We derive the multiple scattering expression within the framework of an IEM
model for rough surface scattering, The complementary field coefficients a
re rederived based on a new surface slope expressions which are dependent o
n spatial variables. This leads to a more complete expression of the multip
le scattering terms, thus allowing us to account for multiple effects more
accurately, Numerical calculations and comparisons with numerical simulatio
n are provided to demonstrate the results.