Algorithm for solving 3-D problems of em induction by means of a vector integral equation

Summary An algorithm is presented for solving the problem of electromagnetic induction in a halspace with a 3-D perturbing body under a harmonically variable exciting field. There are analysed properties of the Green's tensor function elements as well as their integrals in elementary prismatic volumes into which the body is divided. The results, obtained from numerical computations, are given for a long highly conducting prism, which is one of the models in the COMMEMI project.

---

¶rt; azum u a¶rt;au mazum u¶rt;uu ¶rt; zauu nz ¶rt;az n nnmam m au m. ¶rt;a ma m m uu n ma a, a m a¶rt; a m. nu uu mam mm nm, n¶rt; nu, ¶rt; u ¶rt; nma COMMEMI.

     

Low frequency 1/f-like fluctuations of the AE-index as a possible manifestation of self-organized criticality in the magnetosphere

Low frequency stochastic variations of the geomagnetic AE-index characterized by 1/f^b-like power spectrum (where f is a frequency) are studied. Based on the analysis of experimental data we show that the B_z-component of IMF, velocity of solar wind plasma, and the coupling function of Akasofu are insufficient factors to explain these behaviors of the AE-index together with the 1/f^b fluctuations of geomagnetic intensity. The effect of self-organized criticality (SOC) is proposed as an internal mechanism to generate 1/f^b fluctuations in the magnetosphere. It is suggested that localized spatially current instabilities, developing in the magnetospheric tail at the initial substorm phase can be considered as SOC avalanches or dynamic clusters, superposition of which leads to the 1/f^b fluctuations of macroscopic characteristics in the system. Using the sandpile model of SOC, we undertake numerical modeling of space-localized and global disturbances of magnetospheric current layer. Qualitative conformity between the disturbed dynamics of self-organized critical state of the model and the main phases of real magnetospheric substorm development is demonstrated. It is also shown that power spectrum of sandpile model fluctuations controlled by real solar wind parameters reproduces all distinctive spectral features of the AE fluctuations.     

Flow and transport through two-dimensional isotropic media of binary conductivity distribution. Part 2: NUMERICAL simulations and comparison with theoretical results

In the present part the results of numerical simulations of flow and transport in media made up from circular inclusions of conductivity K that are submerged in a matrix of conductivity K ₀, subjected to uniform mean velocity, are presented. This is achieved for a few values of =K/K ₀ (0.01, 0.1 and 10) and of the volume fraction n (0.05, 0.1 and 0.2). The numerical simulations (NS) are compared with the analytical approximate models presented in Part 1: the composite elements (CEA), the effective medium (EMA), the dilute system (DSA) and the first-order in the logconductivity variance (FOA). The comparison is made for the longitudinal velocity variance and for the longitudinal macrodispersivity. This is carried out for n<0.2, for which the theoretical and simulation models represent the same structure of random and independent inclusions distribution. The main result is that transport is quite accurately modeled by the EMA and CEA for low , for which _L is large, whereas in the case of =10, the EMA matches the NS for n<0.1. The first-order approximation is quite far apart from the NS for the values of examined . This material is based upon work supported by the National Science Foundation under Grant No. 0218914. Authors also wish to thank the Center of Computational Research, University at Buffalo for assistance in running numerical simulations.     

An asperity model to simulate rupture along heterogeneous fault surfaces

A model has been developed to simulate the statistical and mechanical nature of rupture on a heterogeneous strike-slip fault. The model is based on the progressive failure of circular asperities of varying sizes and strengths along a fault plane subjected to a constant far-field shear displacement rate. The basis of the model is a deformation and stress intensity factory solution for a single circular asperity under a unidirectional shear stress. The individual asperities are unified through the fault stiffness and the far-field stress and displacement. During fault deformation asperities can fail and reheal, resulting in changes in the local stresses in the asperities, stress drops, and changes in the stiffness of the fault. Depending on how the stress is redistributed following asperity failure and on the strenghts of the neighboring asperities an earthquake event can be the failure of one or more asperities. Following an earthquake event seismic source parameters such as the stress drop, energy change, and moment magnitude are calculated. Results from the model show a very realistic pattern of earthquake rupture, with reasonable source parameters, the proper magnitude-frequency behavior, and the development of characteristic earthquakes. Also the progression ofb-values in the model gives some insight into the phenomenon of self-organized criticality.     

