A spatial random field model to characterize complexity in earthquake slip

Abstract

[1] 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.INDEX TERMS: 7209 Seismology: Earthquake dynamics and mechanics; 7215 Seismology: Earthquake parameters; KEYWORDS: earthquake source characterization, complexity of earthquake slip, spatial random fields, correlation length of asperities growing with earthquake magnitude, earthquake rupture dynamics, strong ground motion simulation Citation: Mai, P. M., and G. C. Beroza, A spatial random field model to characterize complexity in earthquake slip,

Slip tapers at the tips of faults and earthquake ruptures

“…This is also suggested by seismological observations [e.g., Mai and Beroza, 2002]. When the earthquake rupture propagates to the end of the fault, the FTT is even larger, but about an order of magnitude less than the FTT for faults in igneous rock.…”

Analysing earthquake slip models with the spatial prediction comparison test

“…Mai & Beroza (2002) show that the correlation lengths scale with earthquake size (magnitude), while Hermitian symmetry. This spectral characterization of the slip distribution is then transformed into the spatial domain through inverse Fourier transformation.…”

“…The goals is to also examine which loss function(s) may be best suited to characterize and quantify the differences in slip models with varying degree of spatial heterogeneity. Synthetic slip models are generated using the approach of Mai & Beroza (2002) in which earthquake slip distributions are modelled based on the von Kármán autocorrelation function. Its power spectral density in wave number domain is given by…”

Quantifying variability in earthquake rupture models using multidimensional scaling: application to the 2011 Tohoku earthquake

“…Somerville et al 1999;Mai & Beroza 2002;Lavallée et al 2006). Significant efforts have also been expended on assessing the uncertainties in finite-fault source inversions.…”