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

We introduce new estimators for fracture trace intensity, trace density and mean trace length that exploit the use of circles as efficient sampling to ols. A fracture trace ii the commonly observed surface expression of a frac ture. 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 mea n trace length estimators are derived and shown to Form a self-consistent s et of two-dimensional fracture abundance measures. The intensity estimator n/4r uses the number, n. of intersections between fracture traces and a cir cular scanline of radius r. The density estimator m/2 pir(2) uses the numbe r, in, of tract endpoints inside a circular window. The mean tract length e stimator (n/m) pir/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 sa mpling biases due to orientation and also correct many errors due to censor ing and length bias that plague established scanline and areal measurement techniques. Performance of the estimators ii demonstrated by comparison wit h areal samples of a synthetic fracture trace population with known intensi ty, density and mean trace length. The estimators are also applied successf ully to a natural rock pavement with two orthogonal fracture sets, one of w hich is severely censored. Because the new circle-based estimators only req uire counts of trace-circle intersections and/or trace endpoints. they are more time-efficient than current methods for estimating geometric character istics of fracture traces. (C) 2001 Elsevier Science Ltd. All rights reserv ed.