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Stylolites are rough surfaces formed by localized dissolution, mostly in carbonates and sandstones. They often account for a large degree of dissolution, and their impact on porosity and permeability is well recognized. Understanding their formation mechanism can advance our ability to predict their occurrence and effect on flow, which has appreciable geological and economical implications. Still, many fundamental issues concerning their structure and evolution are still unresolved. This manuscript studies the roughening of long parallel stylolites, which are one of three types of stylolite populations identified by us in a separate paper. Here we report measurements of stylolite surface roughness at a scale larger than ever measured before (10-2-10 1 m). Measurements were performed using ground-based-LIDAR on 6 naturally-exposed surfaces of >km long stylolites in Northern Israel. The outcome of these measurements is a topography model of the surfaces, on which different techniques for calculating their roughness characteristics were used. Our results show that up to scales of ~10cm, the average deviation of the surfaces from a planar surface is related to the scale by a power-law with an exponent H. The surfaces are thus defined as self-affine only up to ~10cm with H~0.7. Above this scale H decreases almost to zero. This observed upper-bound of self-affine roughness measured here for the first time has been predicted by theory [1, 2, 2bis]. Our measurements support these theoretical models and together with them present a scenario in which 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 stylolite 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 of the stylolites in our field site which we calculated from the upper limit to fractality is comparable to our estimates of dissolution from two additional independent techniques.

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