Assessing the work budget and efficiency of fault systems using mechanical models

We examine the work energy budget of actively deforming fault systems in order to develop a means of examining the systemic behavior of complex fault networks. Work done in the deformation of a faulted area consists of five components: ( 1) work done against gravity in uplift of topography (W-grav); ( 2) internal energy of the strained host rock (W-int); (3) work done resisting friction during slip on faults (W-fric); (4) seismic energy released in earthquake events as ground shaking (W-seis); and ( 5) work done in initializing new faults and propagating existing faults (W-prop). The energy budget of a fault system can be expressed as W-TOT = W-grav + W-int + W-fric + W-seis + W-prop. For a balanced energy budget the total of these five components will equal the external tectonic work applied to the system. We examine the work balance within hypothetical and simulated two-dimensional static fault systems using mechanical models. The boundary element method models produce a balanced work budget for both simple and complex fault system models. The presence of slipping faults reduces the internal strain energy of the faulted area (W-int), at a "cost'' of work done against friction and gravity ( and propagation and seismic energy, where applicable). Calculations of minimum work deformation match expected deformation paths, indicating the usefulness of this approach for evaluating efficiency in more complex systems. The partitioning of various work terms may express the relative efficiency or maturity of fault systems. Furthermore, calculation of potential seismic energy release can provide an upper bound to earthquake seismic moment assessments.