The Botucatu Sandstone of the Paraná basin of Brazil, a Jurassic eolianite, exhibits unusually deep, basinwide penetration of meteoric water. This flow of dilute groundwater has removed calcite cement for an average distance of about 140 km from the outcrop and down to a burial depth of about 250 m. Feldspar has been leached from the framework for about 30 km downdip, transforming what was deposited as a feldspathic sandstone into a diagenetic quartz arenite on outcrop. These two dissolution processes have generated appreciable secondary porosity by weathering reactions at sites far removed from contact with the atmosphere. Between 100 and 500 pore volumes of water have passed through the aquifer system to produce this leaching, making this an end-member case of extensive meteoric diagenesis of sandstone. Consideration of other basins with meteoric incursion suggests that basin-scale leaching is favored when uplift of one margin provides a steep gradient and there is a downdip escape route via faults or outcrop of the aquifer. Cratonic basins close to rifted-continental margins seem to provide the best chance of meeting these conditions.