MEASUREMENT AND CHARACTERIZATION OF SPATIAL DISTRIBUTIONS OF FRACTURES

A variety of line sample (1-D) and map (2-D) datasets of faults and-joints has been used to investigate the spatial distributions of fractures and to test techniques of fractal analysis. The natural fracture datasets have been supplemented by synthetic datasets with known characteristics. The fault datasets investigated range in scale from regional to outcrop and the joint datasets are derived from outcrop, 1-D datasets were analysed by the spacing population, interval counting and fracture number interval counting techniques. 2-D datasets were analysed by box-counting and fracture number box-counting techniques. Results indicate that fracture spacing can be characterised in line samples using either the 1-D interval counting technique or, more simply, by measuring the spacing population as the cumulative frequency distribution of spaces between adjacent fractures. Tectonic faults frequently show a power-law spacing population, indicating fractal dimensions of between 0.4 and 1.0 but, except for outcrop data, truncation effects degrade the analysis. Unrefined joint datasets commonly show negative exponential or lognormal spacing-cumulative frequency distributions. However, single orientation joint sets are characterised by a regular spacing and are therefore non-fractal. For both fault and joint map data, box-counting techniques do not yield the power-law relationship between box size and the number of boxes that is expected of fractal geometries. It is concluded that 2-D box-counting techniques are too insensitive to characterise the many different parameters of a fracture array. The fracture density technique appears not to discriminate between very different fracture patterns and therefore does not provide useful results. A fracture pattern incorporates several attributes, e.g., size distribution, orientation, linkage, density, roughness, each of which may scale independently and each of which may be fractal with its own fractal dimension. Full characterisation of fracture patterns will therefore require independent analysis of each of these attributes.