Geostatistical downscaling of fracture surface topography accounting for local roughness

This study proposes a new geostatistical methodology that accounts for roughness characteristics when downscaling fracture surface topography. In the proposed approach, the small-scale fracture surface roughness is described using a “local roughness pattern” that indicates the relative height of a location compared to its surrounding locations, while the large-scale roughness is considered using the surface semivariogram. By accounting for both components–the minimization of the local error variance and the reproduction of the local roughness characteristics–into the objective function of simulated annealing, the fracture surface topography downscaling process was improved compared to standard geostatistical methodologies such as ordinary kriging and sequential Gaussian simulation. Downscaled topography data were then assessed in terms of prediction errors and roughness distribution.