## 3 Modified SBR-FBSSA Method for Composite Scattering  
### Composite Scattering Model of Target above Canyon/Valley Environment  
The composite scattering model for an ultra-low target above the canyon/valley is depicted in Figure 4 as operating inside the modified SBR-FBSSA technique framework. It is composed of five main components.  
1. Direct scattering from the ultra-low target, denoted by C1.  
This part is calculated by the SBR method. Not only should the target's self-occlusion be taken into account throughout the computation, but also the target's and the composite surface's mutual occlusion. Moreover, the scattering caused by the edge structure should not be neglected. This paper adopts the method of equivalent currents to improve the scattering results.  
2. Direct scattering from composite rough surface, denoted by C2.  
The facet-based small-slope approximation (FBSSA) method is adapted to calculate the direct scattering from the canyon/valley rough surface. The composite surface, which is created in Section 2, has numerous facets. The small slope approximation method in the local coordinate system determines the scattering field for each facet. The vector superposition of the facet-scattering fields in a global coordinate system defines the total scattering field. In a similar vein, mutual and self-occlusion should be considered.  
3. Multiple scattering from the target, denoted by C3.  
This part is calculated by the SBR method. Ultra-low targets usually contain complex structures, similar to dihedrals, which can cause multiple reflections. This interactional component will produce strong scattering fields. Thus, it is necessary to calculate multiple scattering from the target.  
4. Multiple scattering from canyon/valley composite rough surface, denoted by C4.  
In contrast to typically terrestrial environments, sea surfaces, and other composite rough surfaces, canyon/valley environments have a natural cavity structure that is semi-enclosed. Due to the multiple scattering from the environment, the particular structure increases the complexity of the composite scattering. To calculate this portion of composite scattering, a modified SBR method is implemented.  
5. Coupling scattering between the target and canyon/valley composite rough surface, denoted by C5.  
In the composite scattering model, coupling scattering between the target and environment is commonly present. Higher-order reflection makes the coupling between the target and canyon/valley more complex, which could be solved well and efficiently by utilizing the modified SBR algorithm.  
Figure 4: Illustration of SBR-FBSSA composite scattering model for canyon/valley environment.  
It is worth noting that the MSBR method is improved by replacing the Snell reflection coefficients in the traditional SBR method with a high-order reflection model introduced in Section 3.2. The MSBR method can also handle the cases that the SBR method can handle. At last, components C1, C3, C4, and C5 are calculated by the MSBR method, and component C2 is calculated by FBSSA. As described above, composite scattering can be generated by superimposing the scattering fields that have been acquired.