Effects of a uniaxial compression on remanent magnetizations of igneous rocks

Summary Characteristics of remanent magnetization of an igneous rock under a uniaxial compression are divided into those of the soft component and those of the hard component. The soft component of remanent magnetization irreversibly decreases with an increase of compression () regardless whether the axis of is parallel or parpendicular to the direction of magnetization. The hard component changes reversibly with : the magnetic intensity of hard component increases with when the axis of is perpendicular to the magnetization, whereas it decreases with when the axis of is parallel to the magnetization.Theoretically, the irreversible change of the soft component is attributable to the irreversible movement of 90° domain walls which results in the pressure demagnetization effect, while the reversible change of the hard component is due to the reversible rotation of spontaneous magnetization within those domains which are so tightly fixed by large effective anisotropy energy that the induced magnetoelastic energy cannot drive their 90° walls.In natural remanent magnetization of igneous rocks, the soft component corresponds to either one or all of isothermal remanent magnetization, viscous remanent magnetization and piezo-remanent magnetization, whereas the hard component is mostly due to thermo-remanent magnetization.     

Analysis of State of Stress During The 1997 Earthquake Swarm In Western Bohemia

Focal mechanisms of 70 events of the January 1997 earthquake swarm were analysed using the Gephart and Forsyth method to determine the state of stress in the West Bohemia/Vogtland region and to reveal possible stress variations during the swarm activity. The method was applied to the whole set of 70 focal mechanisms and to several subsets distinguishing magnitudes of events and the spatial and temporal distribution of the swarm. The three representative stress models A ( ₁ ,A: 0/45 (az/dip), ₂ A: 134/35, ₃ A: 243/25), B ( ₁ ,B: 162/38, ₂ B: 263/14, ₃ B: 10/49), and C ( ₁ C: 135/30, ₂ C: 1/50, ₃ C: 239/23) which could characterise the state of stress in the region were found. Model C can be considered to be the most probable stress model because of its consistency with the European stress field. The results of the stress analysis applied to the individual subsets of focal mechanisms indicate that the state of stress was more uniform during the first phase of the swarm. To distinguish between the fault plane and the auxiliary plane of fault plane solutions a statistical approach was used. The results showed that the fault planes striking NW-SE and dipping 45° to NE were activated during the swarm.     

Mass transport in rotatory tidal currents

Summary A perturbation method is used to calculate steady non-linear effects in rotatory tidal currents. The inclusion of the Coriolis acceleration leads to a uniquely determined second order current system in the tidal stream. This is shown to be absent in high frequency gravity waves. It is found that particle drift, or mass transport, is critically dependent on this mean current, and consequently on the value off/,f being the Coriolis parameter, and the angular frequency of the oscillation.     

Anisotropic magnetic susceptibility of rocks under mechanical stresses

Summary The magnetic susceptibility of a rock under a uniaxial compression () decreases along the axis of compression and increases along the direction perpendicular to the axis, with an increase of . Thus, the magnetic susceptibility of a compressed rock becomes anisotropic.The decrease of longitudinal susceptibility,K (), and the increase of transverse susceptibility,K (), are theoretically derived from a model of rock which assumes the uniaxial anisotropy and the isotropic magnetostriction of magnetic minerals in rocks and a random orientation of the minerals. Results show thatK () decreases toward zero whereasK () increases and approaches a finite asymptotic value with an increase of , and –(/)K () is twice as large as /K () for small values of . These results are in good agreement with experimental data.

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Zusammenfassung Die magnetische Suszeptibilität eines Steines unter zunehmender uniachsigen Druckspannung () nimmt ab längs der Achse der Druckspannung und nimmt zu längs der Richtung senkrecht der Achse. Somit wird die magnetische Suszeptibilität des gedrückten Steines anisotrop.Die Abnahme der longitudinalen Suszeptibilität,K (), und die Zunahme der transversalen Suszeptibilität,K (), werden theoretisch von einem Modell eines Steines hergeleitet, das die uniachsige Anisotropie, die isotrope Magnetostriktion, und eine nichtbevorzugte Orientierung der magnetischen Minerals im Stein annimmt. Die Ergebnisse zeigen, dass mit einer Zunahme des ,K () gegen Null abnimmt, währendK () zunimmt und sich einem begrenzten asymtotitschen Wert nähert und, dass für kleine Werte des , –(/)K () zweimal so gross wie /K () ist. Diese Ergebnisse stimmen gut mit den Versuchangaben überein.

