## 1. Introduction

[2] In recent years, electromagnetic scattering problems of targets above or beneath a rough surface have drawn more and more attentions, because of its extensive applications on radar surveillance, target identification, GPR (ground-penetration radar) probing, etc. Numerical simulation of the composite target/surface model should take into account the complicated interactions between target and rough surface background. Some numerical approaches of target-surface modeling have emerged recently, such as the generalized forward backward method with spectral acceleration algorithm (GFBM/SAA) [*Pino et al.*, 1999, 2002], the finite element method and domain decomposition method (FEM-DDM) [*Liu and Jin*, 2004], the steepest descent path method and the fast multipole method (SDP/FMM) [*El-Shenawee et al.*, 2001], the coupled canonical grid/discrete dipole approach (CCG/DDA) [*Johnson and Burkholder*, 2001], etc. However, most of them are restricted to 2-D model because of large computation complexity of rough surface scattering. Very few exceptive examples of 3-D models can be found, e.g., the steepest descent path (SDP) method and the fast multipole method (FMM) for analyzing the scattering from a target beneath a rough surface. But it still requires tremendous memory and CPU time as in the order of O(*N*lg*N*) [*El-Shenawee*, 2002; *El-Shenawee et al.*, 2001].

[3] If the underlying surface is flat, the image method with Green's function of half-space is usually employed, e.g., complex image method and multilevel fast multipole algorithm (MLFMA) [*Li et al.*, 2003]. As the underlying surface becomes randomly rough, the Green's function becomes the sum of infinite series due to the multiple scattering of rough surface. It causes a large difficulty for numerical simulation.

[4] In a 2-D target-surface model [*Ye and Jin*, 2006], it has been found that scattering computation of rough surface costs most of CPU time. This yields a hybrid analytic-numerical method applying the analytic Kirchhoff approximation (KA) method to coarsely compute the induced currents on rough surface [*Ye and Jin*, 2007]. Then the computation cost is significantly reduced, and good efficiency and precision are preserved.

[5] In this paper, the hybrid KA-MoM algorithm is generalized to the 3-D model of a PEC target above a 2-D dielectric randomly rough surface. The difference electric and magnetic fields induced on the dielectric rough surface are introduced in coupling interactions. The KA expressions for the coupling scattering fields between the target and the underlying rough surface are presented, based on the tangential plane approximation and the local orthogonal decomposition of the radiation fields of target's currents. Induced currents on the target are obtained in an iterative procedure: 1) compute the radiation field of the target's induced currents (solved in the previous iteration step) over the rough surface; 2) use the surface equivalence theorem and the KA method to derive the induced fields on the rough surface; 3) calculate the radiation fields of these equivalent induced surface fields to generate the difference scattering field of the rough surface; 4) update the RHS excitation of the discrete MoM equation with the difference scattering fields and solve it to obtain the new induced currents on the target.

[6] In numerical process, the target and the randomly rough surface samples (generated by Monte-Carlo method) are discretized into small patches, and the interaction is numerically calculated for each patch. In order to derive the KA expression for coupling scattering fields of the rough surface, it is presumed that the radiation electric and magnetic fields from the source current unit on the target to the discrete patches of the rough surface satisfy the right-handed helix relationship, just the same as the general TEM plane wave, which leads the validity condition of *kR* > 20. Moreover, the incident and scattering angles should satisfy tan θ_{i} < *s*^{−1} and θ_{s} < *s*^{−1} to avoid the shadowing effects.

[7] As a code validation, the hybrid algorithm is first examined for the composite model of a sphere above a PEC flat surface, and is compared with the image Green's function method. Then, it is applied to numerically study the bistatic difference scattering from different-shaped targets above a dielectric randomly rough surface.