The mean transmission properties of a fault with imperfect facial contact

A model of a fault where the two faces do not exactly conform is characterized by a distribution of approximately circular contacts; elsewhere, the faces are stress-free. This contrasts with most earlier models, which have assumed the contact geometry to be equivalent to a plane distribution of approximately circular cracks. The contact regions in the present model are taken to be sparsely distributed, and averaged interface conditions are derived that are accurate to second order. At lowest order they agree with established formulae for the normal stiffness of non-conforming surfaces. These averaged, or mean, conditions are expected to hold at wavelengths long compared with the radii and spacing distance of the contact points. Unsurprisingly, they are equivalent to the continuity conditions for a thin elastic layer whose properties are given here in terms of the parameters of the contact surface.