Integral Equations for Kinematic Dynamo Models

A new technique for the treatment of the kinematic dynamo problem is presented. The method is applicable when the dynamo is surrounded by a medium of finite conductivity and is based on a reformulation of the induction equation and boundary conditions at infinity into an integral equation. We show that the integral operator involved here is compact in the case of homogeneous conductivity, which is important for both mathematical and numerical treatment. A lower bound for the norm of then yields a necessary condition for the generation of magnetic fields by kinematic dynamos. Numerical results are presented for some simple ²-dynamo models. The far-field asymptotics for stationary and time-dependent field modes are discussed.     

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.     

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.     

Compaction of a Rock Fracture Moderated by Competing Roles of Stress Corrosion and Pressure Solution

Unusually rapid closure of stressed fractures, observed in the initial stages of loading and at low temperatures, is examined using models for subcritical crack growth and pressure solution. The model for stress corrosion examines tensile stress concentrations induced at the Hertzian contact of propping fracture asperities, and mediates fracture growth according to a kinetic rate law. Conversely, pressure solution is described by the rate-limiting process of dissolution, resulting from the elevated stresses realized at the propping asperity contact. Both models are capable of following the observed compaction of fractures in novaculite. However, closure rates predicted for stress corrosion cracking are orders of magnitudes faster than those predicted for pressure dissolution. For consistent kinetic parameters, predictions from stress corrosion better replicate experimental observations, especially in the short-term and at low temperature when mechanical effects are anticipated to dominate. Rates and magnitudes of both stress corrosion and pressure solution are dependent on stresses exerted over propping asperities. Rates of closure due to stress corrosion cracking are shown to be always higher than for pressure solution, except where stress corrosion ceases as contact areas grow, and local stresses drop below an activation threshold. A simple rate law is apparent for the progress of fracture closure, defined in terms of a constant and an exponent applied to the test duration. For current experimental observations, this rate law is shown to replicate early progress data, and shows promise to define the evolution of transport properties of fractures over extended durations.     

Body-wave Attenuation in the Region of Garda, Italy

We analyzed the spectral amplitude decay with hypocentral distance of P and S waves generated by 76 small magnitude earthquakes (M_L 0.9–3.8) located in the Garda region, Central-Eastern Alps, Italy. These events were recorded by 18 stations with velocity sensors, in a distance range between 8 and 120 km. We calculated nonparametric attenuation functions (NAF) and estimated the quality factor Q of both body waves at 17 different frequencies between 2 and 25 Hz. Assuming a homogeneous model we found that the Q frequency dependence of P and S can be approximated with the functions Q _P = 65 f ^0.9 and Q _S = 160 f ^0.6 , respectively. At 2 Hz the Q _S /Q _P ratio reaches the highest value of 2.8. At higher frequencies Q _S /Q _P varies between 0.7 and 1.7, suggesting that for this frequency band scattering may be an important attenuation mechanism in the region of Garda. To explore the variation of Q in depth, we estimated Q at short (r ≤ 30 km) and intermediate (35–90 km) distance paths. We found that in the shallow crust P waves attenuate more than S (1.3 < Q _S /Q _P < 2.5). Moreover, P waves traveling along paths in the lower crust (depths approximately greater than 30 km) attenuate more than S waves. To quantify the observed variability of Q in depth we considered a three-layer model and inverted the NAF to estimate Q in each layer. We found that in the crust Q increases with depth. However, in the upper mantle (~40–50 km depth) Q decreases and in particular the high frequency Q _S (f > 9 Hz) has values similar to those estimated for the shallow layer of the crust.     

Lateral variations of coda Q and attenuation of seismic waves in Southwest Anatolia

The seismic quality factor (Q _c) and the attenuation coefficient (δ) in the earth’s crust in southwest (SW) Anatolia are estimated by using the coda wave method based on the decrease of coda wave amplitude by time on the seismogram. The quality factor Q _o, the value of Q _c at 1 Hz, and its frequency dependency η are determined from this method depending on the attenuation properties of scattered coda waves. δ is determined from the observations of amplitude variations of seismic waves. In applying the coda wave method, firstly, a type curve representing the average pattern of the individual coda decay curves for 0.75, 1.5, 3.0, 6.0, 12.0, and 24.0 Hz values was estimated. Secondly, lateral variation of coda Q and the attenuation coefficients for three main tectonic patterns are estimated. The shape of the type curve is controlled by the scattering and attenuation in the crustal volume sampled by the coda waves. The Q _o and η values vary from 30 to 180 and from 0.55 to 1.25, respectively for SW Anatolia. In SW Anatolia, coda Q–f relation is described by and δ = 0.008 km⁻¹. These results are expected to help in understanding the degree of tectonic complexity of the crust in SW Anatolia.     

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.     

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.     

First Order Seismic Microzonation of Haldia, Bengal Basin (India) Using a GIS Platform

The seismic microzonation of the Bengal Basin, Haldia region, India is carried out using the Analytical Hierarchy Process (AHP) on the Geographic Information System (GIS). Three themes are used for the seismic microzonation, namely Peak Ground Acceleration (PGA), predominant frequency and elevation map. An analysis of the maximum magnitude (m _max) and the b value is carried out after preparing the earthquake catalogue from various sources. On the basis of the tectonic set up and seismicity of the region, five seismic zones are delineated which can be a threat to Haldia. They are broadly classified as Zone 1: Arakan-Yoma Zone (AYZ), Zone 2: Himalayan Zone (HZ), Zone 3: Shillong Plateau Zone (SPZ), Zone 4: Bay of Bengal Zone (BBZ) and Zone 5: Shield Zone (SZ). The m _max for Zones 1, 2, 3, 4 and 5 are 8.30 ± 0.51, 9.09 ± 0.58, 9.20 ± 0.51, 6.62 ± 0.43 and 6.61 ± 0.43, respectively. The PGA value is computed for Haldia following the attenuation relationship taking the m _max of each source zone. The expected PGA at Haldia varies from 0.09–0.19 g. The predominant frequency of Haldia is also calculated using the H/V ratio with a frequency ranging from 0.1–3.0 Hz. The elevation map of Haldia is also generated using the Shuttle Radar Topography Mission (STRM) data. A first-order seismic microzonation map of Haldia is prepared in which four zones of hazard have been broadly classified for Haldia as very high seismic hazard zone, high seismic hazard zone, moderate seismic hazard zone and less seismic hazard zone. The very high seismic hazard zone is observed along the southern part of Haldia where there are major industrial and port facilities. The PGA for the four hazard zones are: 0.09–0.13 g for low hazard zone, > 0.13–0.15 g for moderate hazard zone, > 0.15–0.16 g for high hazard zone and > 0.16–0.19 g for very high hazard zone.     

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.