  We study the roughness of stylolite surfaces (i.e. natural
pressure-dissolution surfaces in sedimentary rocks) from profiler measurements
at laboratory scales. The roughness is shown to be nicely described by a
self-affine scaling invariance. At large scales, the roughness exponent is
$\zeta_1 \approx 0.5$ and very different from that at small scales where
$\zeta_2 \approx 1.1$. A cross-over length scale at around $\lambda_c =1$mm is
well characterized and interpreted as a possible fossil stress measurement if
related to the Asaro-Tiller-Grinfeld stress-induced instability. Measurements
are consistent with a Langevin equation that describes the growth of stylolite
surfaces in a quenched disordered material with long range elastic
correlations.
