Effects of density contrasts on the orientation of stresses in the lithosphere: Relation to principal stress directions in the Transverse Ranges, California

Abstract

The influence of stresses arising from horizontal density contrasts on the orientation and relative magnitudes of principal stresses in an otherwise uniform lithospheric stress field is investigated. A simple model is constructed, in which a local deviatoric stress due to a density anomaly, embedded within or just below the lithosphere, and a regionally constant deviatoric stress field are each approximated by biaxial tensors. The net stress field is obtained from the sum of the two. Both the relative magnitudes of principal stresses and the magnitude of the angular difference in principal stress direction of the summed tensor compared with that obtained in the absence of buoyancy forces depend on two parameters. The first is the ratio τ/τ′, where τ is a measure of the magnitude of the regional deviatoric stress and τ′ is the magnitude of the stress arising from buoyancy forces associated with the density anomaly. The second parameter is the angle between the trend of the density anomaly and the direction of maximum compressional stress that obtains in the absence of any perturbation by the local buoyancy forces. The directions of the principal axes of the total stress field are found to differ by up to 90° from those of the reference stress field. The model is applied to the Transverse Ranges, California, where the observed 23° difference in orientation of principal horizontal compressive stress compared with the principal compressive stress direction in central California constrains the predicted value of τ/τ′ to be approximately −0.4. This is consistent with an independently calculated range of τ/τ′ in which τ′ is inferred from seismological constraints on the magnitude of density variations underneath the Transverse Ranges and τ is inferred from observations of heat flow along the San Andreas fault in central California. The agreement between the two estimates of τ/τ′ supports the hypothesis that the observed differences in horizontal principal stress orientation in California can be explained by the combined influence of a local negative buoyancy force under the Transverse Ranges and a regional stress field associated with transcurrent deformation within the Pacific‐North American plate boundary zone. The observed counterclockwise angular difference in principal horizontal stress direction in the Transverse Ranges compared with central California implies that the plane of maximum right lateral shear stress is also rotated counterclockwise relative to that in central California. This supports the possibility that the “big bend” in the San Andreas fault may be a consequence of the negative buoyancy forces acting in the Transverse Ranges, and not the cause of Transverse Ranges formation, as has often been assumed.