An elastically-anisotropic sedimentary rock is modeled by a simple cubic packing of identical, contacting spherical particles. The connected pore space is filled with an inviscid, compressible fluid. A set of averaged equations is derived to relate the constitutive and dynamic coupling coefficients, and hence also the effective wave speeds in any given direction explicitly to the microstructural properties of the rock considered. Simple, explicit results are obtained when the propagation of either a purely longitudinal or a purely transverse wave is considered.