  The `plate tectonics' is an observed fact and most models of earthquake
incorporate that through the frictional dynamics (stick-slip) of two surfaces
where one surface moves over the other. These models are more or less
successful to reproduce the well known Gutenberg-Richter type power law in the
(released) energy distribution of earthquakes. During sticking period, the
elastic energy gets stored at the contact area of the surfaces and is released
when a slip occurs. Therefore, the extent of the contact area between two
surfaces plays an important role in the earthquake dynamics and the power law
in energy distribution might imply a similar law for the contact area
distribution. Since, fractured surfaces are fractals and tectonic plate-
earth's crust interface can be considered to have fractal nature, we study here
the contact area distribution between two fractal surfaces. We consider the
overlap set of two self-similar fractals, characterised by the same fractal
dimensions, and look for their distribution. We have studied numerically the
specific cases of both regular and random Cantor sets in one dimension and
gaskets and percolation fractals in two dimension. We find that in all the
cases the distributions show an universal finite size scaling behavior. The
contact area distributions have got a power law decay for both regular and
random Cantor sets and also for gaskets. However, for percolation clusters the
distribution shows Gaussian variation.
