Analytic modelling of the deformation due to plate coupling at subduction zones
Creators: name: Douglass, Julian J.
Publisher: name: University of British Columbia
Year: 2009

description: A majority of the largest earthquakes result from the build-up of coupling stresses between tectonic plates at subduction zones. These earthquakes arise, periodically, when the accumulating stress reaches a level which exceeds the rupture strength of the interface. The stresses along the interface may be inferred from geodetic observations obtained at the Earth's surface. The process of strain accumulation along subduction boundaries is of particular interest due to the hazard associated with great earthquakes. Hence, a significant set of geodetic data has been obtained above subduction zones. However, successful interpretation of this data for the magnitude and distribution of stress along the interface requires that a suitable physical model of the strain accumulation process be available. Here, two approaches to this modelling problem are considered. The first is a kinematic approach to the problem in which dislocation theory is used to represent the stick-slip cycle. According to this representation, the deformation due to locking is constrained by the kinematics of plate convergence, with the most important parameter being the plate convergence rate. Hence, an assumption implicit to models that are based on this representation is that the dynamics of subduction can be physically represented by a model constrained only by kinematic parameters. To evaluate this assumption, model solutions are calculated for the case of an infinite half-space Earth. New analytic expressions are derived for this case which allow for calculation of the stress distribution over the complete half-space. The model solutions reveal a subsurface stress field which is difficult to justify on physical grounds. These difficulties raise questions regarding previous interpretations of geodetic data which were based on this model. By exclusively using this model, other possible dynamic scenarios, other than that which is prescribed by the kinematic approach, are excluded from consideration by the interpreter. Given the limitations of the dislocation represention, a second, alternative approach to the problem is proposed. This approach is based on a dynamic representation of the process of strain build-up. The overthrust wedge is treated as a free body with tractions applied along its surface. The deformation is then calculated for a prescribed distribution of force along the plate interface. A uniform elastic rheology is assumed. Thus, the fundamental elasticity problem to be solved is that of an infinite elastic wedge subjected to traction boundary conditions. Solutions are obtained by two different, but complementary techniques. In the first, the wedge is conformally mapped to an infinite strip and solutions obtained by Fourier transform methods. Equivalent solutions are also obtained by applying the Mellin transform directly to the biharmonic equation for the Airy stress function. The results of these calculations show that entirely different distributions of basal tractions can lead to very similar deformation signals along the top surface of the wedge. Thus, an ambiguity in the interpretation of the geodetic data is confirmed which is not accounted for in deformation predictions based on the dislocation approach.