On the problem of equal area block on a sphere

Summary A new untraditional way of dividing the sphere surface into an arbitrary number of equal area blocks by means of a spiral is proposed and its statistical properties are analysed.     

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.     

Elastic Parameters of West Bohemian Granites under Hydrostatic Pressure

—The West Bohemian seismoactive region is situated near the contact of the Moldanu bian, Bohemian and Saxothuringian units in which a large volume is occupied by granitoid massifs. The spatial distribution of P-wave velocities and the rock fabric of five representative samples from these massifs were studied. The P-wave velocities were measured on spherical samples in 132 independent directions under hydrostatic pressure up to 400 MPa, using the pulse-transmission method. The pressure of 400 MPa corresponds to a depth of about 15 km in the area under study. The changes of P-wave velocity were correlated with the preferred orientations of the main rock fabric elements, i.e., rock forming minerals and microcracks. The values of the P-wave velocity from laboratory measurements on granite samples fit the velocity model used by seismologists in the West Bohemian seismoactive region.     

Experimentally Determined P-Wave Velocity Anisotropy for Rocks Related to the Western Bohemia Seismoactive Region

The elastic properties of granites from Western Bohemia which we measured and published earlier have been supplemented with measurements of olivine nephelinite from the same region and with data on lherzolitic xenolith from the vicinity of elezný Brod. The set of velocities measured under laboratory conditions has been compared with depth profiles suggested for the purpose of locating seismic swarm events which occur in this region. P-wave velocities were measured under pressures of up to 400 MPa. This pressure corresponds to depths of about 15 km for this region. The data were extrapolated for larger depths. Comparing laboratory measurements and seismic profiles, we can conclude that the rocks under study may be constituents of crust structures.     

Search for orthorhombic or higher symmetry in rocks

Summary The properties of quadrics of stress and strain, which were derived from the eigenvectors of the matrix of elastic constants, are analysed for a medium with orthorhombic or higher symmetry. It was found that the orientation of the axes of the quadrics can be employed to determine the crystallographic axes of the medium. This formalism derived for minerals is used for finding the axes of the internal symmetry of a rock for which we assume a distribution close to that of the orthorhombic system with a view to the spatial distribution of P-wave velocities.     

Magnitude classification of rock bursts based on seismic records of mining stations

Summary A method was developed for classifying the intensity of seismic events observed in the Karviná part of the Ostrava—Karviná mining district. The method is based on determining the magnitude of events, using the homogenized maximum amplitudes of the S-wave group. The amplitude observations were homogenized by means of station corrections estimated by successive approximation simultaneously with the derivation of the optimum calibrating function. The magnitude classification developed enables an objective and relatively simple estimation of the intensity of seismic events in mines with an accuracy corresponding to the quality of observations. The correlation between the so-called accepted energy, currently used for classifying rock bursts in the Ostrava—Karviná mining district, and the corresponding magnitudes was established.

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Резюме Оnuсaн меmо?rt; меmо?rt; каaссuфuкaцuu сеŭсмuческuх явлеuŭ нaблю?rt;aемых в кaрвuнскоŭ чaсmu Осmрaвско-Кaрвuнскоŭ у?rt;ольноŭ облaсmu. Меmо?rt; основaн нa оnре?rt;еленuu мa?rt;нumу?rt;ы явленuŭ. Для эmоŭ зa?rt;aчu uсnользовaны мaксuмaльные aмnлumу?rt;ы в ?rt;руnnе S-волн. О?rt;норо?rt;носmь нaблю?rt;енuŭ ?rt;осmu?rt;нуma сmaнцuоннымu nоnрaвкaмu, коmорые оnре?rt;елялuсь о?rt;новременно с оnmuмaльноŭ кaлuбровочноŭ функцuеŭ. Пре?rt;ложеннaя клaссuфuкaцuя ?rt;aёm нa?rt;ёжную u оmносumельно nросmую оценку uнmенсuвносmu сеŭсмuческuх явленuеŭ в у?rt;ольном бaссеŭне с mочносmью оmвечaюшеŭ кaчесmву нaблю?rt;енuŭ. Усmaновленa корреляцuя меж?rt;у, maк нaзывaемоŭ, nрuняmоŭ энер?rt;uеŭ явленuя, оnре?rt;елённоŭ nо меmо?rt;uке uсnользуемоŭ нa nрaкmuке Осmрaвско-Кaрвuнскuх щaхm, u сооmвеmсmвуюшеŭ мa?rt;нumу?rt;оŭ.

     

Laboratory Approach to the Study of Elastic Anisotropy on Rock Samples

—The experimental approach (hardware and software) to the study of the elastic an isotropy of rocks on spherical samples under hydrostatic pressure up to 400 MPa is discussed. A substantial innovation of the existing measuring system and processing methods enabled us to make a detailed investigation and evaluation of the kinematic as well as dynamic parameters of elastic waves propagating through anisotropic media. The innovation is based on digital recording of the wave pattern with a high sampling density of both time and amplitude. Several options and results obtained with the innovated laboratory equipment are presented.