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AAPG Bulletin


AAPG Bulletin, V. 86, No. 12 (December 2002), P. 2089-2104.

Copyright ©2002. The American Association of Petroleum Geologists. All rights reserved.

Estimating fracture trace intensity, density, and mean length using circular scan lines and windows

M. B. Rohrbaugh Jr.,1 W. M. Dunne,2 M. Mauldon3

1Tennessee Department of Environment and Conservation, Division of Underground Storage Tanks, 540 McCallie Avenue, Suite 550, Chattanooga, Tennessee, 37402-2013
2Department of Geological Sciences, 306 G&G Building, University of Tennessee, Knoxville, Tennessee, 37996-1410; email: [email protected]
3Department of Civil and Environmental Engineering, Virginia Tech, 200 Patton Hall, Mail Code 0105, Blacksburg, Virginia, 24061; email: [email protected]


M. Bruce Rohrbaugh Jr. received his B.S. degree in geology from West Virginia University in 1997 and his M.S. degree in structural geology from the University of Tennessee, Knoxville in 2000. His research interests include hydrogeology, application of computers to solving geologic problems, and structural geology. He is currently employed as a geologist with the Tennessee Department of Environment and Conservation.

William M. Dunne, although born in the United States, received his B.S. degree and Ph.D. in geology from the University of Bristol, England. He joined the Department of Geological Sciences at the University of Tennessee in 1988 as an associate professor and is now is a professor and department head. His research interests include fracture characterization particularly in younger rocks, deformation in thrust belts from large to small scale, and deformation analysis of sedimentary rocks.

Matthew Mauldon, although born in England, has geology (B.A.) and civil engineering (M.S.) degrees and a Ph.D. in civil engineering from the University of California at Berkeley. He spent eight years on the faculty at the University of Tennessee, where he collaborated with Dunne and Rohrbaugh. Mauldon is now an associate professor in the Via Department of Civil and Environmental Engineering at Virginia Tech, where he teaches and conducts research in the areas of rock mechanics, engineering geology, and geotechnical engineering.


Acknowledgment is made to the donors of The Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. Additionally, the Geological Society of America and the Southeastern Section of the Geological Society of America are thanked for their partial support of the field work. We would also like to thank M. F. Schaeffer for permission to use the fracture trace map from Rocky Creek, South Carolina, and Camilo Montes, Yen-Yit Chan, You Li, and Jim Calcagno for programming assistance. Steve Laubach, John Lorenz, and Bill Dershowitz are thanked for their insightful and constructive reviews.


Fracture characterization protocols that reduce sampling bias are likely to yield higher quality input for exploration and development decisions when dealing with naturally fractured reservoirs. A new set of estimators for fracture density, intensity, and mean trace length corrects for sampling biases and provides a useful integrated description for bulk aspects of a fracture network. These estimators are based on counts of intersections between fracture traces and circular scan lines and of trace terminations in circular windows. Application to synthetic fracture patterns with known parameters validates the use of the new estimators, which are then applied to natural fault trace maps from seismic volumes and joint trace maps from rock pavements. The new estimators are distribution independent and eliminate the effects of orientation, censoring, and length biases, which limit the effectiveness of other sampling techniques. Estimator accuracy improves as sample size increases, particularly for larger circles that exceed a fracture-defined block size. Estimator accuracy for mean trace length improves when the sample exceeds threshold count values for fracture terminations based on guidance from the analysis of similar synthetic patterns. These new estimators also provide both inputs and independent checks of predictions for fracture-generator programs used to model fracture populations in a rock volume.

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