Masters Theses

Date of Award


Degree Type


Degree Name

Master of Science



Major Professor

William M. Dunne, Matthew Mauldon

Committee Members

Robert D. Hatcher


The purpose of this thesis is to evaluate and demonstrate the performance of new circular scanline and circular window estimators of joint intensity, density and mean tracelength. The estimators are distribution independent and provide a rapid means of estimating parameters, because only counts of fracture trace intersections and/or trace endpoints are needed. These estimators defeat the problems of orientation bias, censoring and length bias, which plagued previous methods. Using synthetic patterns with known parameters, the estimators reliably match control values. When applied to nine different joint sets or pavements, the estimators also correctly estimate fracture characteristics. A 95% prediction interval is used to establish confidence in measurements by defining the likely range for new predicted values. Plots for prediction interval show that the interval for predicted values is reduced and hence, estimate quality improved more efficiently by using sampling schemes that increase radius rather than number of circles. Larger circles are more efficient because they effectively average out spatial heterogeneity. When estimating mean tracelength, reliability of estimates is also improved by sampling schemes that yield large counts of fracture endpoints. Analysis of synthetic patterns shows that for trace centers described by a Poisson process, sampling schemes that capture 20 endpoints, on average, are needed to produce reliable results. This value should not be applied literally to natural patterns, as they are not typically Poissonian, but this analysis emphasizes the benefits of large sample size. These estimators may be applied to any type of data set that consists of linear traces, including fault traces on a planar slice through a 3-d seismic reflection data cube. (8719 kB)
Files over 3MB may be slow to open. For best results, right-click and select "save as..."