Characterization of Fault Related Folding from High Resolution Topography: Implications for Time-Dependent Rheology of the Brittle Crust

We test candidate constitutive laws for the brittle crust using detailed three-dimensional characterization of fault-related folding. High-resolution topography reveals the presence of coseismic folds at fault tips. The shape of these folds is consistent with prediction from elasticity, with supported strains approaching the elastic limit of rock. However, over multiple earthquakes, cumulative fault-tip slip gradients and folding are 10-100 times larger than elasticity can support. Thus, there must be a mechanism for dissipation of these large stresses over the interseismic period. We focus on folding associated with normal fault growth to 1) show that fold wavelength scales with fault length by a factor of 0.15-0.25, 2) demonstrate the folding load is supported primarily within the upper crust up to wavelengths of ~10²km and down to an effective elastic thickness of ~5km, with negligible compensation from the lower crust or mantle, 3) analyze the three-dimensional fold shape and its deviation from that predicted from a linear, isotropic, elastic solution, and 4) quantify the folding contribution as a sink of tectonically accumulated strain energy. We pair these results with slip rate observations to assess candidate rheologies to describe nonelastic behavior of the brittle crust. We show that linear Maxwell viscoelasticity is inconsistent with the large range of recurrence intervals observed across natural fault systems (e.g. San Andreas fault and Eastern California Shear Zone). Alternatively, Drucker-Prager plasticity does not reproduce the shape of fault-related folding. Any plausible rheology for the brittle crust, such as non-linear viscous, must agree with both geologic and geodetic observations, allowing for both widely distributed yielding and localized fault slip. The results of our work call for a reassessment of constitutive laws assigned to the brittle crust in current earthquake cycle models.