The theory of rate and state friction unifies field, laboratory, and
theoretical analysis of the evolution of slip on natural faults. While
the observational study of earthquakes and aseismic fault slip is
hampered by its strong multi-scale character in space and time,
numerical simulations are well-positioned to link the laboratory study
of grain-scale processes to the scale at which rock masses move.
However, challenges remain in accurately representing the complex and
permanently evolving sub-surface fault networks that exist in nature.
Additionally, the common representation of faults as interfaces may miss
important physical aspects governing volumetric fault system behavior.
In response, we propose a transient viscous rheology that produces shear
bands that closely mimic the rate- and state-dependent sliding behavior
of equivalent fault interfaces. Critically, we show that the expected
tendency of the continuum rheology for runaway localization and mesh
dependence can be halted by including an artificial diffusion-type
regularization of anelastic strain rate in the softening law. We
demonstrate analytically and numerically using a simplified fault
transect that important aspects of the frictional behavior are not
significantly affected by the introduced regularization. Any
discrepancies with respect to the interfacial description of fault
behavior are critically evaluated using 1D numerical velocity stepping
and spring-slider experiments. ;Since no new physical parameters are
introduced, our model may be straightforwardly used to extend the
existing modeling techniques. The model predicts the emergence of
complex patterns of shear localization and delocalization that may
inform the interpretation of complex damage distributions observed
around faults in nature.