An elastic plate model for interseismic deformation in subduction zones

Geodetic observations of interseismic surface deformation in the vicinity of subduction zones are frequently interpreted using simple kinematic elastic dislocation models (EDM). In this theoretical study, we develop a kinematic EDM that simulates plate subduction over the interseismic period (the elastic subducting plate model (ESPM)) having only 2 more degrees of freedom than the well-established back slip model (BSM): an elastic plate thickness and the fraction of flexural stresses due to bending at the trench that are released continuously. Unlike the BSM, in which steady state deformation in both plates is assumed to be negligible, the ESPM includes deformation in the subducting and overriding plates (owing to plate thickness), while still preserving the correct sense of convergence velocity between the subducting and overriding plates, as well as zero net steady state vertical offset between the two plates when integrated over many seismic cycles. The ESPM links elastic plate flexure processes to interseismic deformation and helps clarify under what conditions the BSM is appropriate for fitting interseismic geodetic data at convergent margins. We show that the ESPM is identical to the BSM in the limiting case of zero plate thickness, thereby providing an alternative motivation for the BSM. The ESPM also provides a consistent convention for applying the BSM to any megathrust interface geometry. Even in the case of nonnegligible plate thickness, the deformation field predicted by the ESPM reduces to that of the BSM if stresses related to plate flexure at the trench are released either continuously and completely at shallow depths during the interseismic period or deep in the subduction zone (below similar to 100 km). However, if at least a portion of these stresses are not continuously released in the shallow portion of the subduction zone (via seismic or aseismic events), then the predicted surface velocities of these two models can differ significantly at horizontal distances from the trench equivalent to a few times the effective interseismic locking depth.