Scaling analysis, correlation length and compaction estimates of natural and simulated stylolites. (August 2022) - Köehn, D.; Köehler, S.; Toussaint, R.; Ghani, I.; Stollhofen, H.
Abstract: Stylolites are rough dissolution surfaces that show three different scaling regimes in space and time. On the small scale surface energy dominates and stylolites roughen very slowly with a growth exponent of about 0.5 and a roughness exponent of about 1.0. On the intermediate scale elastic energy dominates and the surfaces roughening is happening faster with a growth exponent of about 0.8 and a roughness exponent of about 0.5. The transitional length between these two scaling regimes is determined by the stress during stylolite growth and termed as cross-over length scale. On the large scale another transition is reached beyond which the stylolite amplitude remains constant, this length scale is termed the correlation length. The correlation length is determined by time of growth or by the amount of compaction that happened at the interface as well as by the stylolite's system size. This length scale grows as a function of time and the dynamic exponent, which is about 2 in the surface energy dominated regime and 0.625 in the elastic energy dominated regime. We present examples of these scaling regimes for numerical as well as natural stylolites and show how the exponents can be used to determine the stylolite compaction through the different regimes. The numerical stylolites show an increase of correlation length as a function of system size in self-affine time series. Large samples of natural tectonic stylolites from Jurassic limestones of the Franconian Alb (SE Germany) exhibit all three scaling regimes in a self-affine space series. The important length scales in the natural system are the grain size or noise at 30 μm, the cross-over length between the surface and elastic energy dominated regimes at 1.4 mm and the correlation length at 5.7 cm. The overall compaction on the tectonic stylolite is estimated to be in the range of 8 cm. Highlights: Stylolites grow in 3 distinct scaling regimes. Stylolites experience 3 characteristic length scales, the grain-size, cross-over and the correlation length.