Modeling fragmentation in two dimensions

Three cellular automaton toy-models of fragmentation in two-dimensional lattices are explored. Of the three models, two can be considered in the class of simple bond percolation, and one as correlated bond percolation. Fractal fragment-size distribution in all models is found away from criticality, providing a certain fraction of the bonds is designated with considerably larger strengths than the rest in the system. As the fraction of these bonds is raised from zero, the fragment-size distribution transforms smoothly from exponential forms into a power law. Though each model takes a different path to the fractal distribution, they all show the same fractal exponent of 1.85(5). As might be expected in one dimension, the same models of their variants, failed to produce fractal distributions.     

Accelerating Precursory Activity within a Class of Earthquake Analogue Automata

— A statistical fractal automaton model is described which displays two modes of dynamical behaviour. The first mode, termed recurrent criticality, is characterised by quasi-periodic, characteristic events that are preceded by accelerating precursory activity. The second mode is more reminiscent of SOC automata in which large events are not preceded by an acceleration in activity. Extending upon previous studies of statistical fractal automata, a redistribution law is introduced which incorporates two model parameters: a dissipation factor and a stress transfer ratio. Results from a parameter space investigation indicate that a straight line through parameter space marks a transition from recurrent criticality to unpredictable dynamics. Recurrent criticality only occurs for models within one corner of the parameter space. The location of the transition displays a simple dependence upon the fractal correlation dimension of the cell strength distribution. Analysis of stress field evolution indicates that recurrent criticality occurs in models with significant long-range stress correlations. A constant rate of activity is associated with a decorrelated stress field.     

Spatio-temporal variations of seismicity in the southern Peru and northern Chile seismic gaps

The spatio-temporal variation of seismicity in the southern Peru and northern Chile seismic gaps is analyzed with teleseismic data (m _b 5.5) between 1965 and 1991, to investigate whether these gaps present the precursory combination of compressional outer-rise and tensional downdip events observed in other subduction zones. In the outer-rise and the inner-trench (0 to 100 km distance from the trench) region, lower magnitude (5.0m _b <5.5) events were also studied. The results obtained show that the gaps in southern Peru and northern Chile do not present compressional outer-rise events. However, both gaps show a continuous, tensional downdip seismicity. For both regions, the change from compressional to tensional regime along the slab occurs at a distance of about 160 km from the trench, apparently associated with the coupled-uncoupled transition of the interplate contact zone. In southern Peru, an increase of compressional seismicity near the interplate zone and of tensional events (5.0m _b 6.3) in the outer-rise and inner-trench regions is observed between 1987 and 1991. A similar distribution of seismicity in the outer-rise and inner-trench regions is observed with earthquakes (m _b <5.5). In northern Chile there is a relative absence of compressional activity (m _b 5.5) near the interplate contact since the sequence of December 21, 1967. After that, only a cluster of low-magnitude compressional events has been located in the area 50 to 100 km from the trench. The compressional activity occurring near the interplate zone in both seismic gaps represents that a seismic preslip is occurring in and near the plate contact. Therefore, if this seismic preslip is associated with the maturity of the gap, the fact that it is larger in southern Peru than in northern Chile may reflect that the former gap is more mature than the latter. However, the more intense downdip tensional activity and the absence of compressional seismicity near the contact zone observed in northern Chile, may also be interpreted as evidence that northern Chile is seismically more mature than southern Peru. Therefore, the observed differences in the distribution of stresses and seismicity analyzed under simple models of stress accumulation and transfer in coupled subduction zones are not sufficient to assess the degree of maturity of a seismic gap.     

