Dynamics of fault creep

Observations along the surface traces of active faults in California and elsewhere indicate that tectonic displacement can occur as seismic slip or as aseismic fault creep. Fault creep occurs as secular displacement and as displacement episodes, called “creep events,” which last a few hours to days and include from a millimeter or less to a few tens of millimeters of displacement. Instrumental measurements of displacement versus time during creep events show that many events have a characteristic, simple form, including a steep beginning, followed by a gradual decay in the rate of displacement. Some creep events display small amounts of precursory slip, and many seem to be composed of several discrete “simple” events. Propagation of creep events along the San Andreas, Calaveras, and Imperial faults in California has been inferred from the nearly simultaneous observation of creep events at nearby creepmeters and from kinematic modeling of continuous measurements of strain during creep events. Fault creep can be viewed as arising from the interplay of three factors: stress applied to the fault from external sources; stress caused by the geometry and distribution of displacement on the fault, arising from the elastic response of the surrounding medium to the displacements within the anelastic fault zone itself; and the constitutive relations characterizing the resistance to slip on the fault. Analytic solutions are presented for a simple, rectangular dislocation, quasi-static model of nonpropagating fault creep assuming viscous and quasi-plastic (power law creep) fault zone rheology and for a multi-element (composed of several rectangular or striplike dislocation surfaces), quasi-static model assuming a viscous rheology. Viscous rheology implies solutions composed of exponentials that decay with time. The simple, one-element, quasi-plastic model is in agreement with the form of creep events observed at Melendy Ranch, California. A matrix formulation is presented to calculate dislocation stresses on a fault zone in a half-space or plate. The formulation involves the division of the dislocation surface into strips or rectangles and the use of published solutions to calculate the stress resulting from displacement on each individual element. Results from the matrix method agree with analytic results for equilibrium displacements on “stress-free” cracks. The matrix formulation is then used as the basis for a numerical method to simulate one- and two-dimensional propagating creep assuming a quasi-plastic rheology on the fault zone. Results from this method agree reasonably well with observations of afterslip from the 1966 Parkfield, 1975 Oroville, and 1979 Imperial Valley, California, earthquakes and of a propagating creep event observed along the southern Calaveras fault, central California, during July 1977. This method of analysis, and the assumption that creep at each point on the fault zone follows a power law rheology after the applied stress reaches a spatially varying yield stress, can explain the secular and episodic nature of fault creep; afterslip; the simple shape of some individual events and the multiple, composite shape of others; and the propagation of creep events. On the southern Calaveras fault, observations of propagating creep indicate a yield stress near zero at the surface and throughout much of the fault zone. However, they also indicate the presence of a zone at a depth of about 0.5 km, and about 5 km long, with a yield stress of about 15 bars (1.5 MPa). The methods of solution presented here should be applicable to many problems in the dynamics of faulting.