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Terzaghi simplifies Biot's model by
decoupling the stress tensor into hydrostatic stress and stresses
of the solid skeleton. Terzaghi's approximation, which are popular
in the field of geomechanics, imply

| |
(36) |

| (37) |

| (38) |

| (39) |

If we further assume that the tortuosity *a*=1 is one
and that we can ignore dissipation due to viscosity, we find
again two non-dissipative P-waves with velocities
| |
(40) |

| (41) |

The first P-wave only involves the rock matrix,
the second only involves the fluid.
If we continue to ignore loss due to viscosity
but allow for tortuosity
and a fluid bulk modulo much smaller
than the solid bulk modulo ()than the wave velocities are

| |
(42) |

| (43) |

| (44) |

But Tzeraghi's assumption of decoupled stresses is considered
unrealistic for usually highly consolidated hydrocarbon reservoir rocks.

** Next:** Wyllie's model
** Up:** Alternative rock velocity models
** Previous:** Biot's model
Stanford Exploration Project

3/9/1999