Simulating synthetic aperture radar (SAR) images of crater terrain is a crucial technique for expanding SAR sample databases and facilitating the development of quantitative information extraction models for craters. However, existing simulation methods often overlook crucial factors, including the explosive depth effect in crater morphology modeling and the double-bounce scattering effect in electromagnetic scattering calculations. To overcome these limitations, this article introduces a novel approach to simulating SAR images of crater terrain. The approach incorporates crater formation theory to describe the relationship between various explosion parameters and craters. Moreover, it employs a hybrid ray-tracing approach that considers both surface and double-bounce scattering effects. Initially, crater morphology models are established for surface, shallow burial, and deep burial explosions. This involves incorporating the explosive depth parameter into crater morphology modeling through crater formation theory and quantitatively assessing soil movement influenced by the explosion. Subsequently, the ray-tracing algorithm and the advanced integral equation model are combined to accurately calculate electromagnetic scattering characteristics. Finally, simulated SAR images of the crater terrain are generated using the SAR echo fast time-frequency domain simulation algorithm and the chirp scaling imaging algorithm. The results obtained by simulating SAR images under different explosion parameters offer valuable insights into the effects of various explosion parameters on crater morphology. This research could contribute to the creation of comprehensive crater terrain datasets and support the application of SAR technology for damage assessment purposes.

Fractals are widely recognized as one of the best geometric models to depict soil roughness on various scales from tillage to micro-topography smaller than radar wavelength. However, most fractal approaches require an additional geometric description of experimental sites to be analysed by existing radiative transfer models. For example, fractal dimension or spectral parameter is often related to root-mean-square (RMS) height to be characterized as the microwave surface. However, field measurements hardly represent multi-scale roughness. In this study, we rescaled Power Spectral Density with Synthetic Aperture Radar (SAR)-inverted rms height, and estimated non-stationary fractal roughness to accommodate multi-scale roughness into a radiative transfer model structure. As a result, soil moisture was retrieved over the Yanco site in Australia. Local validation shows that the Integral Equation Model (IEM) poorly simulated backscatters using inverted roughness as compared to fractal roughness even in anisotropic conditions. This is considered due to a violation of time-invariance assumption used for inversion. Spatial analysis also shows that multi-scale fractal roughness better illustrated the hydrologically reasonable backscattering partitioning, as compared to inverted roughness. Fractal roughness showed a greater contribution of roughness to backscattering in dry conditions. Differences between IEM backscattering and measurement were lower, even when the isotropic assumption of the fractal model was violated. In wet conditions, the contribution of soil moisture to backscattering was shown more clearly by fractal roughness. These results suggest that the multi-scale fractal roughness can be better adapted to the IEM even in anisotropic conditions than the inversion to assume time-invariance of roughness.