Using surface velocities and subsurface stressing rate tensors to resolve interseismic deep slip distribution on closely spaced faults
Authors: Loveless Jack , Elston Hanna , Cooke Michele , Marshall Scott 
Published: March 2022

&lt;p&gt;Inversions of interseismic surface velocities alone often struggle to uniquely resolve the 3D fault slip rate distribution along systems with branching or closely spaced faults, such as the southern San Andreas Fault (SAF) in California, USA. Local stress states inferred from microseismic focal mechanisms may provide additional constraints on interseismic deep slip because they contain information about stress at depth and closer to the interseismic deep slip than GPS surface velocities. Here, we invert forward-model generated stressing rate tensors and surface velocities, individually and jointly, to assess how well the inverse approach estimates the distribution of slip rates along both simple and complex fault systems. The inverse approach we present can constrain both the interseismic deep slip rates that reveal fault locking depths and the relative activity of faults.&amp;#160;&lt;/p&gt;&lt;p&gt;We assess the inverse approach by inverting forward model-generated stressing rate tensors and surface velocities to recover fault slip distribution for two models. Forward models that include either a single, planar strike-slip fault or the 3D complex geometry of the southern SAF simulate interseismic loading in a two-step back-slip like approach. The forward models produce surface velocities with a 15 km spacing, which is similar to the GPS station density near the southern SAF, or at GPS station locations in southern California. We utilize the planar fault model to determine the smoothing parameters and stressing rate tensor spacing (&gt;10 km) that minimize the misfit. The 10 km minimum spacing samples crustal volumes that are likely to have &gt;39 focal mechanisms needed to robustly determine a stress tensor. The planar fault model inversions and the availability of focal mechanisms along the southern SAF inform the stressing rate tensor locations that we use to assess the complex model inversion performance. Because focal mechanisms provide normalized deviatoric stress tensors, we invert the full forward-model generated stress tensor as well as the deviatoric and normalized deviatoric stress tensors; this allows us to assess the impact of removing stress magnitude from the inversion.&amp;#160;&amp;#160;&lt;/p&gt;&lt;p&gt;The inversions of the forward model-generated stressing rate tensors and surface velocities recover the slip rate distribution well with the exception of the normalized deviatoric stressing rate tensor inversion, which struggles to resolve the fault slip rates in both models. The inversions recover the locking depth with a broader transition zone than prescribed in the forward model due to the smoothing-based regularization within the inversion. The full stressing rate tensor inversion resolves slip rates better than the surface velocity inversions. The deviatoric stressing rate tensor inversion resolves slip rates better than the surface velocity inversion in the complex fault model but not in the planar fault model. Inverting stress and surface velocity information jointly improves the fit to the forward model slip distribution for both models. Joint inversions of both surface velocities and local stress states derived from focal mechanisms may improve constraints on the interseismic deep slip rates and locking depths in regions of complex faulting.&lt;/p&gt;