Fracture roughness characterization by shadow image analysis

Surface roughness of sandstone fractures was described by shadow image analysis. The analysis is based on a model for the Shadow Length Distribution (SLD) in a self-affine landscape by Hansen et al. (1995). A Shadow Imaging Technique (SIT) was developed that comprises the following: an optical setup, a method to distinguish shadows from light zones, and data analysis. Shadow and light zone classification methods were evaluated and a new local method is recommended. The SLD model fitted the experimental data in a limited regime with a roughness exponent of about 0.6-0.7. This is close to exponents obtained from profile data. Experimental light intensity histograms contained discontinuities and singularities. The Phong model for specular scattering was applied statistically to Lambertian diffuse faceted self-affine surfaces. Modeled and experimental histograms were similar.