Fault geometry is a key factor in controling the mechanics of faulting. However, there is currently limited theoretical knowledge regarding the effect of non-planar fault geometry on earthquake mechanics. Here, we address this gap by introducing an expansion of the relation between fault traction and slip, up to second order, relative to the deviation from a planar fault geometry. This expansion enables the separation of the effects of non-planarities from those of planar faults. This expansion is realised in the boundary integral equation, assuming a small fault slope. It provides an interpretation for the effect of complex fault geometry on fault traction, for any fault geometry and any slip distribution. Hence the results are also independent of the friction that applies on the fault. The findings confirm that fault geometry has a strong influence on in-plane faulting (mode II) by altering the normal traction on the fault and making it more resistant to slipping for any fault geometry. On the contrary, for out-of-plane faulting (mode III), fault geometry has a much smaller influence. Additionally, we analyse some singularities that arise for specific fault geometries often used in earthquake simulations and provide guidelines for their elimination. To conclude this study, we discuss the limits of the small strain approximation when non-planar faults are considered.

Decades of seismological observations have highlighted the variability of foreshock occurrence prior to natural earthquakes, making thus difficult to track how earthquakes start. Here, we report on three stick-slip experiments performed on cylindrical samples of Indian metagabbro under upper crustal stress conditions (30-60 MPa). Acoustic emissions (AEs) were continuously recorded by 8 calibrated acoustic sensors during the experiments. Seismological parameters of the detected AEs (-8.8 <= Mw <= -7 ) follow the scaling law between moment magnitude and corner frequency that characterizes natural earthquakes. AE activity always increases towards failure and is found to be driven by along fault slip velocity. The stacked AE foreshock sequences follow an inverse power-law of the time to failure (inverse Omori), with a characteristic Omori time c inversely proportional to normal stress and nucleation length. AEs moment magnitudes increase towards failure, as manifested by a decrease in b-value from ~ 1 to ~ 0.5 at the end of the nucleation process. During nucleation, the averaged distance of foreshocks to mainshock continuously decreases, highlighting the fast migration of foreshocks towards the mainshock epicenter location, and stabilizing at a distance from the latter compatible with the predicted Rate-and-State nucleation size. Finally, the seismic component of the nucleation phase is orders of magnitude smaller than that of its aseismic component, which suggests that foreshocks are the byproducts of a process almost fully aseismic. Seismic/aseismic energy release ratio continuously increases during nucleation, which starts as a fully aseismic process and evolves towards a cascading process.

We report laboratory experimental results to reveal the factors that control the occurrence and magnitude of foreshocks. We conducted rock friction experiments using an apparatus that can shear 4-meter-long rock specimens. We observed many stick-slip events, as well as very slow (several tens of μm/s) but long-lasting slips between those main events. These long-term slow slips individually initiated from both the leading and trailing edges of the fault, and kept propagating steadily towards each other. Such steady slips did not immediately trigger any seismic events, regardless of the accumulated slip amount. After the coalescence of the two long-term slow slip fronts, a second phase of slow slip with higher slip rate (several hundreds of μm/s) — called precursory slow slip, began at the central area and was accompanied by the occurrence of small seismic events (foreshocks). Subsequently, the main fast rupture eventually developed. We propose that the asperities that hosted foreshocks had similar size to the local critical nucleation length h*; the asperities slipped stably when the local loading rate was low, but could also slip unstably and radiated seismic waves when the local loading rate became high. We further found a clear positive correlation between foreshock magnitude and local slip rate. These results suggest that local loading rate has a significant influence on the occurrence and magnitude of foreshocks. Therefore, its effect should be taken into account during the studies of earthquake nucleation process and other similar phenomena such as Episodic Tremor and Slip (ETS), icequakes, and repeating earthquakes.