Influence of crack distribution of rocks on P‐wave velocity anisotropy – a laboratory and field scale study‡

The purpose of this paper is the comparison of P‐wave velocity and velocity anisotropy, measured at different scales under laboratory and field conditions. A shallow seismic refraction survey with shot/receiver spacing of up to 10 m was carried out on a flat outcrop of lhertzolite in the southern part of the Balmuccia massif. Oriented rock samples were also obtained from the locality. The particular advantage of the laboratory method used is the possibility of measuring velocity in any direction under controlled conditions. Laboratory tests were made on spherical peridotite samples, 50 mm in diameter, by ultrasonic velocity measurements in 132 directions (meridian and parallel networks) under confining stress ranging from atmospheric to 400 MPa. The mean P‐wave velocity of the field and laboratory data differed by between 20–30%. In addition, P‐wave velocity anisotropy of 25% was detected in the field data. Whereas the anisotropy in the laboratory samples in the same orientation as the field surveys was less than 2%. This observed scaling factor is related to the different sampling sizes and the difference in frequencies of applied elastic waves. With an ultrasonic wavelength of 10 mm, laboratory samples represent a continuum. The field velocities and velocity anisotropy reflect the presence of cracks, which the laboratory rock samples do not contain. Three sub‐vertical fracture sets with differing strikes were observed in the field outcrop. Estimates of fracture stiffness from the velocity anisotropy data are consistent with other published values. These results highlight the difficulty of using laboratory velocity estimates to interpret field data.     

Flaring arches

We discuss first the development of the coronal arch-shaped structure of 57000 km length which was born at or before 08:00 UT on 6 November, 1980 and became the site of 13 quasi-periodic brightenings in hard X-rays from 10:00 to 14:30 UT. The same structure became the site of a series of 17 flaring arches between 15:30 and 24:00 UT on that day. The periodicity of 19 min, defined well for the quasi-periodic variations, seems to be partly retained during the occurrence of the flaring arches.The flaring arch studied in Paper I (called SB arch) was the brightest event of this set of events. This paper presents its extended analysis and also an analysis of three other flaring arches that occurred in this configuration. All these events exhibit similar characteristics and thus demonstrate that the flaring arch is a distinct solar phenomenon with specific characteristic properties.A comparison of H, Ov, and X-ray data for the SB arch essentially confirmed, in a quantitative way, the qualitative interpretation of the flow of emitting plasma through the arch proposed in Paper I. In particular, these data show: (1) a hot conduction front producing X-rays in the least dense plasma ahead, a decelerating more dense plasma bulk seen next in Ov, and still more decelerating very dense plasma eventually visible in emission in H; (2) a gradient of densities from the primary towards the secondary footpoint, by factor 3 in X-rays, one order of magnitude in Ov, and probably more in the densest loops emitting in H; (3) the secondary footpoint with hard X-ray spectrum, predominantly excited by particle streams.Member of the Carrera del Investigador, CONICET, Argentina.     

Revivals of a coronal arch

The giant post-flare arch of 6 November 1980 revived 11 hr and 25 hr after its formation. Both these revivals were caused by two-ribbon flares with growing systems of loops. The first two brightenings of the arch were homologous events with brightness maxima moving upwards through the corona with rather constant speed; during all three brightenings the arch showed a velocity pattern with two components: a slow one (8–12 km^?1), related to the moving maxima of brightness, and a fast one (～ 35 km s^?1), the source of which is unknown. During the first revival, at an altitude of 100000 km, temperature in the arch peaked ～ 1 hr, brightness ～ 2 hr, and emission measure ～ 3.5 hr after the onset of the brightening. Thus the arch looks like a magnified flare, with the scales both in size and time increased by an order of magnitude. At ～ 100000 km altitude the maximum temperature was ?14 × 10⁶K, max.n _e? 2.5 × 10⁹cm^?3, and max. energy density ? 11.2 erg cm^?3. The volume of the whole arch can be estimated to 1.1 × 10³⁰ cm³, total energy ?1.2 × 10³¹ erg, and total mass ?4.4 × 10¹⁵g. The density decreased with the increasing altitude and remained below 7 × 10⁹ cm^?3 anywhere in the arch. The arch cooled very slowly through radiation whereas conductive cooling was inhibited. Since its onset the revived arch was subject to energy input within the whole extent of the preexisting arch while a thermal disturbance (a new arch?) propagated slowly from below. We suggest that the first heating of the revived arch was due to reconnection of some of the distended flare loops with the magnetic field of the old preexisting arch. The formation of the ‘post’-flare loop system was delayed and started only some 30–40 min later. Since that time a new arch began to be formed above the loops and the velocities we found reflect this formation.     

