Estimation of fracture energy of large earthquakes based on heterogeneous stress drops and fault rupture velocities: Implications for earthquake scaling

Abstract:

Fracture energy (G) is a fundamental physical property of earthquakes governing its nucleation, rupture growth and arrest. The most widely used approach to estimate fracture energy is based on the energy budget during an earthquake (usually referred to G’). To make this problem tractable using the seismological approach, several simplifications have to be assumed such as the use of simple averages for displacement and stress on the fault plane. However it is well known that slip and stress across the fault plane can be highly variable and complex for large earthquakes.

To estimate fracture energy in this study I use the LEFM (Linear elastic fracture mechanics) approach and assume that heterogeneous fault rupture can be approximately described as the superposition of anti-plane and in-plane fault rupture modes. I calculate local fracture energy across the fault plane as the product of a ‘static’ stress intensity factor K* and a function of local fault rupture velocity at the rupture front.

I estimated fracture energy of 173 earthquakes worldwide (Mw>7.0) using the extensive database of slip models compiled by the National Earthquake Information Center of USGS. I first calculate the stress drop distributions, as well as local rupture velocity distributions (Pulido and Dalguer, 2009) using the slip models and sub-faults rupture times available in the database. My results show highly heterogeneous distribution of stress drops and local fault rupture velocities. Fault rupture across the fault largely takes place in the sub-shear domain for most of the earthquakes considered in this study, although it can typically become super-shear at local patches within the fault. For this study I calculated fracture energy only for ruptures in the sub-shear domain. My results indicate that fracture energy is highly correlated with fault slip. However the rate of growth of G with increasing slip for large earthquakes is weaker compared to the growth for small earthquakes. My results also show that G’ systematically underestimates fracture energy for large earthquakes. Finally, I estimated the slip weakening distance (Dc) as well as S values (the fault strength coefficient), based on my estimations of G, for all the slip models in this study.