[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,

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We use a database of more than 80 finite-source rupture models for more than 50 earthquakes (M w 4.1-8.1) with different faulting styles occurring in both tectonic and subduction environments to analyze the location of the hypocenter within the fault and to consider the correlation between hypocenter location and regions of large slip. Rupture in strike-slip and crustal dip-slip earthquakes tends to nucleate in the deeper sections of the fault; subduction earthquakes do not show this tendency. Ratios of the hypocentral slip to either the average or the maximum slip show that rupture can nucleate at locations with any level of relative displacement. Rupture nucleates in regions of very large slip (D Ն 2/3 D max ) in only 16% of the events, in regions of large slip (1/3 D max Ͻ D Ͻ 2/3 D max ) in 35% of the events, and in regions of low slip (D Յ 1/3 D max ) in 48% of the events. These percentages significantly exceed the percentages of fault area with very large (ϳ7%) and large (ϳ28%) slip. Ruptures that nucleate in regions of low slip, however, tend to nucleate close to regions of large slip and encounter a zone of very large slip within half the total rupture length. Applying several statistical tests we conclude that hypocenters are not randomly located on a fault but are located either within or close to regions of large slip.

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We calculate near-source broadband (0-10 Hz) seismograms by combining low-frequency three-dimensional (3D) finite-difference seismograms (0-0.5 Hz) computed in a 3D velocity model using site-specific scattering Green's functions for random, isotropic scattering media. The scattering Green's functions are convolved with a slip-rate function to form local scattering operators (scatterograms), which constitute the high-frequency scattered wave field. The low-frequency and highfrequency scatterograms are then combined in the frequency domain to generate broadband waveforms. Our broadband method extends the Mai et al. (2010) approach by incorporating dynamically consistent source-time functions and accounting for finite-fault effects in the computation of the high-frequency waveforms. We used the proposed method to generate broadband ground motions at 44 sites located 5-100 km from the fault, for M w 7.7 earthquake scenarios (TeraShake) on the southern San Andreas fault, which include north-to-south, south-to-north, and bilateral rupture propagation from kinematic and spontaneous dynamic rupture models. The broadband ground motions computed with the new method are validated by comparing peak ground acceleration, peak ground velocity, and spectral acceleration with recently proposed ground-motion prediction equations (GMPEs). Our simulated ground motions are consistent with the median ground motions predicted by the GMPEs. In addition, we examine overturning probabilities for 18 precariously balanced rock sites (PBR). Our broadband synthetics for the M w 7.7 TeraShake scenarios show no preferred rupture direction on the southern San Andreas fault but are inconsistent with the existence of PBRs at several of the sites analyzed.

[1] We perform three-dimensional spontaneous dynamic rupture models of potential earthquakes on the geometrically complex North Anatolian fault zone (NAFZ) under the Marmara Sea, Turkey. The NAFZ south of the city of Istanbul consists of a large-scale extensional stepover, with right lateral strike-slip segments linked by an oblique normal segment. We find that earthquakes nucleating near the stepover do not propagate across the entire fault system due to the statically unfavorable stress field on the oblique fault, and lead to moderate-size events only. However, earthquakes initiating a significant distance from the stepover cause significant dynamic unclamping of the oblique fault, and thus generate large through-going ruptures. Dynamic unclamping also produces supershear rupture propagation in the vicinity of fault discontinuities. The results emphasize that estimations of earthquake size, rupture propagation, and slip distribution cannot be decoupled from the location of the hypocenter and the orientation of the geometrically complex fault system within the tectonic stress field.

With the global challenge to satisfy an increasing demand for energy while at the same time stabilizing or reducing carbon dioxide (CO2) concentrations in the atmosphere, geothermal energy from enhanced geothermal systems (EGSs) increasingly is being recognized as an attractive alternative energy source throughout the world. However, the risks associated with the seismicity necessarily induced during the development of an EGS constitute a significant challenge for the widespread implementation of this technology. This article provides a preliminary overview of lessons learned from an attempt to develop an EGS beneath the city of Basel, Switzerland.