Vibration Effect of Near Earthquakes at Different Depths in a Shallow Medieval Mine

The shallow medieval Jeroným Mine is located at a distance of about 25 km southeast of the Nový Kostel focal zone where the most intensive seismic activity in West Bohemia (Czech Republic) has been documented. Permanent seismological monitoring has been carried out since 2004 in this mine. During the 2011 and 2014 seismic swarms, more than 1000 triggered records comprising almost 1500 earthquakes were recorded at the permanent station in the mine. Three short-term seismological experiments were accomplished during these swarms. Several temporary seismic stations were simultaneously placed in different parts of underground spaces which enabled comparison of vibration effect caused by near earthquakes in different parts of the mine. Although the depth of the lowest parts of mine is only about 60 m, a vibration effect generated by earthquakes from the Nový Kostel focal zone is not the same for the whole underground complex.     

Fourier analysis of the light curves of eclipsing variables,V

The methods of analysis of the light changes of eclipsing variables in the frequency-domain, developed in our previous papers (Kopal 1975a, b, c, d) for an interpretation of mutual eclipses in systems consisting of spherical stars, have now been extended to analyse the light variations — between minima as well as within eclipses — ofclose binaries whose components are distorted by axial rotation and mutual tidal action. Following a brief introduction (Section 1) in which the need of this new approach will be expounded, in Sections 2 and 3 we shall deduce the theoretical changes of close eclipsing systems between minima (Section 2) as well as within eclipses (Section 3), which in Sections 4 and 5 will be analysed in the frequency-domain; and explicit formulae obtained which should enable us to separate the photometric proximity and eclipse effects directly from the observed data as they stand-without the need of any preliminary ‘rectification’. Section 6 will contain the explicit forms of the expressions for photometric perturbations in the frequency-domain, due to rotational and tidal distortion of both stars; and the concluding Section 7 will then be concerned with practical aspects of the application of these new methods to an analysis of the observed light changes of close eclipsing systems — in which the proximity and eclipse effects cannot be distinguished from each other by mere inspection.     

On secular stability of rapidly rotating stars of arbitrary structure

The aim of the present paper will be to utilize Poincaré's criteria to investigate secular stability of self-gravitating configurations, of arbitrary structure, in the state of rapid rotation. The potential energy, a knowledge of which is necessary for application of these criteria, will be determined by an extension of Clairaut's method; and its evaluation in terms of suitably chosen generalized coordinates carried out explicitly to quantities of fourth order in superficial oblateness, for configurations of arbitrary internal structure.The method employed can, moreover, clearly be extended to attain accuracy of any order — at the expense of mere manipulative work which lends itself to machine automation; and the angular velocity of axial rotation can be an arbitrary function of position as well as of the time. An application of our results to homogeneous configurations in rigig-body rotation will be undertaken to demonstrate that our method, when applied to a case for which a closed solution exists, leads to results which are consistent with it.     

Computation of the elements of close eclipsing systems in the frequency-domain

The aim of the present paper will be to generalize the methods for computation of the elements of eclipsing binary systems in the frequency-domain, summarized in our recent Paper I (Kopal, 1981), to the case ofclose systems, in which photometric proximity effects become conspicuous and must be taken into account before the methods previously outlined in Paper I become directly applicable.Following a brief introduction to the subject given in Section 1, Section 2 summarizes (and comments upon) the difficulties previously encountered in separation of the photometric proximity and eclipse effects. In Section 3 we develop an alternative new approach to the problem by modulation of the light curves throughout the entire orbital cycle, intended to filter out proximity effects from the observed light changes and isolate those due to eclipses; while in Section 4 we shall present a numerical application of the new method to an analysis of the observed light changes of the eclipsing system W Ursae Maioris.In Section 5 we shall present a quantitative investigation of the photometric effects of distortion on the light changes of close eclipsing systems within eclipses-the most complicated part of the whole problem-with numerical application to the system of U Sagittae carried out in the concluding Section 6.Appendices 1–3 contain numerical data which should facilitate application of the methods developed and illustrated in Sections 3–4; while Appendix 4 will be reserved for a mathematical proof of certain expansions used in Section 5, which would have been too discursive for the main text.     

Theory of the light curves of eclipsing systems with oscillating components,II

In continuation of our preceding investigation (Kopal, 1982c) of photometric consequences of free oscillations — radial or nonradial — of the eclipsing component on the light changes of close binary systems, the aim of the present paper will be to extend the scope of our inquiry to include the effects of similar oscillations of the component which undergoes eclipse, with arbitrary period and phase.In Sections 2 and 3 which follow a brief introduction to the particular aspect of the problem treated in this paper, a theory will be given of photometric effects caused by arbitrary harmonic oscillations of the components of eclipsing binary systems distorted by equilibrium tides, or by axial rotation with constant angular velocity. A translation of these effects into the frequency domain constitutes a problem which is solvable in a closed form only if the eclipse in question ends in totality. In any other case, the desired effects can be mathematically described only in terms of infinite series (of satisfactory asymptotic properties); and a construction of their explicit forms will be given in the Appendix.