  Stylolites are natural pressure-dissolution surfaces in sedimentary rocks. We
present 3D high resolution measurements at laboratory scales of their complex
roughness. The topography is shown to be described by a self-affine scaling
invariance. At large scales, the Hurst exponent is $\zeta_1 \approx 0.5$ and
very different from that at small scales where $\zeta_2 \approx 1.2$. A
cross-over length scale at around $\L_c =1$~mm is well characterized.
Measurements are consistent with a Langevin equation that describes the growth
of a stylolitic interface as a competition between stabilizing long range
elastic interactions at large scales or local surface tension effects at small
scales and a destabilizing quenched material disorder.

Materials Science;Disordered Systems and Neural Networks;Statistical Mechanics