DOI: 10.1029/2000jb900260. Practicalities of extrapolating one‐dimensional fault and fracture size‐frequency distributions to higher‐dimensional samples

Practicalities of extrapolating one‐dimensional fault and fracture size‐frequency distributions to higher‐dimensional samples

10.1029/2000jb900260

Crossref journal-article

American Geophysical Union (AGU)

Journal of Geophysical Research: Solid Earth (13)

Abstract

Previously published theory, which extrapolates fault and fracture population statistics observed in a one‐dimensional sample to two‐ and three‐dimensional populations, is found to be of limited value in practical applications. We demonstrate how significant the discrepancies may be and how they arise. There are two main sources for the discrepancies: (1) deviations from ideal spatial uniformity (spatial Poisson process) of a fault or fracture pattern and (2) non‐power law scaling of the size frequency distributions of the population. We show that even small fluctuations in spatial density, combined with variance in the estimator of population statistics, can lead to considerable deviations from the theoretical predictions. Ambiguity about power law scaling or otherwise of the underlying population is a typical characteristic of natural data sets, and we demonstrate how this can affect the extrapolation of one‐dimensional data to higher dimensions. In addition, we present new theoretical approaches to the problem of extrapolation when clustering of faults and fractures is explicitly considered. Clustering is commonly observed in the field as en echelon arrays of fault or fracture segments and we show how this property of natural patterns can be quantified and included in the theory. These results are relevant to building more realistic three‐dimensional models of the physical properties of fractured rocks, such as fracture permeability and seismic anisotropy.

Bibliography

Borgos, H. G., Cowie, P. A., & Dawers, N. H. (2000). Practicalities of extrapolating oneâdimensional fault and fracture sizeâfrequency distributions to higherâdimensional samples. Journal of Geophysical Research: Solid Earth, 105(B12), 28377â28391. Portico.

Authors 3

Hilde G. Borgos (first)
Patience A. Cowie (additional)
Nancye H. Dawers (additional)

References 40 Referenced 19

{'key': 'e_1_2_1_2_1', 'first-page': '198', 'article-title': 'Systematics of an evolving population of normal faults in scaled physical models', 'volume': '29', 'author': 'Ackermann R. V.', 'year': '1997', 'journal-title': 'Geol. Soc. Am.'} / Geol. Soc. Am. / Systematics of an evolving population of normal faults in scaled physical models by Ackermann R. V. (1997)
{'key': 'e_1_2_1_3_1', 'article-title': 'The effects of mechanical layer thickness on the systematics of an evolving population of normal faults in experimental models', 'author': 'Ackermann R. V.', 'year': '2000', 'journal-title': 'J. Struct. Geol.'} / J. Struct. Geol. / The effects of mechanical layer thickness on the systematics of an evolving population of normal faults in experimental models by Ackermann R. V. (2000)
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{'key': 'e_1_2_1_13_1', 'first-page': '88', 'volume-title': 'Extended Abstract Volume: Faulting, Fault Sealing and Fluid Flow in Hydrocarbon Reservoirs', 'author': 'Dawers N. H.', 'year': '1996'} / Extended Abstract Volume: Faulting, Fault Sealing and Fluid Flow in Hydrocarbon Reservoirs by Dawers N. H. (1996)
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Dates

Type	When
Created	21 years, 6 months ago (Feb. 3, 2004, 6:41 p.m.)
Deposited	1 year, 11 months ago (Sept. 22, 2023, 2:48 p.m.)
Indexed	1 month, 1 week ago (July 14, 2025, 11:22 p.m.)
Issued	24 years, 8 months ago (Dec. 10, 2000)
Published	24 years, 8 months ago (Dec. 10, 2000)
Published Online	24 years, 8 months ago (Dec. 10, 2000)
Published Print	24 years, 8 months ago (Dec. 10, 2000)

Funders 0

None

BibTeX

@article{Borgos_2000, title={Practicalities of extrapolating one‐dimensional fault and fracture size‐frequency distributions to higher‐dimensional samples}, volume={105}, ISSN={0148-0227}, url={http://dx.doi.org/10.1029/2000jb900260}, DOI={10.1029/2000jb900260}, number={B12}, journal={Journal of Geophysical Research: Solid Earth}, publisher={American Geophysical Union (AGU)}, author={Borgos, Hilde G. and Cowie, Patience A. and Dawers, Nancye H.}, year={2000}, month=dec, pages={28377–28391} }

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