Rupture Directivity Characteristics of the 2003 Big Bear Sequence

Abstract

We have developed a forward modeling technique to retrieve rupture characteristics of small earthquakes (3 < M < 5), including rupture propagation direction, fault dimension, and rupture speed. The technique is based on an empirical Green's function (EGF) approach, where we use data from collocated smaller events as Green's functions to study the bigger events. We tend to choose smaller events with similar focal mechanisms for EGFs; however, we show that the events with different focal mechanisms can work equally well when corrected for radiation pattern effect. Compared to deconvolution, this forward modeling approach allows full use of both the shape and amplitude information produced by rupture propagation. Assuming a simple 1D source model, we parameterize the source time function of a target event as the convolution of two boxcars, featuring the rise time τ r and the rupture time τ c ; we solve for τ r and τ c in a grid search manner by minimizing the waveform misfit between the three-component data and the synthetics constructed from the EGFs. The rupture propagation direction, fault length, and rupture speed can then be estimated by fitting the observed azimuthal pattern of τ c from P and S waves. We apply the approach to the 12 largest events (M w ≥ 3:3) of the 2003 Big Bear sequence (excluding the mainshock) in southern California. Among them, seven events are found to exhibit robust rupture directivity. The fact that the ruptures of these events propagate in all directions reveals complicated fault geometry at depth. We compute the stress drop Δσ ∼ 2 π M 0 L 3 for each event using the resolved fault length. The results show large variations ranging from ∼1 to 90 Mpa, with no dependence on moment. However, Δσ appears inversely correlated with rupture speed V r ; in particular, events with larger Δσ tend to propagate at smaller V r , whereas events with smaller Δσ propagate faster.

Toward automated directivity estimates in earthquake moment tensor inversion

“…This derivation naturally results in the preservation of source time function area as is often assumed in previous studies (Lay & Wallace 1995;Tan & Helmberger 2010), as shown by the red curves relative to blue curve in Fig. 2.…”

“…Although there is variability in the manner in which an earthquake ruptures on a fault plane (Wald & Heaton 1994;Beroza 1995;Ide & Takeo 1997;Yue et al 2012;Ye et al 2013), unilateral rupture is generally predominant in a wide range of earthquake magnitudes (McGuire et al 2002;Tan & Helmberger 2010;Kane et al 2013). As unilateral rupture occurs, seismic waves radiated in the direction of rupture could be greatly amplified, and even moderate magnitude earthquakes can sometimes cause serious damage (Huang et al 2011;Kanamori et al 2016).…”

“…Although these methods provide a spatiotemporal history of the rupture process, their application is mainly restricted to large earthquakes. More commonly, directivity for small-to-moderate earthquakes is estimated based on differences in source duration (Velasco et al 1994;Tan & Helmberger 2010) or peak ground amplitude (Boatwright 2007;Convertito et al 2012;Kurzon et al 2014) observed between stations in the time domain, or differences in spectral ratios (Wang & Rubin 2011;Ross & BenZion 2016) or corner frequencies (Kane et al 2013) in the frequency domain. These studies convert observations of a single source parameter at each station to estimate directivity and therefore rely on a good azimuthal coverage of stations to resolve directivity since information at each station has been reduced to a single parameter.…”

Estimating the Radiated Seismic Energy of the 2010 ML 6.4 JiaSian, Taiwan, Earthquake Using Multiple-Event Analysis

“…The static stress drop is close to the value (~5 bars) from the inversion of GPS data yielded by Ching et al (2011). The 2010 JiaSian earthquake is therefore a low static stress drop event relative to a high rupture velocity (e.g., Tan and Helmberger 2010;Hwang et al 2012). Such a low static stress drop for the JiaSian earthquake lapses from the values for the interplate and intraplate earthquakes (Kanamori and Anderson 1975).…”

“…A special feature of the 2010 JiaSian earthquake is a low static stress drop of approximately 5 bars, which was derived from GPS data using an elastic uniform stress drop inversion by Ching et al (2011). Such a low stress drop for the JiaSian earthquake departs from the values (30 -100 bars) for the so-called interplate and intraplate earthquakes (Kanamori and Anderson 1975), but is comparable with a reciprocal relationship between stress drop and rupture velocity (Tan and Helmberger 2010). A low stress drop is therefore relative to a high rupture velocity for the 2010 JiaSian earthquake (Hwang et al 2012).…”