CALCULATING FRACTURE FREQUENCY BOUNDARIES USING LINEAR PIECEWISE REGRESSION AND THE AKAIKE INFORMATION CRITERION: A NEW APPROACH TO REGIONAL FRACTURE ANALYSIS

We present a new approach to regional fracture analysis using a linear piecewise regression to calculate boundaries in cumulative fracture frequency (CFF) curves along transects and the Akaike Information Criterion (AIC) to determine the optimal number of linear segments in the CFF. Results from the statistical analysis produced three CFF slope intervals that define the distribution of possible fracture frequencies unique to the geologic setting from which they were derived.

A total of 3678 fracture and vein measurements were collected using scanline, scangrid, and abbreviated methods at 38 sites in the Utica black shale and overlying coarser clastics of the Mohawk Valley in eastern New York State. To produce CFFs, fracture frequency is summed along a transect perpendicular to the strike of the set. The piecewise function in the R package, “Segmented”, calculates break points where the slope of the CFF changes. The AIC method of model selection produces piecewise regressions with the optimal number of breakpoints and segments by penalizing additional parameters introduced with each new segment. A comparison with the Bayesian Information Criterion (BIC) found that AIC models outperformed the BIC method because the BIC equation over-penalized additional parameters.

Segmenting the CFFs produced three unique slope intervals, each with a set of defining characteristics. Background frequencies are defined by an average CFF slope of 8 with no significant changes in slope (including prominent frequency peaks). The average background fracture frequency is 2.4 fractures/m. Transition frequencies exhibit higher CFF slopes, averaging 111, and higher average fracture frequency of 12.3 fractures/m. Fracture intensification domains (including fractures in fault damage zones) are defined by the highest average CFF slope of 1649, produce prominent frequency peaks (>50 fractures/m) and have the highest average fracture frequency of 44.6 fractures/m. Results of the piecewise analysis provide quantified boundaries that can be used to create a fracture frequency framework for a defined geologic setting, aiding in predictions of fracture frequency variations due to local structural features.