Fault geometry and earthquake mechanics
Earthquake mechanics may be determined by the geometry of a fault system. Slip on a fractal branching fault surface can explain: 1) regeneration of stress irregularities in an earthquake; 2) the concentration of stress drop in an earthquake into asperities; 3) starting and stopping of earthquake slip at fault junctions, and 4) self-similar scaling of earthquakes. Slip at fault junctions provides a natural realization of barrier and asperity models without appealing to variations of fault strength. Fault systems are observed to have a branching fractal structure, and slip may occur at many fault junctions in an earthquake. Consider the mechanics of slip at one fault junction. In order to avoid a stress singularity of order 1/r, an intersection of faults must be a triple junction and the Burgers vectors on the three fault segments at the junction must sum to zero. In other words, to lowest order the deformation consists of rigid block displacement, which ensures that the local stress due to the dislocations is zero. The elastic dislocation solution, however, ignores the fact that the configuration of the blocks changes at the scale of the displacement. A volume change occurs at the junction; either a void opens or intense local deformation is required to avoid material overlap. The volume change is proportional to the product of the slip increment and the total slip since the formation of the junction. Energy absorbed at the junction, equal to confining pressure times the volume change, is not large enongh to prevent slip at a new junction. The ratio of energy absorbed at a new junction to elastic energy released in an earthquake is no larger than P/µ where P is confining pressure and µ is the shear modulus. At a depth of 10 km this dimensionless ratio has th value P/µ= 0.01. As slip accumulates at a fault junction in a number of earthquakes, the fault segments are displaced such that they no longer meet at a single point. For this reason the volume increment for a given slip increment becomes larger. A juction with past accumulated slip ??0 is a strong barrier to earthquakes with maximum slip um < 2 (P/µ) u0 = u0/50. As slip continues to occur elsewhere in the fault system, a stress concentration will grow at the old junction. A fresh fracture may occur in the stress concentration, establishing a new triple junction, and allowing continuity of slip in the fault system. The fresh fracture could provide the instability needed to explain earthquakes. Perhaps a small fraction (on the order of P/µ) of the surface that slips in any earthquake is fresh fracture. Stress drop occurs only on this small fraction of the rupture surface, the asperities. Strain change in the asperities is on the order of P/µ. Therefore this model predicts average strais change in an earthquake to be on the order of (P/µ)2 = 0.0001, as is observed.