Circular scanlines and circular windows: new tools for characterizing the geometry of fracture traces

Abstract

We introduce new estimators for fracture trace intensity, trace density and mean trace length that exploit the use of circles as efficient sampling tools. A fracture trace is the commonly observed surface expression of a fracture, i.e. the intersection of a fracture with an exposed surface such as a rock pavement or a mine drive wall. Trace intensity, trace density and mean trace length estimators are derived and shown to form a self-consistent set of two-dimensional fracture abundance measures. The intensity estimator n/4 r uses the number, n, of intersections between fracture traces and a circular scanline of radius r. The density estimator m/2 πr 2 uses the number, m, of trace endpoints inside a circular window. The mean trace length estimator ( n/ m) πr/2 uses the ratio of the number of trace intersections on the circle to the number of endpoints in the circle. The circular sampling tools and estimators described here eliminate most sampling biases due to orientation and also correct many errors due to censoring and length bias that plague established scanline and areal measurement techniques. Performance of the estimators is demonstrated by comparison with areal samples of a synthetic fracture trace population with known intensity, density and mean trace length. The estimators are also applied successfully to a natural rock pavement with two orthogonal fracture sets, one of which is severely censored. Because the new circle-based estimators only require counts of trace–circle intersections and/or trace endpoints, they are more time-efficient than current methods for estimating geometric characteristics of fracture traces.