Analysis and Generation of Rough-Surfaced Fractures with Variable Aperture Based on Self-Affine Methods Using Surface Scan Measurements

Methods founded on self-affine principles have successfully been used to generate synthetic rough-surfaced fractures, which can be based on properties inferred from measurements of fracture surfaces. Two key parameters, the Hurst exponent H and a scaling parameter Sp, together with a function describing the correlation between the surfaces forming the fracture, are needed. There are several methods for determining H and Sp in the literature, which are primarily adopted for measurements of 1-dimensional fracture traces. However, comparatively few studies have used these methods and applied them to aperture generation. In this study, we evaluate two commonly employed methods, the root-mean-square correlation function (RMS-COR) and the Fourier power spectrum (FPS) approach, each with several variations of their possible implementation when applied to measurements of fracture surfaces. We use high-resolution surface scans of a natural fracture sample to obtain an accurate representation of the aperture field and rough surfaces. Multiple realisations of aperture fields are generated for each method variation and their respective ensembles are evaluated against the aperture distribution of the measured fracture sample. For the fracture studied, the RMS-COR method is the most accurate method for obtaining H and Sp. We show that a linear relationship exists between H and Sp which provides a best fit of synthetically generated fractures when compared to the measured sample. Additionally, we introduce an improved approach for representing the correlation function between the two rough surfaces. Finally, we demonstrate that the model can successfully generate upscaled fracture apertures based on restricted subsections of the sample.