Flow of non-Newtonian fluid through circular tubes

Summary According to Newton's law of viscosity _y = Dv_y/dy. But experiments have shown that _y is indeed proportional to –dv _x/dy for all gases and for homogeneous nonpolymeric liquids. There are however, a few industrially important materials, e.g. plastics, asphalts, crystalline materials that are not described by the equation given by Newton's law of viscosity and they are referred to as non-Newtonian fluids. The steady state rheological behaviour of most fluids can be expressed by the generalised form, _y = –(dv_y/dy) where may be expressed as a function of eitherdv _x/dy or _y (where is independent of the rate of shear, the behaviour is Newtonian with =). Numerous empirical equations or models have been proposed to express the steady-state relation between _y anddv _x/dy. The flow of Newtonian fluids through circular tubes have been discussed before by many. Here we shall discuss the case of two such models of non-Newtonian fluids through circular tubes. The flow of fluids in circular tubes is encountered frequently in Physics, Chemistry, Biology and Engineering.     

P-wave amplitude spectra of Nevada underground nuclear explosions

Summary Short-period vertical-componentP-wave spectra have been determined for twelve Nevada underground nuclear explosions recorded by the Swedish seismic station network. Selected events cover the magnitude range fromm _b =5.9 tom _b =7.0 and the shot-depth range from 460 m to 1400 m. All explosion spectra show pronounced minima near 1 sec period. Within individual test areas the period at which the minimum occurs increases systematically with increasing shot-depth. This dependence makes it possible to interpret the observed minima in terms of interference betweenP- andpP-waves. One atmospheric explosion from Novaya Zemlya is analyzed to verify the inferred minima intrpretation.The minimum-period shows also a systematic linear dependence upon the magnitude. However, the physical explanation for this dependence is not evident and it may just be a consequence of a magnitude-depth relation.On leave from the Geophysical Institute, Czechosl. Acad. Sci., Prague 4-Spoilov, Boni II.     

Die F-Ionisation in den Morgenstunden

Zusammenfassung Die Elektronenkonzentration in derF-Schicht der Ionosphäre wächst in den Morgenstunden nicht einfach proportional dem Cosinus des Einfallswinkels der Sonnenstrahlung, sondern sie folgt einem linearen Gesetz von der Formn=a. cos +b. Diese Gestzmässigkeit kann erklärt werden, wenn man die Schichtbildung nach denChapman'schen Ansätzen für eine gekrümmte Erde berechnet und einen Ionenvernichtungsprozess voraussetzt, demzufolge die Vernichtung der Ionen ihrer jewwiligen Konzentration linear proportional ist.Die genannten Grössena andb sind zeitlich und örtlich variabel, aus ihren Veränderungen schliessen wir auf Temperaturverhältnisse in der Ionosphäre, die dadurch ausgezeichnet sind, dass sie in ähnlicher Weise auch in der viel tiefer liegenden Stratosphäre wiedergefunden werden: In polaren Gegenden herrschen darnach im Polarsommer höhere, im Polarwinter dagegen tiefere Temperaturen als in den gemässigten Breiten.

---

Summary In the ionospheric F-layer the electron densityn increases with the formulan=a. cos+b in the morning ( is meaning the zenithangle of the sun). This experimental result may be explained by consideration of earth-curvature and by assumption of a linear recombination-law equally an attachment process. The constantsa andb vary with season and location. We conclude the temperature from these variations and we find for polar locations a greater temperature in the summer and on the other hand a smaller temperature in the winter as for temperate latitudes.

