A plate flexure approximation to postseismic and interseismic deformation

Abstract

The rather large postseismic deformation that is associated with two‐dimensional dip‐slip faulting in the lithosphere is related to the bending of a free plate generated by dip‐slip faulting. In the absence of gravity, asthenosphere relaxation eventually permits the faulted lithosphere to assume the dihedral configuration of a faulted free plate. For thrust faulting, the faulted area is depressed into the asthenosphere, and the flanks of the plate slope uniformly upward. In the presence of gravity, buoyancy forces act upon the plate, and the ultimate (t→∞) postseismic uplift is approximated (y/α > 0.2) by w1 exp (−y/α) (cos y/α ‐ sin y/α), where w1 is an explicit function of the fault parameters and lithosphere properties, y is the horizontal distance from the downdip end of the fault, and α is the flexural parameter for the lithosphere plate. The relaxed‐asthenosphere response is the sum of the coseismic deformation (unrelaxed‐astheriosphere response) and this ultimate postseismic deformation. The annual, steady deformation associated with strain accumulation at a subduction zone is simply the relaxed‐asthenosphere response to virtual, normal slip on the main thrust zone of an amount equal to the annual plate convergence. From these relations we have estimated the deformation (strain and uplift) expected along the Pacific coast of northern Honshu. The estimated deformation is about twice the observed deformation, but the predicted geographical distribution of the deformation is similar to the observed deformation.