J. Phys. I France 6 (1996) 1127-1139
DOI: 10.1051/jp1:1996119

The Imaginary Part of Rock Jointing

G. Ouillon¹, D. Sornette^{1, 2}, A. Genter³ and C. Castaing<sup>3

1</sup>  Laboratoire de Physique de la Matière Condensée CNRS URA 190, Université de Nice-Sophia Antipolis, Parc Valrose, BP 71, 06108 Nice Cedex 2, France
²  Department of Earth and Space Science and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095, USA
³  B.R.G.M., avenue de Concyr, BP 6009, 45060 Orléans Cedex 2, France

Received 20 February 1996, revised 3 April 1996, accepted 2 May 1996

Abstract
The distribution of joint spacings in a granitic massive in Saudi Arabia is found to be well-described by a power-law with characteristic exponent . We compare the cumulative and density distributions and show how to correct the cumulative distribution for bias due to the finite sampling size. the exponent is close to those obtained for size distribution in fragmentation processes. We study simple models of fragmentation/jointing processes, which predict that the power law distribution must be decorated by a log-periodic modulation if the fragmentation involves a preferred ratio (even approximately so, i.e. with disorder) corresponding to an approximate discrete scale invariance. We corroborate this prediction by carrying out a more detailed analysis of the density distribution and find at least 6 log-periodic oscillations. This implies that the exponent possesses an imaginary part, embodying the existence of an average discrete scaling structure with preferred fragmentation ratio close to 1/2. The confidence level of this result is found better than 97% from synthetic tests.

© Les Editions de Physique 1996