Micromorphic continuum with defects and Taylor-Bishop-Hill theory for polycrystals: Anisotropic propagation of seismic waves and the Golebiewska gauge

Jun Muto, Yusuke Kawada, Hiroyuki Nagahama

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)


Internal structures and discontinuities in the earth's crust and mantle seem to have an essential influence on deformation in rocks. So, it is reasonable to believe that the notion of continuum with microstructure is an applicable tool in describing earthquake phenomena. The generalized micromorphic continuum is especially suitable for treating the microstructure (e.g. Suhubi and Eringen 1964, Eringen and Claus 1970). From this point of view, Teisseyre and Nagahama (1999) applied the micromorphic continuum to discuss the generation and propagation of the rotation seismic waves. Basic relations of the micromorphic continuum will now be applied to another phenomenon in solid Earth, i.e. lattice preferred orientation (LPO) of polycrystals. The LPO has been observed within the polycrystals for a long time (e.g. Schmidt 1925, Sander 1930). The nature of the LPO due to the intracrystalline slip (dislocation slip and twinning) depends on geometric constrains on the deformation. The LPO of the polycrystals is applied to infer deformed conditions of the rocks, because the LPO pattern depends on several physical conditions during the deformation, such as temperature and strain rate (e.g. Lister et al. 1978). In this analysis, the Taylor'Bishop'Hill (TBH) model has been often used to simulate development of the LPO patterns (e.g. Lister et al. 1978), which was first introduced by Taylor (1938) and treated more mathematically by Bishop and Hill (1951). Based on an assumption that strain is homogeneous through the polycrystals, the TBH model has reproduced the observed LPO in quartzite (Lister et al. 1978), calcite (Takeshita et al. 1987) and olivine (Ribe and Yu 1991). Yamasaki and Nagahama (2002) theoretically derived the TBH model with the help of differential forms and a gauge theory. However, geometrical relations between the theory of micromorphic continuum and the TBH model have not been obtained yet. The plastic deformation or flows in the lower crust and upper mantle induces the seismic (elastic) anisotropy, which affects how fast seismic waves propagate in different directions. In the lower crust, the seismic anisotropies indicate the presence of faults or plastic shear zones (mylonite zones) (Ji and Salisbury 1993). On the other hand, the seismic anisotropies in the upper mantle reflect mantle flow related to global tectonics (see the review by Park and Levin 2002). Thus, the research on the seismic anisotropy of the rocks is essential for investigating the propagation of the seismic waves. Here we briefly introduce the relationship between the theory of micromorphic continuum with defects and the Taylor'Bishop'Hill theory, and review the LPO development and seismic anisotropy of the deformed rocks based on the relations between the TBH model and the micromorphic continuum. Moreover, analyzing differential forms of defects, we discuss relations between the TBH model and the Golebiewska gauge according to Yamasaki and Nagahama (2002).

Original languageEnglish
Title of host publicationEarthquake Source Asymmetry, Structural Media and Rotation Effects
PublisherSpringer Berlin Heidelberg
Number of pages12
ISBN (Print)3540313362, 9783540313366
Publication statusPublished - 2006 Dec 1

ASJC Scopus subject areas

  • Environmental Science(all)
  • Earth and Planetary Sciences(all)


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