Self-induced deformation on the fault plane during an earthquake part I: Continuous normal displacements

The problem of the coseismic deformation induced by an earthquake on its own fault plane is investigated here. The analysis concentrates on the on-fault displacement field accompanying the occurrence of an earthquake in response to a prescribed uniform shear slip and it is carried out on the basis of the classical analytical model by OKADA (1992) for a rectangular fault buried in an elastic homogeneous half-space delimited by a planar free surface. The analysis is subdivided into two separate papers: the first dealing with normal and the second with tangential on-fault displacements. In this first paper, concerning the study of the normal displacement component, the contributions of the source and of the correction introduced by the free surface are investigated separately and their dependence on the fault characteristics is thoroughly discussed. Particular attention is also devoted to the effects of the normal displacement on the fault surface geometry. It will be shown that the main effect is that of deforming the fault itself, with deformation consisting chiefly in a rotation of the plane and in a bending of the fault edges. The rotation angle is negligibly small (on the order of 1-10 μrad) for a single earthquake, although repeated seismic events occuring on the same fault might result in rotations of several degrees over geological time scales.