The equations of motion in a macroscopically inhomogeneous porous medium saturated by a fluid are derived. As a verification of their validity, these equations are reduced and solved for rigid frame porous systems. The reflection and transmission coefficients and their corresponding time signals are calculated numerically using wave splitting Green's function approach for a two-layer porous system considered as one single porous layer with a sudden change in physical properties. The results are compared to experimental results and to those of the classical transfer matrix method for materials saturated by air in the ultrasonic frequency range. (c) 2007 American Institute of Physics.