     

Attenuation and dispersion ofSH waves due to scattering by randomly distributed cracks

The effect of randomly distributed cracks on the attenuation and dispersion ofSH waves is theoretically studied. If earthquake ruptures are caused by sudden coalescence of preexisting cracks, it will be crucial for earthquake prediction to monitor the temporal variation of the crack distribution. Our aim is to investigate how the property of crack distribution is reflected in the attenuation and dispersion of elastic waves.We introduce the stochastic property, in the mathematical analysis, for the distributions of crack location, crack size and crack orientation. The crack size distribution is assumed to be described by a power law probability density (p(a) a ^– fora _minaa _max according to recent seismological and experimental knowledge, wherea is a half crack length and the range 13 is assumed. The distribution of crack location is assumed to be homogeneous for the sake of mathematical simplicity, and a low crack density is assumed. The stochastic property of each crack is assumed to be independent of that of the other cracks. We assume two models, that is, the aligned crack model and the randomly oriented crack model, for the distribution of crack orientation. All cracks are assumed to be aligned in the former model. The orientation of each crack is assumed to be random in the latter model, and the homogeneous distribution is assumed for the crack orientation. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.We observe the following features common to both the aligned crack model and the randomly oriented crack model. The attenuation coefficientQ ^–1 decays in proportion tok ^–1 in the high frequency range and its growth is proportional tok ² in the low frequency range, wherek is the intrinsic wave number. This asymptotic behavior is parameter-independent, too. The attenuation coefficientQ ^–1 has a broader peak as increases and/ora _min/a _max decreases. The nondimensional peak wave numberk _p a _max at whichQ ^–1 takes the peak value is almost independent ofa _min/a _max for =1 and 2 while it considerably depends ona _min/a _max for =3. The phase velocity is almost independent ofk in the rangeka _max<1 and increases monotonically ask increases in the rangeka _max>1. While the magnitude ofQ ^–1 and the phase velocity considerably depend on the orientation of the crack in the aligned crack model, the above feature does not depend on the crack orientation.The accumulation of seismological measurements suggests thatQ ^–1 ofS waves has a peak at around 0.5 Hz. If this observation is combined with our theoretical results onk _p a _max, the probable range ofa _max of the crack distribution in the earth can be estimated for =1 or 2. If we assume 4 km/sec as theS wave velocity of the matrix medium,a _max is estimated to range from 2 to 5 km. We cannot estimatea _max in a narrow range for =3.     

Nonequilibrium thermodynamics of pressure solution

This paper is concerned with the thermodynamic theory of solution and precipitation processes in wet crustal rocks and with the mechanism of steady pressure-solution slip in contact zones, such as grain-to-grain contacts, fracture surfaces, and permeable gouge layers, that are infiltrated by a mobile aqueous solution phase. A local dissipation jump condition at the phase boundary is fundamental to identifying the thermodynamic force driving the solution and precipitation process and is used here in setting up linear phenomenological relations to model near-equilibrium phase transformation kinetics. The local thermodynamic equilibrium of a stressed pure solid in contact with its melt or solution phase is governed by Gibbs's relation, which is rederived here, in a manner emphasizing its independence of constitutive assumptions for the solid while neglecting surface tension and diffusion in the solid. Fluid-infiltrated contact zones, such as those formed by rough surfaces, cannot generally be in thermodynamic equilibrium, especially during an ongoing process of pressure-solution slip, and the existing equilibrium formulations are incorrect in overlooking dissipative processes tending to eliminate fluctuations in superficial free energies due to stress concentrations near asperities, defects, or impurities. Steady pressure-solution slip is likely to exhibit a nonlinear dependence of slip rate on shear stress and effective normal stress, due to a dependence of the contact-zone state on the latter. Given that this dependence is negligible within some range, linear relations for pressure-solution slip can be derived for the limiting cases of diffusion-controlled and interface-reaction-controlled rates. A criterion for rate control by one of these mechanisms is set by the magnitude of the dimensionless quantityk/2C _pD, wherek is the interfacial transfer coefficient, is the mean diffusion path length,C _p is the solubility at pressurep, andD is the mass diffusivity.     

