The influence of rock heterogeneity on the scaling properties of simulated and natural stylolites

Stylolites are among the most prominent deformation patterns in sedimentary rocks that document localized pressure solution. Recent studies revealed that stylolite roughness is characterized by two distinct scaling regimes. The main goal of the present study is to decipher whether this complex scaling behavior of stylolites is caused by the composition of the host-rock, i.e. heterogeneities in the material, or is governed by inherent processes on respective scales, namely the transition from a surface energy to an elastic energy dominated regime, as theoretically predicted. For this purpose we have developed a discrete numerical technique, based on a lattice spring model, to simulate the competition between stress, strain, and dissolution during stylolite roughening. We varied systematically the quenched noise, initially present in the material, which controls the roughening. We also changed the size, amount, and dissolution rate of the heterogeneities introduced in our model and evaluated the influence on the scaling exponents. Our findings demonstrate that the roughness and growth exponents are independent of the exact nature of the heterogeneities. We discovered two coinciding crossover phenomena in space and time that separate length and time scales for which the roughening process is either balanced by surface or elastic energies. Our observations are consistent with analytical predictions and with investigations quantifying the scaling laws in the morphology of natural stylolites. The findings presented here can further be used to refine volume loss (compaction) estimates from the finite strain pattern of stylolites.