     

Identity of the characteristics of electrodynamic seismographs with non-standard periods of seismometers and galvanometers

Summary The maximum changes of magnification were determined for electrodynamic seismographs with standard characteristics and for some experimental long-period seismographs, the constants of which are given in Tab. 1, when the period of the seismometer or galvanometer has a deviation of not more than 5% from the standard value. Under the assumption of control of the other constants of the seismograph, identical amplitude and phase responses with a small change of the absolute magnification of the seismograph may be achieved with characteristicsAII ( ² >0.2), AIV ( ² 0.4), B ( ² >0.3) Nos28, 32 and33. This deviation can also be compensated by adjusting the optical distance. The procedure of adjusting the identical characteristics is suitable for systems with which an accurate setting of the period is difficult and for systems with an uncontrollable period, provided their values are within the limits of allowed deviations from the standard constants.     

Sealing law of far-field spectra based on observed parameters of the specific barrier model

A set of acceleration source spectra is constructed using the observed parameters of the specific barrier model of Papageorgiou and Aki. The spectra show a significant departure from the ²-model at the high frequency range. Specifically, the high frequency spectral amplitudes of seismic excitation are higher as compared to the level predicted by the ²-model. This is also supported by other observational evidence. The high frequency amplitudes of acceleration scale proportionally to the square root of the rupture areaS, to the rupture spreading velocityv, and to the local strain drop (/) (=strain drop in between barriers). The local strain drop in between barriers is not related in a simple way to the global strain drop, which is the strain drop estimated by assuming that it is uniform over the entire rupture area. Consequently, the similarity law does not apply. Using the source spectra which we constructed, we derive expressions for high frequency amplitudes of acceleration such asa _rms anda _max. Close to the fault both are independent of fault dimensions and scale as (/µ)(f)^1/2, while away from the fault plane they scale asW ^1/2(/µ)(f)^1/2, whereW is the width of the fault and f is the effective bandwidth of the spectra.     

Complexities of rock fracture and rock friction from deformation of Westerly granite

A series of rock friction experiments has been carried out to study the complexities in rock fracture and rock friction. Intact Westerly granite samples were loaded to shear failure in a laboratory polyaxial loading apparatus. The resultant fractured samples were reloaded to cause frictional sliding. Both polyaxial loading (₁ > ₂ > ₃ > 0) and equal confining condition (₁ > ₂ = ₃ > 0) were used. The deformation processes were monitored by macroscopic axial stress-strain, optical holography, and ultrasonic velocity measurements.Intense localized deformation along the fracture occurred very early in the loading of fractured samples. Contacts on the fracture surfaces continuously broke during loading. No acoustic velocity anomaly was observed for the fractured sample, in contrast to a 25% drop in the velocity before the failure of the corresponding intact sample. The current study and previous research suggest that the deformation localization is an important process in governing the instability of rock friction. Instability analysis of rock friction needs to include not only the deformation processes along the sliding surfaces, but also those adjacent to the fractures such as the localized deformation along the fractures observed in the current study. The instability analysis of rock friction with rate- and state-dependent friction laws does not specifically include the deformation localization adjacent to the faults and thus ignores an important class of instability as described byRudnicki (1977).A dependence of frictional strengths on the stress components normal to the sliding and in the plane of the fracture surface was observed. This dependence can be understood by considering the loading of the irregular fracture surface under polyaxial loading conditions. This observation requires the friction laws in the macroscopic scale to be modified for those cases where the three principal stresses (₁, ₂, and ₃) are significantly different.     

Velocity changes associated with generalized triaxial deformation of pyrophyllite

Compressional and shear-wave velocities (V _p andV _s ) were measured during the generalized triaxial deformation (i.e. _{1 2}=2 ₃) of pyrophyllite. Observed velocity changes could be ascribed to crack development during dilatancy. Velocity changes were very localized with respect to the ultimate failure plane. The orientation and development of the failure plane was continuously observed with laser holography. Velocity reverals, i.e. changes from a decreasing trend to an increasing trend, were documented in a wet sample in bothV _p andV _s . These changes in bothV _p andV _p are inconsistent with dialatancy-diffusion models. The reversals were interpreted as a reflection of local stress reorientation caused by a slowly propagating fault.     

Zur Analyse der Genauigkeit von mehrmals mit einer Gravimetergruppe gemessenen gravimetrischen Verbindungen

Summary In order to evaluate the accuracy of measurements repeated by a set of gravimeters the semi-systematic errors ₂ and ₃ were introduced besides the random error ₁ in[1]. It is shown that Eqs.(10) and(11), given in[1], should not be used to determine these errors, but Eqs.(8) and(9).     

On one generalization of trochoidal waves

Summary The concept of the generalized trochoidal waves discussed in[1] is revised and modified. A new formula defining the auxiliary function (b, c) was found with the aid of the results derived in[3] and some physical considerations.     