The upper mantle structure of the yakutian kimberlite province,eastern Russia

Deep seismic sounding in the region of the Mirnyi kimberlite field indicates that the boundary velocity of the uppermost mantle is elevated (v _b=8.6–8.8 km/sec) and extremely variable near the Mir kimberlite pipe. These velocity heterogeneities are probably associated with the kimberlite magmatism and may be useful in the identification of other kimberlite fields.     

The dependence of water potential in shoots of Picea abies on air and soil water status

Where there is sufficient water storage in the soil the water potential (_x) in shoots of Norway spruce [Picea abies (L.) Karst.] is strongly governed by the vapour pressure deficit of the atmosphere, while the mean minimum values of _x usually do not drop below -1.5 MPa under meteorological conditions in Estonia. If the base water potential (_b) is above -0.62 MPa, the principal factor causing water deficiency in shoots of P. abies may be either limited soil water reserves or atmospheric evaporative demand depending on the current level of the vapour pressure deficit. As the soil dries the stomatal control becomes more efficient in preventing water losses from the foliage, and the leaf water status, in turn, less sensitive to atmospheric demand, Under drought conditions, if _b falls below -0.62 MPa, the trees water stress is mainly caused by low soil water availability. Further declines in the shoot water potential (below -1.5 MPa) can be attributed primarily to further decreases in the soil water, i.e. to the statie water stress.     

Temporal variations in the fractal properties of seismicity in the North Anatolian Fault Zone between 31°E and 41°E

We investigate the nature of temporal variations in the statistical properties of seismicity associated with the North Anatolian Fault Zone between longitudes 31°–41°E during the instrumental period 1900–1992. Temporal variations in the seismicb value and the fractal (correlation) dimensionD _c of earthquake epicenters are examined for earthquakes of magnitudeM _S 4.5, using sliding windows of 100 consecutive events.b varies temporally between 0.6 and 1.0, andD _c between 0.6 and 1.4, both representing significant fluctuations above the errors in measurement technique. A strong negative correlation (r=–0.85) is observed betweenb andD _c , consistent with previous observation of seismicity in Japan and southern California. Major events early in this century (M _S 7) are associated with lowb and highD _c , respectively consistent with greater stress intensity and greater spatial clustering of epicenters—both implying a greater degree of stress concentration at this time.     

The gravitational field of topographic-isostatic masses and the hypothesis of mass condensation II-the topographic-isostatic geoid

In Part I we focussed on a convergent representation of the gravitational potential generated bytopographic masses on top of the equipotential surface atMean Sea Level, thegeoid, and by those masses which compensate topography. Topographic masses have also been condensated, namely represented by a single layer. Part II extends the computation of the gravitational field of topographic-isostatic masses by a detailed analysis of itsforce field in terms ofvector-spherical harmonic functions. In addition, the discontinuous mass-condensated topographic gravitational force vector (head force) is given. Once we identify theMoho discontinuity asone interface of isostatically compensated topographical masses, we have computed the topographic potential and the gravitational potential which is generated by isostatically compensated masses atMean Sea Level, the geoid, and illustrated by various figures of geoidal undulations. In comparison to a data oriented global geoid computation ofJ. Engels (1991) the conclusion can be made that the assumption of aconstant crustal mass density, the basic condition for isostatic modeling, does not apply. Insteaddensity variations in the crust, e.g. betweenoceanic and continental crust densities, have to be introduced in order to match the global real geoid and its topographic-isostatic model. The performed analysis documents that thestandard isostatic models based upon aconstant crustal density areunreal.     

