Four shear moduli are easily and unambiguously
defined for the anisotropic system under
study. Furthermore, since we are treating only soft anisotropy, all
of these moduli are the same, *i.e.*,
*G*_{i} = *G*_{dr} for . These are all
related to the four shear eigenvectors of the systems, and they do
not couple to the pore-fluid mechanics.
But, the eigenvectors in the reduced system studied
here are usually mixed in character, being quasi-compressional or
quasi-shear modes. It is therefore somewhat problematic to find a
proper definition for a fifth shear modulus. The author has analyzed
this problem previously (Berryman, 2004b), and concluded that a
sensible (though approximate) definition can be
made using *G _{5}* =

(31) |

(32) |

(33) |

(34) |

TABLE. Elastic and poroelastic parameters of the
three rock samples considered in
the text. Bulk and shear moduli of the grains *K*_{m} and *G*_{m}, bulk
and shear moduli of the drained porous frame *K*_{dr} and *G*_{dr},
the effective and undrained shear moduli *G*_{eff} and *G*_{u},
and the Biot-Willis parameter .The porosity is .

Elastic/Poroelastic | Sierra White | Schuler-Cotton Valley | Spirit River |

Parameters | Granite | Sandstone | Sandstone |

G_{m} (GPa) |
31.7 | 36.7 | 69.0 |

G_{u} (GPa) |
28.3 | 17.7 | 12.41 |

G_{dr} (GPa) |
26.4 | 15.7 | 11.33 |

G_{eff} (GPa) |
39.8 | 35.8 | 20.11 |

K_{m} (GPa) |
57.7 | 41.8 | 30.0 |

K_{dr} (GPa) |
38.3 | 13.1 | 7.04 |

0.336 | 0.687 | 0.765 | |

0.008 | 0.033 | 0.052 |

5/23/2004