Preconditioned Splitting Series Approximation for 2D Rough Surface Scattering

Scattering sensitivity of waves to surface roughness has been widely observed in many fields. Some series approximations for rough surface scattering, such as the general Born, the splitting, and the preconditioned splitting series, are presented for a numerical description of rough surface scattering by multiscale surfaces. In fact, the splitting series approximation is a specific form of the preconditioned splitting series. Numerical tests with several benchmark models are compared with the full-waveform numerical solution and the general Born series approximation to investigate the range of validity of the splitting and the preconditioned splitting series approximations. The splitting and the preconditioned splitting series approximations to multiscale surfaces are not subject to the strict limit applied to the general Born series approximation. Each order of the splitting series represents an increase of multiple scatterings between surface points. Therefore, higher-order splitting series approximation accounts for stronger surface scattering. A suitable preconditioned splitting and the splitting series approximations improve the general Born series approximation for the convergence of high-incident angle scattering, and, therefore, become realistic methods for multiscale surfaces with infinite gradients and extremely large surface heights. This series approximation mathematically provides a unified framework for rough surface scattering, which contains Born or Rytov series approximation as specific cases.