Dependence of sandpile avalanche frequency–size distribution on coverage extent and compactness of embedded toppling threshold heterogeneity: implications for the variation of Gutenberg–Richter <i>b</i> value

Abstract

Abstract. The effects of the spatiotemporal evolution of failure threshold heterogeneity on the dynamics of fault criticality, and thus on regional seismogenesis, have attracted strong interest in the field of regional seismotectonics. The heterogeneity might be a manifestation of the macroscopic distribution and multiscale strength variation of asperities, the distinct regional stress level, and (microscopically) heterogeneous fault surface roughness or friction regimes. In this study, rather than attempting to mimic the complex microscale slipping physics on a fault surface, sandpile cellular automata were implemented with a straightforward toppling rule. The objective is to examine the influence of distinct configurations of the embedded heterogeneous toppling threshold field on the global system avalanche event statistics. The examination results revealed that increasing the coverage extent and decreasing the compactness of the heterogeneous failure threshold, rather than the magnitude, range of contrast, diversity, or the geometric configuration of the threshold heterogeneity, leads to a systematic increase in the scaling exponent of the avalanche event power law statistics, implying the importance of mutual interaction among toppling sites with distinct thresholds. For tectonic provinces with differing stress regimes evolving spatiotemporally, it is postulated that the distinct extent and compactness of the heterogeneous failure threshold are critical factors that manifest in the reported dynamic variations of seismicity scaling.

Systematic correlations of the earthquake frequency‐magnitude distribution with the deformation and mechanical regimes in the Taiwan orogen

“…Since the pioneering laboratory work of Mogi [], the spatial variation of b value has been studied extensively and linked to the mechanical heterogeneity in the crust which can differ substantially from one region to another. The presence of material inhomogeneity tends to yield higher b values for the frequency‐size distributions of rock microfactures [ Mogi , ] and sandpile avalanches [ Chiao and Liu , ]. On the other hand, Scholz [] was the first to recognize the inverse dependence of b value on applied stress from observations of small cracking events in rocks during compression tests.…”