The fractal geometry of some stylolites from the Calcare Massiccio Formation, Italy

Stylolites are serrated surfaces that form by stress enhanced dissolution. Though their geometry and morphology reflects their formation and evolution, only a few studies have attempted to quantify them. Here we present results indicating that stylolites in limestone of the Calcare Massiccio Formation (Jurassic, Italy) are fractal over 4.5 orders of magnitude in spatial bandwidth, with an average fractal dimension (obtained by spectral and scaled windowed variance analyses) clustering at 1.47. Some stylolites from the Skene (Cambrian, USA) and Tamar (Cenomanian, Israel) formations are fractal over 3 orders of magnitude, with fractal dimensions of 1.26 and 1.43. These values are high relative to other natural surfaces, and reflect the jagged topography of the stylolites. Preliminary results indicate that the fractal dimension and power are constant throughout the stylolite surface, and are not orientation dependent. Furthermore, we show that stylolite contours are fractal too. The grain size does not register in our analyses, implying that the grain is not a cutoff between processes. Rather, stylolite generating processes operate similarly below and above the grain size. Our results suggest that the geometry of these stylolites, especially at long wavelengths, may not be sensitive to the immediate fabric surrounding them.