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AAPG Bulletin


AAPG Bulletin, V. 87, No. 8 (August 2003),

P. 1255-1272.

Copyright copy2003. The American Association of Petroleum Geologists. All rights reserved.

Improving curvature analyses of deformed horizons using scale-dependent filtering techniques

Stephan Bergbauer,1 Tapan Mukerji,2 Peter Hennings3

1The Rock Fracture Project, Department of Geological and Environmental Sciences, Stanford University, California; Current address: BP Exploration (Alaska) Inc., P.O. Box 196612 Anchorage, Alaska 99519-6612; email: [email protected]; email: [email protected]
2Department of Geophysics, Stanford University, California
3Phillips Petroleum Company, Bartlesville, Oklahoma


Stephan Bergbauer is a development geologist with BP Exploration (Alaska). He received a B.S. degree in geology from the RWTH Aachen, Germany, an M.S. degree in geology from the University of Hawaii at Manoa, and a Ph.D. from Stanford University. The research described in this paper is part of Stephan's Ph.D. work with the Rock Fracture Project at Stanford University. Stephan's thesis investigates the folding and fracturing of sedimentary strata.

Tapan Mukerji is a research associate with the Stanford Rock Physics Lab at Stanford University. He received his Ph.D. in geophysics in 1995 from Stanford University, and his B.S. and M.S. degrees from Banaras Hindu University, India. His research expertise includes rock physics, wave phenomena, and geostatistics. Tapan Mukerji is a co-author of The Rock Physics Handbook and is a recipient of Society of Exploration Geophysicists' Karcher Award (2000) for outstanding young geophysicists.

Peter Hennings is the structure and tectonics technology leader at Phillips Petroleum in Houston, Texas. His role at Phillips involves exploration and production consultation worldwide, technology development and implementation, and training. From 1988 to 1999, Peter worked for Mobil Technology in a similar capacity. Peter received his B.S. and M.S. degrees in geology from Texas AampM University and his Ph.D. in geology from the University of Texas, Austin.


S. Bergbauer was supported by the National Science Foundation under Grant No. EAR-0125935. T. Mukerji is supported by the Stanford Rock Physics Project and by the Department of Energy funding. The authors wish to thank Dave Pollard, Martin Mai, and Stephanie Prejean for their productive comments on the manuscript. The manuscript benefited from review by A. Lacazette, S. Cooper, and W. Devlin. Many thanks to Eric Flodin and Frank Schneider for their help with the field data collection.


Fractures, which are common structural heterogeneities in geological folds and domes, impact the charge, seal, and trapping potential of hydrocarbon reservoirs. Because of their effects on reservoir quality, the numerical prediction of fractures has recently been the focus of petroleum geoscientists. A horizon's curvature is commonly used to infer the state of deformation in those strata. It is assumed that areas of elevated calculated curvatures underwent elevated deformation, resulting in a concentration of fractures and faults there. Usually, curvatures are calculated from spatial data after sampling the continuous horizon at discrete points. This sampled geometry of the horizon includes surface undulations of all scales, which are then also included in the calculated curvatures. Including surface undulations of all scales in the curvature analysis leads to noisy and questionable results. We argue that the source data must be filtered prior to curvature analysis to separate different spatial scales of surface undulations, such as broad structures, faults, and sedimentary features. Only those surface undulations that scale with the problem under consideration should then be used in a curvature analysis. For the scale-dependent decomposition of spatial data, we test the suitability of four numerical techniques (Fourier [spectral] analysis, wavelet transform filtering, singular value decomposition, factorial kriging) on a seismically mapped horizon in the North Sea. For surfaces sampled over a regular grid (e.g., seismic data), Fourier (spectral) analysis extracts meaningful curvatures on the scale of broad horizon features, such as structural domes and basins.

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