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Spin and twist motions in a homogeneous elastic continuum and cross-band geometry of fracturing

Teisseyre R.

Acta Geophysica Polonica

2004

Vol. 52, nr 2

173-183

A uniform continuum with rotation motions of spin and twist type is presented; in this approach we supplement the ideal elasticity constitutive law, the strain-stress relation, by the rotation-asymmetric stress relation. In such a way, we can evade an influence of the Hook law, which, when used as the unique law in the ideal elasticity, rules out an existence of rotation waves. Thus, in the ideal elastic continuum the rotation vibrations can propagate and are not attenuated. The asymmetric elastic rotation fields and their relation to asymmetric elastic stresses are proposed and discussed, under the condition that the total fields with the elastic and self parts remain symmetric or antisymmetric as required by the compatibility conditions. The tensor of incompatibility splits into the symmetric or antisymmetric parts. The conservation and balance laws for spin and twist fields and the stress -related equations of motion for symmetric and antisymmetric parts of stresses are given. The relations obtained for elastic fields, expressed by difference of the total and self-fields, can be split into the self-parts prevailing on the fracture plane and the total parts describing seismic radiation field in a surrounding space. The role of rotation processes in premonitory and rebound time domains is considered in estimating the most effective fracture patterns.

Time-domain filtering of seismic rotation waves

Nowożyński K., Teisseyre K.

Acta Geophysica Polonica

2003

Vol. 51, nr 1

51-61

Rotational parts of seismic waves are extracted from recordings of differential seismic signals. Thus, all differences in responses of the seismometers cause disturbances which obscure these hidden components. The method of removing great part of these disturbances is developed, based on the time-domain filtering and using the data collected over a selected period of seismic monitoring called the test phase. Examples of seismic rotation components for some events registered in the Ojców observatory are shown, together with results of checking the adequacy of the presented method.

Discussion on the recording of seismic rotation waves

Teisseyre R., Moriya T.

Acta Geophysica Polonica

1999

Vol. 47, nr 4

351-362

The new instrumentation technique permits to record the seismic rotational waves. In the case of a non-ideal elasticity the rotation waves appear due to defect content (the non-symmetric disclinations) in a medium or due to internal structure of a medium (micromorphic or micropolar media). Rotations may be attributed either to distortion from the plane wave state (rigid rotation related to the displacement field) or, more generally, to an independent microdisplacement tensor with rotation and twist-bend components. In this paper we analize the observed examples of records of rotation waves and we discuss the instrumental possibilities to record complex rotation phenomena of a non-rigid type.