Fault growth and fault scaling laws: Preliminary results

We report progress made in the last few years on the general problem of the mechanism of fault growth and the scaling laws that result. Results are now conclusive that fault growth is a self‐similar process in which fault displacement d scales linearly with fault length L . Both this result and the overall nature of along‐strike fault displacement profiles are consistent with the Dugdale‐Barenblatt elastic‐plastic fracture mechanics model. In this model there is a region of inelastic deformation near the crack tip in which there is a breakdown from the yield strength of the unfractured rock to the residual frictional strength of the fault over a breakdown length S and displacement d 0 . Limited data also indicate that S and d 0 also scale linearly with L , which implies that fracture energy G increases linearly with L . The scaling parameters in these relationships depend on rock properties and are therefore not universal. In our prime field locality, the Volcanic Tableland of eastern California, we have collected data over 2 orders of magnitude in scale range that show that faults obey a power law size distribution in which the exponent C in the cumulative distribution is ∼1.3. If the fault is growing within the brittle field, the zone of inelastic deformation consists of a brittle process zone which leaves a wake of fractured rock adjacent to the fault. Preliminary results of modeling the process zone are consistent with observations now in hand both in predicting the preferred orientation of cracks in the process zone wake and the rate of falloff of crack density as a function of distance from the fault. The preferred orientation of these cracks may be used to infer the mode and direction of propagation of the fault tip past the point in question. According to the model, the width of the process zone wake may be used to infer the length of the fault at the time its tip passed the measurement point, but data have not yet been collected to verify this prediction. If the fault displacement has been accumulated by repeated seismic slips, each of these will sweep the fault with a crack tip stress field of a smaller spatial extent than that of the fault tip stress field, producing an inner, more intensely fractured, process zone wake. This may be the mechanism that creates the cataclasite zone, rather than simple frictional wear, as has been previously supposed.