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General energetic analysis of fracture instabilities in elastic media and the elastic field rupture

Domański B.M.

Acta Geophysica

2010

Vol. 58, no. 2

174-194

The singular integral equations method makes it possible to determine a general analytical solution to the problem of a crack subjected to any stresses, including singular ones. The singularity of stresses means that they tend to infinity in the concentration point. In exponential functions describing this relationship, the exponent characterizes the stress curvature growth. Also the energy released by crack opening can be described by a simple analytical formula. The problem is solvable for an exponent greater than –1. The class of all the cracks subject to stresses that exponentially grow to one of the crack ends is divided into three sub-classes. One of these embraces most of crack types, also Griffith’s. The remaining two are a source of microcracks in an elastic medium. The onset of such a stress concentration gives rise to a microcrack which cancels the stress singularity up to that with the exponent of –1/2, ensuring a strong stability of the medium. An analysis of the nucleation of such cracks brought about a concept of elastic field rupture without destruction of interatomic bonds, which has implications relating to the conductivity of metals. A general formula for the crack energy singles out a special crack of unit length, whose energy is constant and independent of stress concentration.

Source parameters of the 2004 Kaliningrad earthquakes

Domański B.M.

Acta Geophysica

2007

Vol. 55, no. 3

267-287

An analysis of source parameters of the two unexpected earthquakes from the Kaliningrad (Russia) area is presented. The earthquakes occurred on 21 September 2004 at 11:05:01 and 13:32:31 UT, respectively. The first event was located at the latitude φ= 54.924°N and the longitude λ= 20.120°E, with a depth h = 16 km, and the second event at φ= 54.876°N, λ= 20.120°E and h = 20 km. Magnitudes Mw of the two events were very similar: 5.1 and 5.2. The magnitude values reported by various international data centers have been meaningfully different. The reason is the presence of high-frequency components in Z velocity component of the S wavefield. They were observed along the direction defined by two stations, BLEU in Sweden and SUW in Poland, located in opposite sides of the source. Along the direction perpendicular to it, the effects are relatively very small. The high-frequency waves are understood to mean components in the 6-8 Hz band for event 1 and 2-4 Hz for event 2. The effects in question are also clearly visible on displacement spectrograms. The magnitude values calculated at such stations from S-wave amplitudes or from seismic spectra are clearly overestimated and are close to 6. Therefore, we made a careful selection of channels in order to determine the spectral parameters and, on this basis, the source parameters. The size of the source is relatively small, of about 2 km. The closest seismic station is at 100 source radii from the source. One can clearly see the effect of the TT zone which markedly reduces the seismic moment value for seismic stations laying on the opposite sides of the source. Both events have very similar spatial dis-tributions of the source parameters: magnitude, seismic moment and radius.