Percolation description of the global topography of Earth and the moon

Remarkable global correlations exist between geometrical features of terrestrial surfaces on Earth, current mean sea level, and its geological internal processes whose origins have remained an essential goal in the earth sciences. Theoretical modeling of the ubiquitous self-similar fractal patterns observed on Earth and their underlying rules is indeed of great importance. Here I present a percolation description of the global topography of Earth in which the present mean sea level is automatically singled out as a critical level in the model. This finding elucidates the origins of the appearance of scale invariant patterns on Earth. The criticality is shown to be accompanied by a continental aggregation, unraveling an important correlation between the water and long-range topographic evolutions. To have a comparison point in hand, I apply such an analysis to the lunar topography which reveals various characteristic features of the Moon.