SCEC Award Number 13063 View PDF
Proposal Category Travel Only Proposal (SCEC Annual Meeting)
Proposal Title Quantifying variability of seismic source spectra derived from cohesive-zone models of earthquake rupture
Name Organization
Yoshihiro Kaneko GNS Science (New Zealand) Peter Shearer University of California, San Diego
Other Participants
SCEC Priorities 3c, 3d, 3e SCEC Groups FARM
Report Due Date 03/15/2014 Date Report Submitted N/A
Project Abstract
Earthquake stress drops are often estimated from far-field body-wave spectra using measurements of seismic moment, corner frequency, and a specific theoretical model of rupture behavior. The most widely-used model is from Madariaga (1976), who performed finite-difference calculations for a singular crack radially expanding at a constant speed and showed that $\bar{f}_{\rm c} = k \beta/a$, where $\bar{f}_{\rm c}$ is spherically averaged corner frequency, $\beta$ is the shear-wave speed, $a$ is the radius of the circular source, and $k$ = 0.32 and 0.21 for $P$ and $S$ waves, respectively, assuming the rupture speed $V_{\rm r} = 0.9\beta$. Since stress in the Madariaga model is singular at the rupture front, the finite mesh size and smoothing procedures may have affected the resulting corner frequencies. In this work, we have investigated the behaviour of source spectra derived from dynamic models of a radially expanding rupture on a circular fault with a cohesive zone that prevents a stress singularity at the rupture front. We have found that in the small-scale yielding limit where the cohesive-zone size becomes much smaller than the source dimension, $P$- and $S$-wave corner frequencies of far-field body-wave spectra are systematically larger than those predicted by Madariaga (1976). In particular, the model with rupture speed $V_{\rm r} = 0.9\beta$ shows that $k = 0.38$ for $P$ waves and $k = 0.26$ for $S$ waves, which are 19 and 24 percent larger, respectively, than those of Madariaga (1976). Thus for these ruptures, the application of the Madariaga model overestimates stress drops by a factor of 1.7. In addition, the large dependence of corner frequency on take-off angle relative to the source suggests that measurements from a small number of seismic stations are unlikely to produce unbiased estimates of spherically averaged corner frequency.
Intellectual Merit One of the SCEC science objectives is ``to develop physics-based models of the nucleation, propagation, and arrest of dynamic earthquake rupture" that will ``contribute to our understanding of earthquakes in Southern California fault system.'' Our research has established the relationship between corner frequencies and the source radius for dynamic models of a circular fault. As stress drop is often estimated in a way that relies on the validity of a specific theoretical model of rupture dynamics, our results have led to more accurate estimates of stress drops of earthquakes in Southern California and other regions. The results have also impacted interpretations of other source parameters used to infer earthquake mechanics.
Broader Impacts Characterization of earthquake source parameters is important for understanding the physics of source processes and seismic hazard. Static stress drop is one of the key earthquake source parameters, which provides hints on earthquake source scaling and insights into tectonic environments in which earthquakes occur. Stress drop is also used as a primary input parameter for ground motion simulations with stochastic techniques for quantification of seismic hazards. Hence our project has linked advances in earthquake seismology, crustal deformation, and earthquake hazard. Results from our research have been disseminated through conference presentations, seminars, and publications in peer-reviewed literature.
Exemplary Figure Figure 2: (a) Spherical average of corner frequencies for models with different weakening rates {\rm w}'$. As {\rm w}'$ becomes larger, the mean of fracture energy $\overline{G}$ over the circular source becomes smaller but eventually becomes independent of {\rm w}'$. In this small-scale yielding limit, the averages of corner frequencies differ from those obtained by Madariaga (1976) by 19 percent for $ waves and 24 percent for $ waves. (b) Simulated slip-weakening curves for the cases with {\rm w}'$ = 168 and the zero-cohesive-zone case.