Permeability tensors of both macrofracture and microfracture systems were measured progressively along the depth of limestone formations at severed sites. It was found that the principal permeability values KX, Ky and Kz in these permeability tensors all decrease simultaneously and logarithmically with depth. However, the limestone aquifers are composed of an upper region where the larger permeability ellipsoid is upright or prolate and characterized by Kz>Kx and Kz>Ky, a transitional zone, and a lower zone whose smaller permeability ellipsoid is horizontal or oblate and characterized by KZ