Variability in fault size scaling due to rock strength heterogeneity: a finite element investigation

Practical application of fault size scaling relationships usually involves extrapolation of a limited data set over a scale range beyond that observed or into adjacent unstudied areas. Here we investigate the validity of such extrapolations by considering the variability in the size–frequency distributions of fault populations that develop under identical tectonic conditions using a numerical model to generate conjugate, normal fault populations in cross-section. The deforming material is modelled using a strain-softening, Von Mises rheology with Gaussian heterogeneity in yield strength distributed randomly throughout the mesh. We present eight deformation experiments that differ only in the random spatial pattern of yield strengths. We observe power law size–frequency scaling, i.e. N=ax^?c (where N is the cumulative number of faults and x is a measure of fault size) but with a range of values of c. The ensemble average value of c decreases with increasing percentage extension. However, for individual model runs the dependence of c on total strain shows significant variability that we can relate to small but important differences in fault growth and strain localisation. At any particular strain, the range of values of c is ～10 times greater than the error estimate derived from least squares regression of the cumulative frequency data. Our results suggest therefore that large uncertainties should be associated with extrapolating fault population data from one scale or region to another even if the lithology and tectonic history are similar.