Changes of electric conductivity in the neighbourhood of the curie temperature of basalts

Summary In investigating the electric conductivity of rocks as a function of the temperature it was found that rocks containing ferrimagnetic minerals display a change in the slope of the functionlg =f(1/T) in the neighbourhood of the Curie temperature . In order to explain these changes the curveslg =f(1/T) and the Curie temperatures , obtained from the temperature dependence of the saturated magnetization J_s=f(T), were compared. Eight samples of basalts, 2 samples of haematite and magnetite were used to demonstrate the relation between and the changes in the pattern of the electric conductivity, caused by the variations of the exchangeable energy of ferrimagnetic minerals.     

Variation of certain parameters of regional stress tensor under condition of rockburst hazard

The feasibility of gaining valuable geomechanical information derived from seismological data and its specialist interpretation for utilisation in the area of assessing hazards due to mining tremors and rockbursts has become a development of signal importance in mining seismology. Undoubtedly of particular interest is a certain knowledge of the directions of the principal stresses ₁, ₂, ₃ of the regional stress tensor. For their determination, use is made of a set of parameters from the mining tremors' regional focal mechanism solutions (angular parameters of nodal planes and axes of principal stresses in the tremor focus —P andT). Results of research conducted at the Szombierki and Wujek mines and analysis of calculated results for parameters of regional stress tensor show that there exist appreciable differences between values of these parameters and also a clear correlation with local extraction conditions that is of significance from the point of view of seismic hazard.     

Solution of stochastic groundwater flow by infinite series,and convergence of the one-dimensional expansion

This paper investigates analytical solutions of stochastic Darcy flow in randomly heterogeneous porous media. We focus on infinite series solutions of the steady-state equations in the case of continuous porous media whose saturated log-conductivity (lnK) is a gaussian random field. The standard deviation of lnK is denoted . The solution method is based on a Taylor series expansion in terms of parameter , around the value =0, of the hydraulic head (H) and gradient (J). The head solution H is expressed, for any spatial dimension, as an infinite hierarchy of Green's function integrals, and the hydraulic gradient J is given by a linear first-order recursion involving a stochastic integral operator. The convergence of the -expansion solution is not guaranteed a priori. In one dimension, however, we prove convergence by solving explicitly the hierarchical sequence of equations to all orders. An infinite-order stochastic solution is obtained in the form of a -power series that converges for any finite value of . It is pointed out that other expansion methods based on K rather than lnK yield divergent series. The infinite-order solution depends on the integration method and the boundary conditions imposed on individual order equations. The most flexible and general method is that based on Laplacian Green's functions and boundary integrals. Imposing zero head conditions for all orders greater than one yields meaningful far-field gradient conditions. The whole approach can serve as a basis for treatment of higher-dimensional problems.     

On the diffusion of the perturbing toroidal magnetic field from the core to the mantle

Zusammenfassung Es werden die Wurzeln einer charakteristischen Gleichung für die Randbedingung der Diffusion des toroidalen magnetischen Störungsfeldes berechnet, das in dünner Schicht unterhalb der Grenze Kern — Mantel, als eine Folge von Störung der Winkelgeschwindigkeit dieser Schicht in Anwesenheit des magnetischen Dipolfeldes induziert wird. Die Wurzeln werden für verschiedene Werte des Verhältnisses der Leitfähigkeit des Erdmantels und Erdkerns ausgerechnet. Es wird gezeigt, dass das aus dem Milieu mit der elektrischen Leitfähigkeit in das Milieu mit elektrischer Leitfähigkeit _m diffundierende toroidale magnetische Störungsfeld vom Werte _m/<10^–2 an von dem Verhältnis elektrischer Leitfähigkeiten beider Milieus unabhänging bleibt.     

A remark on the hydrostatic approximation

Summary For an autobarotropic atmosphere the exact linearized equations of motion can be solved for the pressure oscillation when =0 and =2 (=frequency of oscillation, =angular velocity of the earth's rotation). The pressure computed in this way is shown to be in close agreement to the pressure computed by using the hydrostatic approximation.     

On the Upper Bound of the Liquid Core Viscosity

By using Molodensky and Sasao (1995a) and Molodensky and Groten (1998) an approach of expansion in powers of the small parameter =(+)/ (where + and are the frequencies of nutational motion in space and in a mantle-fixed reference frame, respectively, is tidal frequency) a theory of diurnal Earth tides and nutation for a realistic model of the Earth with an inhomogeneous, viscous liquid core and an anelastic mantle is constructed. It is shown that our approach is self-consistent for semi-annual, annual, and principal nutational components (when ||1/180). By comparing the results of modern VLBI-nutational data and the results of our calculations, we have found the region of possible values of the parameters which describe the anelastic properties of the Earth's lower mantle and the viscosity of the liquid core. It is shown that modern VLBI-data are about six orders of magnitude more sensitive to the liquid core viscosity than modern seismic data or Earth free oscillations data.     

