A spatial random field model to characterize comlexity in earthquake slip

Finite-fault source inversions reveal the spatial complexity of earthquake slip over the fault plane. We develop a stochastic characterization of earthquake slip complexity, based on published finite-source rupture models, in which we model the distribution of slip as a spatial random field. The model most consistent with the data follows a von Karman autocorrelation function (ACF) for which the correlation lengths a increase with source dimension. For earthquakes with large fault aspect ratios, we observe substantial differences of the correlation length in the along-strike (a_x) and downdip (a_z) directions. Increasing correlation length with increasing magnitude can be understood using concepts of dynamic rupture propagation. The power spectrum of the slip distribution can also be well described with a power law decay (i.e., a fractal distribution) in which the fractal dimension D remains scale invariant, with a median value D = 2.29 ± 0.23, while the corner wave number k_c, which is inversely proportional to source size, decreases with earthquake magnitude, accounting for larger "slip patches" for large-magnitude events. Our stochastic slip model can be used to generate realizations of scenario earthquakes for near-source ground motion simulations.