Multiple scattering processes in a heterogeneous medium with rough boundaries lead inevitably to coupling of volume and surface effects. Our study of this problem using a statistical wave theory shows the nature of this coupling, brings forth the issues involved, and gives the approximations required to separate volume and surface effects. We hence understand that, only under rather special conditions, these two effects can be decoupled according to the “splitting rule” suggested by Guerin and Sentenac [J. Opt. Soc. Am. A 24, 385 (2007) [CrossRef] ]. One situation where the two effects approximately separate is when the boundary roughness is small. In this case our results are in agreement with [J. Opt. Soc. Am. A 24, 385 (2007) [CrossRef] ] and [Waves Random Media 7, 303 (1997)]. Apart from this special situation, we find that volume and boundary effects always get coupled. Therefore, it is apparent that a splitting rule is a special property rather than a general law.
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