A continuum approach to the development of normal faults

We present a mechanism for the development of normal faults based on continuum flow in brittle-plastic and ductile rheology. A rate-dependent effect, as observed in rock friction studies, leads to strain localization. Analytical solutions in the wavenumber domain for infinitesimal perturbation theory are used to elucidate the nature of uniform extension of a brittle-plastic medium. Finite element models are then used to investigate strain localization under finite extension. We find that the fundamental mode of extensional instability controls the width of rift-like deformation zones, while higher-order wavenumbers produce secondary faulting on the rift floor. These higher order modes arise naturally for a sufficiently high thermal gradient and for a sufficient fraction of velocity-weakening. The superposition of these higher order wave numbers on the fundamental mode provides a simple physical description for the nucleation of fault structures with regular length scales as a function of the thickness of the brittle lithospheric layer.