Roughness of stylolites: a stress-induced instability with non local interactions

Abstract

We study the roughness of stylolite surfaces (i.e. natural pressure-dissolution surfaces in sedimentary rocks) from profiler measurements at laboratory scales. The roughness is shown to be nicely described by a self-affine scaling invariance. At large scales, the roughness exponent is \(\zeta_1 \approx 0.5\) and very different from that at small scales where \(\zeta_2 \approx 1.1\). A cross-over length scale at around \(\lambda_c =1\)mm is well characterized and interpreted as a possible fossil stress measurement if related to the Asaro-Tiller-Grinfeld stress-induced instability. Measurements are consistent with a Langevin equation that describes the growth of stylolite surfaces in a quenched disordered material with long range elastic correlations.