By Roman Teisseyre, Maria Teisseyre-Jeleńska
This publication bargains with a category of simple deformations in uneven continuum thought. It describes molecular deformations and shipping velocities in fluids, pressure deformations in solids in addition to the molecular shipping, vital in fracture approaches.
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Additional resources for Asymmetric Continuum: Extreme Processes in Solids and Fluids (GeoPlanet: Earth and Planetary Sciences)
For displacement it might be a separately found time period when a wave group of displacement correlates with rotational oscillations (Teisseyre 2007), while for the strain component Euu it is a fact that the displacement-related contribution to that field appears negligible in comparison to the contributions caused by a direct strain effect, as discussed in Chap. 1. At the end of these considerations let us analyse one special case related to the natural earthquake events in rocks that are under a vertical gradient of pressure; here, it is convenient to use the cylindrical system (r,a,z), with the z-axis oriented in vertical direction.
Acta Geophys 56:259–269 Teisseyre R (2008b) Asymmetric Continuum: Standard Theory. In Teisseyre R, Nagahama H, and Majewski E (eds) Physics of asymmetric continua : extreme and fracture processes,Springer, p95-109 Teisseyre R (2009) Tutorial on new development in physics of rotation motions. Bull Seismol Soc Am 99(2B):1028–1039 Teisseyre R (2011) Why rotation seismology: confrontation between classic and asymmetric theories. Bull Seismol Soc Am 101(4):1683–1691 Teisseyre R (2012) Rotation and strain seismology.
9a), we could define the molecular displacements: & ' X ous ou1 u ou2 u ou3 wus ¼ ! wu1 ¼ ; w2 ¼ ; w3 ¼ wun ¼ 0 ð2:11aÞ at oxs ox1 ox2 ox3 n and this relation leads us to the equation similar to eqs. , Fig. 2. , such phenomena might be expected near some structure inside the Earth which effectively reflect the seismic waves and also modify the micro-seismic waves. These reflected micro-seismic waves become modified due to the local molecular fields. In this way, the observed reflected micro-seismic parts might bring some earthquake precursory signals as discovered by Sobolev and Lyubushin.