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Micromorphic Continuum and Fractal Fracturing in the Lithosphere

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Fractals and Dynamic Systems in Geoscience

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Abstract

It seems that internal structures and discontinuities in the lithosphere essentially influence the lithospheric deformation such as faulting or earthquakes. The micromorphic continuum provides a good framework to study the continuum with microstructure, such as earthquake structures. Here we briefly introduce the relation between the theory of micromorphic continuum and the rotational effects related to the internal microstructure in epicenter zones. Thereafter the equilibrium equation, in terms of the displacements (the Navier equation) in the medium with microstructure, is derived from the theory of the micromorphic continuum. This equation is the generalization of the Laplace equation in terms of displacements and can lead to Laplace equations such as the local diffusion-like conservation equations for strains. These local balance/stationary state of strains under the steady non-equilibrium strain flux through the plate boundaries bear the scale-invariant properties of fracturing in the lithospheric plate with microstructure.

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Authors and Affiliations

  1. Institute of Geology and Paleontology, Graduate School of Sciences, Tohoku University, Sendai, 980-8578, Japan

    H. Nagahama

  2. Institute of Geophysics, Polish Academy of Sciences, ul. Księcia Janusza 64, 01-452, Warzaw, Poland

    R. Teisseyre

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  1. H. Nagahama
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  2. R. Teisseyre
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Editors and Affiliations

  1. Department of Geology, University of Zimbabwe, Harare, Zimbabwe

    Tom G. Blenkinsop

  2. Institut fĂĽr Angewandte Geologie und Mineralogie, TU MĂĽnchen, MĂĽnchen, Deutschland

    Jörn H. Kruhl

  3. Institute of Materials Research, Slovak Academy of Sciences, Košice, Slovakia

    Miriam Kupková

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Nagahama, H., Teisseyre, R. (2000). Micromorphic Continuum and Fractal Fracturing in the Lithosphere. In: Blenkinsop, T.G., Kruhl, J.H., Kupková, M. (eds) Fractals and Dynamic Systems in Geoscience. Pageoph Topical Volumes. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8430-3_5

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  • DOI: https://doi.org/10.1007/978-3-0348-8430-3_5

  • Publisher Name: Birkhäuser, Basel

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