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

TL;DR

This study investigates stylolite surface roughness, revealing scale-dependent self-affine behavior and linking it to stress-induced instability models, with implications for fossil stress measurement.

Contribution

It introduces a model describing stylolite roughness using a Langevin equation with long-range elastic correlations, connecting laboratory measurements to stress-induced instability theory.

Findings

Roughness exhibits scale-dependent self-affinity with two distinct exponents.

A crossover length scale around 1mm correlates with stress-induced instability.

Measurements support a Langevin equation model with long-range elastic 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.