The kinematics of gouge deformation

The methods and first results of a new approach to examining fault gouge are described. Samples of undisturbed fault gouge from the exhumed Lopez fault zone in the San Gabriel Mountains, California were impregnated with low viscosity epoxy resin and sectioned to produce microscope slides. The slides were photographed using optical and electron microscopy with magnifications ranging in factors of 2 from 12.5 to 1600. At all scales, the particles appeared angular with planar faces, suggesting tensile failure. No shear zones were discernable. The particle size distribution was studied. At each magnification the particles were sorted by diameter into four classes, differing in mean diameter by factors of 2. The numbers in each class were then scaled by the characteristic class dimension. The process revealed a remarkable degree of self-similarity. Over the range examined, the fractal dimension was within 5% of 2.60.On the basis of the observations, a new model for the mechanical processes that generate gouge is offered. It is argued that self-similarity results from repeated tensile splitting of grains. Unlike earlier models that consider splitting probability to be either independent of particle size or due to the preexisting distribution of defects, we propose that failure probability depends largely on the relative size of nearest neighbors. If nearest neighbors of the same size are preferentially broken, any initial distribution of particles will tend toward a self-similar distribution having a fractal dimension of 2.58.The model allows us to outline a procedure whereby the observed comminution in a fault zone can be related to the shear strain that the zone has accommodated and propose a theoretical frequency magnitude relation for the seismic energy emitted by the fracture process.