ORDER IN JOINT SPACING TRAVERSE SEQUENCES

Joint set spacing data is often analyzed for distribution type by plotting the frequency of values in bins. Log normal, normal, fractal and other distributions are reported in the literature. Conceptually, a given set of spacing values defining a distribution can be arranged into different sequences. A set with a random/uniform spacing distribution could be rearranged into a series of all increasing or decreasing values. A set of numbers following a normal distribution could be sequenced randomly or into alternating high and low values. The runs test asks whether the number of runs in a sequence is less or greater than expected from randomness. A run is defined by a string of consistent increases, or of consistent decreases. A single and simple cluster would have two runs, less than expected from a random sequence. If a given value is always flanked by larger or smaller values then there would be (n-1)/2 runs, more than expected from a random sequence. Runs tests were applied to spacing traverses for joint sets in the northern Sierra Nevada batholith and in both more massive and more mechanically layered Mesozoic sandstones units in the Moab area. Data sets were generated both from Google Earth imagery and the field. A null hypothesis of randomness was consistently rejected with a greater number of runs than expected. More massive, thicker units are expected to be more clustered than well layered thinner units. Yet simple clustering should produce fewer runs. For the runs test, the effect of observation scale censoring needs further consideration. Field work suggests that interpreted individual joint traces in Google Earth are composite fracture bundles, indicating that for Google Earth data scale censoring occurs. The use of binomial probability of the number of sequential increases versus decreases for sliding windows to localize the traverse position of significant departures (e.g. clustering) from randomness was also explored. Some cluster centers are associated with departures, but there is trade-off between window size, and spatial versus statistical resolution. A greater instead of fewer number of runs than expected if random suggests that some joint set clustering may have a more complex organization, perhaps due to the interplay of multiple coupled formation ‘rules’.