Stereological and other methods applied to rock joint size estimation - Does Crofton's theorem apply?

Lyman, GJ (2003) Stereological and other methods applied to rock joint size estimation - Does Crofton's theorem apply?. Mathematical Geology, 35 1: 9-23. doi:10.1023/A:1022326927389


Author Lyman, GJ
Title Stereological and other methods applied to rock joint size estimation - Does Crofton's theorem apply?
Journal name Mathematical Geology   Check publisher's open access policy
ISSN 0882-8121
Publication date 2003-01-01
Sub-type Article (original research)
DOI 10.1023/A:1022326927389
Volume 35
Issue 1
Start page 9
End page 23
Total pages 15
Editor W.E. Sharp
Place of publication New York
Publisher Kluwer Academic Publishers
Language eng
Subject C1
290704 Geomechanics
640200 Primary Mining and Extraction Processes
Abstract A number of authors concerned with the analysis of rock jointing have used the idea that the joint areal or diametral distribution can be linked to the trace length distribution through a theorem attributed to Crofton. This brief paper seeks to demonstrate why Crofton's theorem need not be used to link moments of the trace length distribution captured by scan line or areal mapping to the moments of the diametral distribution of joints represented as disks and that it is incorrect to do so. The valid relationships for areal or scan line mapping between all the moments of the trace length distribution and those of the joint size distribution for joints modeled as disks are recalled and compared with those that might be applied were Crofton's theorem assumed to apply. For areal mapping, the relationship is fortuitously correct but incorrect for scan line mapping.
Keyword Mathematics, Interdisciplinary Applications
Geosciences, Multidisciplinary
Trace Length
Discontinuity
Rock Joint
Stereology
Crofton's Theorem
Moments
Size Distribution
Q-Index Code C1

 
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Created: Wed, 15 Aug 2007, 11:18:56 EST