## Stress field models from Maxwell stress functions: Southern California

Peter BirdPublished July 11, 2017, SCEC Contribution #7251

The lithospheric stress field is formally divided into three components: a standard pressure which is a function of elevation (only), a topographic stress anomaly (3-D tensor field), and a tectonic stress anomaly (3-D tensor field). The boundary between topographic and tectonic stress anomalies is somewhat arbitrary, and here is based on the modeling tools available. The topographic stress anomaly is computed by numerical convolution of density anomalies with three tensor Green’s functions provided by Boussinesq, Cerruti, and Mindlin. By assuming either a seismically-estimated or isostatic Moho depth, and by using Poisson ratio of either 0.25 or 0.5, I obtain 4 alternative topographic stress models. The tectonic stress field, which satisfies the homogeneous quasi-static momentum equation, is obtained from particular second-derivatives of Maxwell vector potential fields which are weighted sums of basis functions representing constant tectonic stress components, linearly-varying tectonic stress components, and tectonic stress components that vary harmonically in 1, 2, and 3 dimensions. Boundary conditions include zero traction due to tectonic stress anomaly at sea level, and zero traction due to the total stress anomaly on model boundaries at depths within the asthenosphere. The total stress anomaly is fit by least-squares to both World Stress Map data and to a previous faulted-lithosphere, realistic-rheology dynamic model of the region computed with finite-element program Shells. No conflict is seen between the two target datasets, and the best-fitting model (using an isostatic Moho and Poisson ratio 0.5) gives minimum directional misfits relative to both targets. Constraints of computer memory, execution time, and ill-conditioning of the linear system (which requires damping) limit harmonically-varying tectonic stress to no more than 6 cycles along each axis of the model. The primary limitation on close fitting is that the Shells model predicts very sharp shallow stress maxima and discontinuous horizontal compression at the Moho, which the new model can only approximate. The new model also lacks the spatial resolution to portray the localized stress states that may occur near the central surfaces of weak faults; instead, the model portrays the regional or background stress field which provides boundary conditions for weak faults. Peak shear stresses in one registered model and one alternate model are 120 and 150 MPa, respectively, while peak vertically-integrated shear stresses are 2.9×10^12 and 4.1×10^12 N/m. Channeling of deviatoric stress along the strong Great Valley and the western slope of the Peninsular Ranges is evident. In the neotectonics of southern California, it appears that deviatoric stress and long-term strain-rate have a negative correlation, because regions of low heat-flow are strong and act as stress guides while undergoing very little internal deformation. In contrast, active faults lie preferentially in areas with higher heat-flow, and their low strength keeps deviatoric stresses locally modest.

**Key Words**

neotectonics, dynamics, seismotectonics, rheology, crust, lithosphere, California

**Citation**

Bird, P. (2017). Stress field models from Maxwell stress functions: Southern California. *Geophysical Journal International*, 210, 951-963. doi: 10.1093/gji/ggx207. http://peterbird.name/publications/2017_FlatMaxwell/2017_FlatMaxwell.htm

**Related Projects & Working Groups**

Community Stress Model, Stress and Deformation Over Time (SDOT)