Physical parameters governing the formation of Pele's hair and tears

The physical parameters that affect the formation of Pele's hair and Pele's tears during lava fountaining are discussed. Experiments on ink jets produced from a nozzle under different Weber number (We) and Reynolds number (Re) show the following results: if (Re) is relatively large compared with (We), an ink droplet is produced. However, if (Re) is relatively small and (We) is large, the spurting ink becomes thread-like. I define the Pele number (Pe) as (We)/(Re), which is expressed as v/₀, where v is the spuring velocity from an erupting vent, and are viscosity and interfacial tension of the erupting magma, and and ₀ are density of air and magma. The experimental results from ink jets suggest that Pele's hair will be produced for larger (Pe), while Pele's tears are very likely produced for relatively small (Pe). I conclude that Pele's hair could be produced when the spurting velocity of erupting magmas is high, and Pele's tears when it is relatively low. As an additional point of interest, the similarity of SEM photographs of the characteristic shape of Pele's hair to those of the failed products of commercial glass fibre are shown.     

Mean densities of Pre-Devonian sedimentary rocks in Poland and their depth dependence

Summary Since 1945 in Poland density measurements have been completed on drilling samples to obtain data for reduction and interpretation of geophysical results. In this paper the developments in density measurements techniques and data processing in Poland are reviewed. Mean density maps have been constructed for the following Pre-Devonian divisions: Volhynian, Valdai and Subholmian Cambrian, Holmian and Protoolenus Cambrian, Middle Cambrian, Lower Ordovician, Middle Ordovician, Upper Ordovician, Lower Silurian, Middle Silurian, Upper Silurian. On the basis of the same data the dependence of mean densities on the present depth of all the above divisions has been examined. This dependence has been approximated by regression equations of the following type: (h)= ah + b , (h) = ah² + bh + c, (h)= alnh + b((h): mean density,h: present depth). In addition to the coefficients of these equations the correlation coefficient, regression standard error, and confidence intervals have been calculated. Analysis of the results obtained revealed a dominant effect of compaction on the mean density values. Hypotheses have been presented concerning other geological factors responsible for the variation of these values. Regression curves constructed for the individual stratigraphic horizons served to estimate the maximum earlier depth of the Palaeozoic rocks of the Holy Cross Mountains and their vertical displacement. Similar studies have been completed for two adjacent boreholes situated in the Bug River depression. Their results indicate that mean density values can readily serve to estimate the amount of vertical tectonic displacement.     

Numerical simulations of non-ergodic solute transport in three-dimensional heterogeneous porous media

Numerical simulations of non-ergodic transport of a non-reactive solute plume by steady-state groundwater flow under a uniform mean velocity, , were conducted in a three-dimensional heterogeneous and statistically isotropic aquifer. The hydraulic conductivity, K(x), is modeled as a random field which is assumed to be log-normally distributed with an exponential covariance. Significant efforts are made to reduce the simulation uncertainties. Ensemble averages of the second spatial moments of the plume and the plume centroid variances were simulated with 1600 Monte Carlo (MC) runs for three variances of log K, _Y²=0.09, 0.23, and 0.46, and a square source normal to of three dimensionless lengths. It is showed that 1600 MC runs are needed to obtain stabilized results in mildly heterogeneous aquifers of _Y²0.5 and that large uncertainty may exist in the simulated results if less MC runs are used, especially for the transverse second spatial moments and the plume centroid variance in transverse directions. The simulated longitudinal second spatial moment and the plume centroid variance in longitudinal direction fit well to the first-order theoretical results while the simulated transverse moments are generally larger than the first-order values. The ergodic condition for the second spatial moments is far from reaching in all cases simulated and transport in transverse directions may reach ergodic condition much slower than that in longitudinal direction.     

Estimation of long wave radiation by an empirical method

Summary Utilising two years data collected at two tropical coastal stations, Madras (13°04N, 80°15E) and Waltair (17°42N, 83°18E) and for one tropical continental station, Nagpur (21°09N, 79°07E), the authors have re-evaluated the constants ofBrunt's regression equation. Analyses of the observations for Waltair and Nagpur show good correlation coefficients (r) between the values of the effective emissivity of the atmosphere (the effective emissivity is the ratio of incoming long-wave sky radiation at the surfaceR _s , to black body radiation T ⁴) and the square root values of surface vapour pressuree (mb). The value ofr for Waltair from radiometer observations is 0.98. It is also determined for Waltair and Nagpur from Ångström compensation pyrgeometer observations as 0.83 and 0.91 respectively. A low correlation co-efficient 0.56 is obtained for Madras. It might be due to higher surface vapour pressure values at Madras than at Waltair and Nagpur. The applicability of the reduced regression equations are examined for different years for the different stations. The agreement between the computed values with the new regression equations and the observed long-wave sky radiation at the surface seems to be quite good.