Earthquake cycle, fault zones, and seismicity patterns in a theologically layered lithosphere

We study the coupled evolution of earthquakes and faults in a model consist ing of a seismogenic upper crust governed by damage rheology over a viscoel astic substrate. The damage rheology has two types of functional coefficien ts: (1) a "generalized internal friction" separating states associated with material degradation and healing and (2) damage rate coefficients for posi tive (degradation) and negative (healing) changes. The evolving damage modi fies the effective elastic properties of material in the upper crust as a f unction of the ongoing deformation. This simulates the creation and healing of fault systems in the upper seismogenic zone. In addition to the vertica lly averaged thin sheet approximation we introduce a Green function for thr ee-dimensional elastic half-space for the instantaneous component of deform ation. The formulation accounts in an internally consistent manner for evol ving deformation fields, evolving fault structures, aseismic energy release , and spatiotemporal seismicity patterns. These developments allow us to si mulate long histories of crustal deformation and to study the simultaneous evolution of regional earthquakes and faults for various model realizations . To focus on basic features of a large strike-slip fault system, we first consider a simplified geometry of the seismogenic crust by prescribing init ial conditions consisting of a narrow damage zone in an otherwise damage-fr ee plate. For this configuration, the model generates an earthquake cycle w ith distinct interseismic, preseismic, coseismic, and postseismic periods. Model evolution during each period is controlled by a subset of physical pr operties, which may be constrained by geophysical, geodetic, rock mechanics , and seismological data. In the more generic case with a random initial da mage distribution, the model generates large crustal faults and subsidiary branches with complex geometries. The simulated statistics depend on the sp ace-time window of the observational domain. The results indicate that long healing timescale, th, describing systems with relatively long memory, lea ds to the development of geometrically regular fault systems and the charac teristic frequency-size earthquake distribution. Conversely, short tau (h) (relatively short memory) leads to the development of a network of disorder ed fault systems and the Gutenberg-Richter earthquake statistics. For inter mediate values of tau (h) the results exhibit alternating overall switching of response from periods of intense seismic activity and the characteristi c earthquake distribution to periods of low seismic activity and Gutenberg- Richter statistics.