Identification of stress fields from stress orientations in tsunamigenic zones: SUMATRA and SAMOA

Modelling of stresses in the lithosphere is important for identification of stress regimes (and, consequently, the types of possible earthquakes) in different seismically active regions of the earth’s crust. We have developed a computational technique that allows us to model stress fields (particularly maximum shear stress and mean stress) in the Earth’s crust from discrete data on stress orientations. The approach is based on the hybrid FEM Trefftz formulation. This suggests that the considered domain is discretized into subdomains (elements) where the Kolosov-Muskhelishvili’s complex potentials are approximated by piecewise continuous polynomials. The continuity of the potentials is forced at certain collocation points on the interfaces between subdomains. Continuity of tractions is imposed on the boundaries of tectonic plates. Data on stress orientations from the World Stress Map Project (http://dc-app3-14.gfz-potsdam.de/) are used directly in formulation of a minimisation problem that provides the best fit to the data with the continuity constraints. This approach shows stable results for inhomogeneous WSM data subjected to high errors. The results of modelling are not unique because no data on stress magnitudes were used. Thus, the obtained solution for maximum shear stress contains one free multiplicative parameter and one additive free parameter which is included in the mean stress, while stress trajectories are determined uniquely. Despite this non-uniqueness some conclusions regarding most likely stress regimes in investigated regions can be made. Stress fields in two regions (Samoa and Sumatra) where recent disastrous earthquakes (followed by tsunamis) occurred have been studied. The Samoa region (180W to 168W and 25S to 13S) was discretized with 120 triangular elements and 10 collocation points on every interface. The Sumatra region (20S to 10N and 80E to 110E) was discretized with 147 triangular elements and 6 collocation points on inner element interfaces and 18 collocation points on plate boundary element interfaces. Our calculations reveal low maximum shear stresses in locations close to the epicentres of the 2004 and 2009 earthquakes (see maps of maximum in-plane shear stresses in the figure). This independently confirms the fact that the most likely stress regimes in these areas have to be either thrust or normal faulting. Both of them are potentially tsunamigenic. Therefore the proposed approach can be used for identification of other regions where no reliable data on stress regimes are known. Contour maps of determined maximum shear stress and epicenter locations (dot)