Upper bound on stylolite roughness as indicator for amount of dissolution

Stylolites are rough surfaces that form by localized dissolution. Despite their abundance in carbonates and sandstones, and their importance for fluid flow and rock deformation, many fundamental issues concerning their structure and evolution are still unresolved. This manuscript studies the roughening of long parallel stylolites. Here we report measurements of stylolite surface roughness at a scale larger than ever measured before (10 ^-2-10 ¹m). Measurements were performed using ground-based-LIDAR on 6 naturally exposed surfaces of >km long stylolites in Northern Israel, producing a topographic map of the surfaces, from which roughness characteristics were derived. Our results show that for length scales below ~50cm, the stylolite morphology exhibits self-affine behavior, with a Hurst exponent H~0.65, consistent with previous studies made on smaller samples. The self-affine behavior changes for measurements made on scales above 50cm, with H decreasing almost to zero on long length scales. This observed upper-bound of self-affine roughness is measured here for the first time, but has been previously predicted by theory (Ebner et al., 2009b; Koehn et al., 2007). Our measurements support these theoretical models and together with them present a scenario in which the investigated stylolites evolve from preferential dissolution along an existing surface that was initially smooth and progressively roughened with time. Such a mechanism of stylolites growth is different from previously suggested mechanisms for other classes of stylolites, which might propagate sideways from an initial defect. Based on the theoretical roughening model that we adopted, the upper limit to fractality for this class of stylolites may be used as a measure of the amount of dissolution on stylolites. Indeed, the amount of dissolution on the stylolites in our field site, which we calculated from the upper limit to fractality, is comparable to (though slightly larger than) our estimates of dissolution from two additional independent techniques, reflecting compactive strain of ~50%.