SCEC Project Details
SCEC Award Number  13063  View PDF  
Proposal Category  Travel Only Proposal (SCEC Annual Meeting)  
Proposal Title  Quantifying variability of seismic source spectra derived from cohesivezone models of earthquake rupture  
Investigator(s) 


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 farfield bodywave spectra using measurements of seismic moment, corner frequency, and a specific theoretical model of rupture behavior. The most widelyused model is from Madariaga (1976), who performed finitedifference 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 shearwave 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 smallscale yielding limit where the cohesivezone size becomes much smaller than the source dimension, $P$ and $S$wave corner frequencies of farfield bodywave 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 takeoff 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 physicsbased 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 peerreviewed 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 smallscale 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 slipweakening curves for the cases with {\rm w}'$ = 168 and the zerocohesivezone case. 