Shear waves were not studied explicitly by Berryman and Wang (2000),
but Eq. (5) of that paper can be used for that purpose simply
by applying the *curl* operator to all three of the equations in the
set. When this is done, the result is that the first equation
describes the actual shear mode, while the other two equations
provide constraints on the relative motion of the pore fluid in
each type of porosity versus the displacement of the solid frame.
In particular, the shear components of the differences in fluid and
solid displacements can be uniquely related by complex factors (that
are known explicitly) to the displacement of the solid alone.
Furthermore, as in the case for single-porosity poroelasticity, all
of the interesting behavior of the shear mode -- at least for
isotropic media -- comes from the inertial terms. The form of the
resulting dispersion relation at low frequencies is identical to
(20) with the replacement

(27) |

10/14/2003