The effect of boundaries on wave propagation in a liquidfilled porous solid: VIII. Reflection of planewaves at an irregular boundary

Abstract

A study is made of the reflected field arising from body waves incident on a rough boundary of a saturated porous medium. The perturbation method employed here imposes restrictions on the boundaries; these restrictions are discussed in detail and it is pointed out how the presence of dissipation in the medium places additional constraints on admissible boundaries. Further, it is shown that the reflected field consists of specularly reflected waves and scattered waves which may take on the character of surface motions, and that because of viscosity in the liquid phase of the medium all waves are dispersed and dissipated. In the presence of a periodic boundary, when the frequency of the field is such that these surface waves are true Rayleigh waves, resonances occur in the scattered waves. Finally, numerical and graphical results are given for the problem of reflections generated at a sinusoidal boundary by normally incident waves of low and high frequencies, respectively, in a medium whose material constands correspond to those for a certain sample of a kerosene-saturated sandstone.