Journal de Physique I

| Abstract |

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

The Imaginary Part of Rock Jointing

G. Ouillon¹, D. Sornette^{1, 2}, A. Genter³ and C. Castaing³

¹ 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 $\mu\simeq 0.5$ . 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 $\mu$ 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 $\mu$ 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.