ABSTRACT
Upon substituting equation (2.89) into the equations of motion (2.83) and (2.84), having specified the values of δf and δs one obtains equations of motion valid only for acoustic waves propagating through porous media:
ηo ρfo ∂ ∂t vi
(1-ηo ) µfµm(1-ηo ) µs - 1 ∇ 2 ∂ ∂tui
(s) + 13 ∂i ∇ ⋅
∂us ∂t
+ ηoµf∂k ∂kvif + ∂ivkf - 23δik∂jvj f
(5.1)
-
∂t
+ µM ∇2uis + 1 3∂i (∇ • us) (5.2) +
∂t
Here us is the megascopically averaged solid displacement. Here wave motions where the time dependence is given by e-iωt are considered; thus the megascopically averaged "fluid displacement vector" is defined by
uf = 1 - iω v
Here µm is the megascopic shear modulus of the solid component (cf. Hickey et al., 1995). The parameters δs and δf are process dependent and thus may have different values for wave propagation than for static compressions (cf. de la Cruz et al., 1993). In the present analysis the term ρb
∂t
will be ignored.
