The drag coefficients may be determined by first noting that the equations presented here reduce to those of Berryman and Wang [1995] in the low frequency limit by merely neglecting the inertial terms. What is required to make the direct identification of the coefficients is a pair of coupled equations for the two increments of fluid content and . These quantities are related to the displacements by and .

The pertinent equations from Berryman and Wang [1995] are

.^(1).^(2) =
k^(11) & k^(12)
k^(21) & k^(22)
p_,ii^(1) p_,ii^(2) ,
where is the shear viscosity of the fluid, and the *k*s are
permeabilities including possible cross-coupling terms.
We can extract the terms we need from (finaleom), and then take
the divergence to obtain

b_12+b_23 & - b_23
- b_23 & b_13+b_23
(B<>U^(1) - B<>u)
(B<>U^(2) - B<>u) =
- p_,ii^(1) p_,ii^(2) .
Comparing these two sets of equations and solving for the
*b* coefficients, we find

b_12 = ^(1)(k^(22)-k^(21)) k^(11)k^(22)-k^(12)k^(21),

b_12 = ^(2)(k^(11)-k^(12)) k^(11)k^(22)-k^(12)k^(21), and

b_23 = ^(1)k^(21)
k^(11)k^(22)-k^(12)k^(21)
= ^(2)k^(12)
k^(11)k^(22)-k^(12)k^(21).
For many applications it will be adequate to assume that the
cross-coupling vanishes. In this situation, *b _{23}* = 0,

b_13 = ^(2)k^(22), which also provides a simple interpretation of these coefficients in terms of the porosities and diagonal permeabilities.

This completes the identification of the inertial and drag coefficients introduced in the previous section.

8/21/1998