The Terrain Correction in a Moving Tangent Space

Conventionally the terrain/topographic reduction is based on the Bouguer Plate, which is flat and extends in the local tangent plane/horizontal plane to infinity. Here we aim at an error estimate of such a planar approximation of the Newton integral of the type of a disturbing potential and gravitational disturbance as linearized forms of the gravitational potential and the modulus of gravitational field intensity. To effect this quality control of the conventional terrain reduction, we first transform the spherical Newton functional from an equatorial frame of reference to an oblique meta-equatorial frame of reference with the evaluation point as a meta-North pole, and then by means of an oblique equiareal map projection of the azimuthal type to a tangent plane which moves at the evaluation point. The first term of these transformed Newton functionals is the planar approximation. The difference between the exact Newton kernels and their planar approximation are plotted and tabulated in Tables 1-3. Three configurations are studied in detail: for points at radius r = 10 km around the evaluation point the systematic error varies from 0.26% for a spherical height difference of the order of H – H* = 5 km, more than 0.80% for a spherical height difference of the order of H – H* = 1 km, and more than 1.60% for a spherical height difference of H – H* = 500 m. In contrast, the systematic error for spherical height difference H – H* = 1 km at a distance of r = 1000 km from the evaluation point increases to 44%. Indeed, the newly derived exact Newton kernels which are of the convolution type and are represented in the tangent space moving with the evaluation point can be preferably used with little extra computational effort.     

A branching model for crack propagation

Summary A branching model for crack propagation is proposed, a branch corresponding to an existing microfissure or flaw in the material, and the propagation of the crack to the coalescence of such branches. Increase in external stress increases the probability that a given branch will link into more than a specified number of further branches. Such increases can continue until a critical state is reached when the mean number of branches linking into a given branch is equal to unity; beyond this point, the system becomes unstable, and any slight movement is likely to lead to catastrophic rupture. The distribution of the sums of the lengths of the branches linked together in a cracking episode is investigated, and shown to lead, in the critical case, to a Gutenberg-Richter type relation with parameterb=0.75. Departures from this value are attributed to the influence of the distribution of the lengths of preexisting fissures, this distribution varying with the strength of the material and its stress history. Some difficulties with the theoretical model of Scholz are raised, and it is suggested that a more complete analysis of Scholz's model should lead to results qualitatively similar to those obtained for the branching model.     

First Results of Hydrogeochemical Measurements in the Soos Area,Czech Republic

For some years, the Saxon Academy of Sciences at Leipzig (SAW) is engaged in the research project Contributions to Environmental Research by means of Radiometric-Geochemical Methods in the Vogtland area (Germany). The main goal is to investigate the hydrogeological and hydrochemical parameters of mineral springs in that region and their interrelations. Here, the high CO ₂ degassing rates are of particular interest. The isotopic signature of these gases indicates an anomalous high mantle/crust contribution (Weinlich et al., 1999). A further geoscientifically important phenomenon of this region is the high seismicity, in particular the Vogtland/NW Bohemian earthquake swarms. Therefore, we have tried to use the mantle-originated fluids as transport media for information from the seismogenic horizons. The variations of the parameters recorded continuously at the springs for years show a connection to the seismic events of the epicentral area of Nový Kostel in the Czech Republic. In particular, numerous anomalous degassing intervals were recorded at the mineral spring Wettinquelle (formerly: Radonquelle), Bad Brambach, prior to earthquakes occurred in the region of Nový Kostel.     

Density fluctuations measured by ISEE 1–2 in the Earth’s magnetosheath and the resultant scattering of radio waves

Radio waves undergo angular scattering when they propagate through a plasma with fluctuating density. We show how the angular scattering coefficient can be calculated as a function of the frequency spectrum of the local density fluctuations. In the Earths magnetosheath, the ISEE 1–2 propagation experiment measured the spectral power of the density fluctuations for periods in the range 300 to 1 s, which produce most of the scattering. The resultant local angular scattering coefficient can then be calculated for the first time with realistic density fluctuation spectra, which are neither Gaussian nor power laws. We present results on the variation of the local angular scattering coefficient during two crossings of the dayside magnetosheath, from the quasi-perpendicular bow shock to the magnetopause. For a radio wave at twice the local electron plasma frequency, the scattering coefficient in the major part of the magnetosheath is b(2f_p) 0.5–4 × 10^–9 rad²/m. The scattering coefficient is about ten times stronger in a thin sheet (0.1 to IR_E) just downstream of the shock ramp, and close to the magnetopause.