1887
Volume 70, Issue 6
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

The invariants of the moment tensor such as its norm, eigenvalues and trace are closely related to the physical properties of the seismic source and the focal region, for example, seismic moment, radiation pattern, non‐double‐couple components. In this study, we investigate the relationship between these invariants and the eigenvalues and eigenvectors of the transversely isotropic elasticity tensor of the focal region. More specifically, we study how these invariants change as the source orientations vary with respect to the symmetry axes of the transversely isotropic elasticity tensor, by plotting these invariants on the stereographic net. Fortunately, one can plot them since they are independent of the strike of the fault when the focal region is a vertical transversely isotropic medium . Eigenvalues of the elasticity tensor control the invariants of the moment tensor; for instance, the ratio of the maximum and minimum norms achieved for some orientations of source is equal to the ratio of the two specific eigenvalues of the elasticity tensor. Moreover, the separation of the eigenvectors of the moment tensor from the eigenvectors of the source tensor is related to the deviation of the eigenvalues of the transversely isotropic elasticity tensor from the eigenvalues of the closest isotropic elasticity tensor. It is also found that this deviation is responsible for the percentages of non‐double‐couple components of the resulting moment tensor. This linear algebra point of view makes it easier to understand why and how the structure of the moment tensor changes for different orientations of sources.

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2022-06-16
2022-06-27
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References

  1. Aki, K. and Richards, P.G. (2002) Quantitative Seismology, 2nd edition. University Science Books.
    [Google Scholar]
  2. Bóna, A., Bucataru, I. and Slawinski, M.A. (2007) Coordinate‐free characterization of the symmetry classes of elasticity tensors. Journal of Elasticity, 87, 109‐132.
    [Google Scholar]
  3. Diner, Ç. (2010) On choosing effective symmetry classes for elasticity tensors. The Quarterly Journal of Mechanics and Applied Mathematics, 64(1), 57–74.
    [Google Scholar]
  4. Diner, Ç. (2019) The structure of moment tensors in transversely isotropic focal regions. Bulletin of the Seismological Society of America, 109(6), 2415–2426.
    [Google Scholar]
  5. Foulger, G.R., Julian, B.R., Hill, D.P., Pitt, A.M., Malin, P.E. and Shalev, E. (2004) Non‐double‐couple microearthquakes at Long Valley Caldera, California, provide evidence for hydraulic fracturing. Journal of Volcanology and Geothermal Research, 132, 45–71.
    [Google Scholar]
  6. Gazis, D.C., Tadjbakhsh, I. and Toupin, R.A. (1963) The elastic tensor of given symmetry nearest to an anisotropic elastic tensor. Acta Crystallographica, 16, 917–922.
    [Google Scholar]
  7. Helbig, K. (2013) Review paper: What Kelvin might have written about elasticity. Geophysical Prospecting, 61, 1‐20.
    [Google Scholar]
  8. Kawasaki, I. and Tanimoto, T. (1981) Radiation patterns of body waves due to the seismic dislocation occurring in an anisotropic source medium. Bulletin of the Seismological Society of America, 71, 37–50.
    [Google Scholar]
  9. Kuge, K. and Lay, T. (1994) Data‐dependent non‐double‐couple components of shallow earthquake source mechanisms: Effects of waveform inversion instability. Geophysical Research Letters, 21, 9–12.
    [Google Scholar]
  10. Menke, W. and Russell, J.B. (2020) Non‐double‐couple components of the moment tensor in a transversely isotropic medium. Bulletin of the Seismological Society of America, 110(3).
    [Google Scholar]
  11. Minson, S.E., Dreger, D.S., Bürgmann, R., Kanamori, H. and Larson, K.M. (2007) Seismically and geodetically determined nondouble‐couple source mechanisms from the 2000 Miyakejima volcanic earthquake swarm. Journal of Geophysical Research, 112(B10), 308.
    [Google Scholar]
  12. Norris, A.N. (2006) Elastic moduli approximation of higher symmetry for the acoustical properties of an anisotropic material. Journal of the Acoustical Society of America, 119(4), 2114‐21.
    [Google Scholar]
  13. Ross, A.G., Foulger, G.R. and Julian, B.R. (1996) Non‐double‐couple earthquake mechanisms at the Geysers geothermal area, California. Geophysical Research Letters, 23, 877–880.
    [Google Scholar]
  14. Sipkin, S.A. (1986) Interpretation of non‐double‐couple earthquake mechanisms derived from moment tensor inversion. Journal of Geophysical Research, 91, 531–547.
    [Google Scholar]
  15. Slawinski, M.A. (2010) Waves and Rays in Elastic Continua. World Scientific.
    [Google Scholar]
  16. Tape, W. and Tape, C. (2012) A geometric setting for moment tensors. Geophysical Journal International, 190, 476‐498.
    [Google Scholar]
  17. Vavryc̆uk, V. (2005) Focal mechanisms in anisotropic media. Geophysical Journal International, 161, 334–346.
    [Google Scholar]
  18. Vavryc̆uk, V. (2011) Tensile earthquakes: Theory, modeling, and inversion. Journal of Geophysical Research, 116, B12320.
    [Google Scholar]
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