A Two-scale Model for Composite Rough Surface Scattering

Abstract

A new two-scale model is proposed for wave scattering from a composite surface. For each single scale surface roughness, we use a weighted sum of the newly developed statistical integral equation model and the second-order small slope approximation. With these two unifying models collaborating at each scale, this proposed compound model may capture the actual scattering mechanisms and lead to more accurate predictions. It holds the potential to bridge the gap between the regions of validity of the Kirchhoff approximation and the small perturbation model.The chosen simulation parameters suggest that the new two-scale model holds the potential to expand the validity regions of both its large scale and small scale components. The new model may have promising applications for electromagnetic scattering from the ocean surface, whose entire roughness spectrum can be discomposed into smalland large-scale components. DOI: 10.2529/PIERS061113040537 For electromagnetic scattering from a composite rough surface, different forms of two-scale model (TSM) are usually employed [1, 2]. The surface perturbation is typically divided into the large scale part and the small scale one, which are treated by using different analytical models in these TSM models. To calculate the scattering coefficient, in [1], the Kirchhoff approximation (KA) was used for the large scale and the small perturbation method (SPM) for the small scale, while in [2], the SPM was replaced by the first-order small slope approximation (SSA1) for the small scale calculation, leaving KA representation for the large scale untouched. However, the existence of a gap between the valid regions of the KA and the SPM models may render TSM modles of such combination inaccurate for configurations that are beyond the aforementioned valid regions. Meanwhile, in the literature, some researchers introduced a scaledividing parameter to distinguish large and small scales in the surface spectrum. Values of the cut-off were often chosen in an ad hoc manner. On the other hand, both the second order SSA (SSA2) [3] and the recently developed statistical integral equation model (SIEM) [4] hold the potential to bridge the gap between the valid regions of the KA and SPM models, with varying degree of success. This observation motivates the study in which we use the weighted sum of the SIEM and SSA2 for the single scale computation for our new TSM. We shall briefly review these two models, and then present the new compound model. Finally some numerical simulations will also be provided. Unlike the conventional integral equation model (IEM) and its various variations, the SIEM treats the local coordinates and related field terms statistically over the orientation distribution of the surface unit normal vector, which is characterized by joint probability distribution function. Furthermore, it incorporates rigorously the shadow function in the field calculation. The scattering coefficient of the SIEM model is σ qp = σ 0 qp1 − σ qp2 + σ qp3 (1)