We propose a method to evaluate the stress generated at the local scale by the spatial variations of the gravitational potential energy (GPE), which is related to inhomogeneous topography and mass distribution in the lithosphere. We show that it is possible to infer these local stress sources from the second spatial derivatives of a geoid height grid, used as a proxy of the GPE.
The coherence of the method is validated on a passive margin, the Bay of Biscay. The result is that expected in such a geological configuration, with extensional local stress sources with the maximum horizontal principal stress parallel to the margin and compressive sources with the maximum horizontal principal stress perpendicular to the margin in the continental and oceanic lithosphere, respectively.
We apply the method to Western Europe in order to provide a better understanding of the complex spatial variation of the present-day tectonic activity. Our results indicate a stress pattern from the local sources dominated by short-space-wavelength (of the order of a few tens of kilometers) variations in the tectonic style and in the direction of the maximal horizontal principal stress σH. A comparison of the σH orientations and tectonic style from the local sources with the ones of the World Stress Map (WSM) data set indicates that the local stress sources can be representative of the deviatoric stress state in some regions. Our results explain 71% of the faulting styles for the earthquake fault-plane solutions in the WSM, which is better than the classical compressive NW-SE stress field model. In the central part of the Pyrenees, the agreement between earthquake fault-slip directions and the direction of shear stress from the local sources acting on the associated fault planes is compatible with the extensional stress field evidenced by recent investigations.