In consideration of the necessity to translate magnitude values into intensity values, andvice versa, to find magnitude values for historical earthquakes, we have searched for a correspondence that may exist between intensity and magnitude, hypothesising that magnitude values were distributed as a known function. Therefore, we have analysed two distribution functions, first the Gaussian distribution, then a box function, of which the goodness of fit has been estimated by the ² test. In conclusion, the probability distribution of magnitude vs intensity seems better described by a Gaussian curve.     

Further evidence for radial velocity anomalies in the lower mantle

Summary Wright andLyons (1981) used a least-squares matching technique (LMM) and an adaptive processing method (ADP) to study the behaviour of slowness and azimuth measurements made on two synthetic interfering wavelets having different arrival vectors and onset times. We have applied these results to the analysis of real array seismograms. Some of the effects generated synthetically are frequently observed on real seismograms of earthquakes recorded at Yellowknife at distances close to 50° and 90°. We have also processed sufficient data to illustrate how the interference phenomenon can be used to confirm the presence of radial velocity anomalies in the lower mantle. NumerousP arrivals from South American earthquakes at distances between 78° and 98° suggest the presence of two radial velocity anomalies at depths close to 2400 and 2730 km below the Caribbean region; these anomalies also appear to vary laterally.Contribution No. 864 from the Earth Physics Branch.     

A deep geophysical study in the Baikal region

Experimental data show that in East Siberia resistivity curves, irrespective of their trends, are affected by galvanic (local) distortions. The preliminary step of the magnetotelluric data processing is to obtain a steady shape of resistivity curves reflecting a true deep section. For this purpose statistical averaging and different criteria of impedance rejecting were used. The available MTS curves were normalized by level to the global magnetovariation curves. Two-dimensional modelling was performed from several sublatitudinal profiles crossing the Baikal rift zone. Three-dimensional models based on two-dimensional modelling and on induction vector distribution have been computed via programs of M. N. Yudin. Following other researchers, two conductive layers are distinguished: i) the mid- and low crustal and ii) the mantle one, with the layer surface uplifted from 100–110 km depth in the southern Baikal rift zone to 60–70 km northeastwards along the eastern Baikal coast. The top of this layer seems to correspond to the asthenospheric roof. The asthenosphere deepening in southern BRZ is likely to be related to a decrease in the asthenospheric bulge width and an increase in the rate of lithospheric thickening with mantle degasing. The origin and evolution of the Baikal rift is considered, proceeding from the model of passive rifting with regard to a long-existing lithospheric inhomogeneity between the Siberian platform and the Sayan-Baikal folded area.