Foreshocks on Geometrically Heterogeneous Faults

Abstract:

The occurrence of foreshocks near the mainshock hypocenter is a manifestation of fault heterogeneity: local variations in stress or strength are required to explain why foreshocks remain small. Here we study the conditions under which geometrical roughness generates foreshock sequences, and quantify their spatio-temporal patterns. We model seismic cycles on a fault with fractal roughness at wavelengths exceeding the nucleation length and homogeneous velocity-weakening rate-state friction, loaded by a uniform far-field stressing rate.

Roughness leads to rich slip behavior, including interseismic creep and microseismicity between mainshocks. These processes are well explained by spatial variations in normal stress (σ) caused by roughness: regions with low normal stress creep interseismically, while regions with high normal stress remain locked until they break seismically. Foreshock sequences only appear if σ is sufficiently heterogeneous, with root-mean-square perturbations close to the background normal stress. The nucleation process is controlled by a feedback between creep and foreshocks: groups of nearby asperities break seismically, causing creep to accelerate, which in turns loads other asperities and triggers further foreshocks. A simple analytical treatment of this mutual stress transfer predicts average slip velocities and seismicity rates to increase with time as 1/t, where t is the time to the mainshock, and simulations confirm this trend. Foreshocks and mainshocks both initiate from the rupture of locked asperities, but mainshocks have a tendency to start on stronger asperities, suggesting that local stress conditions near the hypocenter affects rupture evolution and final earthquake size. The model reproduces several seismological observations, including migration of foreshocks towards the mainshock hypocenter, foreshock locations consistent with static stress changes, and the 1/t acceleration in stacked catalogs.