Subsections

Apparent Stress and Corner Frequency Variations in the 1999 Taiwan (Chi-Chi) Sequence

Kevin Mayeda and Luca Malagnini

Introduction

Apparent stress drop and corner frequency are measured for the Chi-Chi, Taiwan sequence beginning with the mainshock ($M_{w}$7.6) on 20 September 1999. Using the recent coda source ratio methodology introduced by Mayeda et al. [2007], we have obtained stable source ratio estimates using broadband local and regional stations on Taiwan. We find the following: (1) For the mainshock and 7 of the larger aftershocks ($>$$M_{w}$ 5.5), apparent stress is tightly clustered around 6 bars ($\pm$ 2 bars); (2) In contrast, events below moment magnitude $\sim$$M_{w}$ 5.0 exhibit lower average apparent stress as well as larger scatter, ranging between $\sim$1.0 and 7.0 bars and are spatially variable; 3) For this dataset, the Brune [1970] omega-square source model fits the spectral shape for events 4.5$<$$M_{w}$$<$7.6; however, a clear, step-wise break in self-similarity exists at around $M_{w}$ 5.0. We hypothesize that the larger events are subject to the average state-of-stress over a broader region, whereas the smaller aftershocks are more sensitive to the local state-of-stress resulting from stress-field redistribution following the mainshock.

Earthquake Source Scaling

Aside from long-period regional and teleseismic waveform modeling estimates for $M_{w}$, broadband studies that extrapolate back to the source have always been hampered by inadequate knowledge of scale-dependent path and site effects. Radiated energy and corner frequency estimation over a broad range of event sizes requires significant frequency-dependent corrections, resulting in significant error that makes interpretation of the results highly questionable. There are, however, a number of local and regional methods that circumvent the problem of path and site corrections, namely the empirical Greens function deconvolution method [e.g., Hough, 1997] and amplitude ratio techniques [e.g., Izutani, 2005]. These approaches have gained popularity because adjacent or co-located events recorded at common stations have shared path and site effects, which therefore cancel. In this study we use a variant of the direct wave amplitude ratio, the coda ratio methodology of Mayeda et al. [2007], which has been shown to be roughly 3 times more stable than direct wave ratios and can be used with event pairs that are separated by several tens of kilometers, with little ill effects on data scatter. More recently, the method has been extended to datasets in Italy such as the San Giuliano di Puglia sequence in October 2001 [Malagnini and Mayeda, 2008] and the Colfiorito sequence of 1997 and 1998 [Malagnini et al., 2008]. Over the past decade, a number of studies have suggested that earthquake scaling is either constant with high scatter or increases with increasing magnitude. Due to large errors and regional variations, it has been difficult to definitively tell which of these two ideas is correct. Knowledge of scaling, whether self-similar or not, is fundamental to earthquake rupture simulations and seismic hazard prediction, especially if there exist region-dependent variations in apparent stress.

Figure 2.67: Map showing epicenters of events used in this study (circles) and broadband stations (triangles). Shading of events corresponds to the average apparent stress that was computed from the coda envelope ratios for each event.
\begin{figure}\begin{center}
\epsfig{file=Taiwan_Map_stress.ps, width=7.5cm} \end{center}\end{figure}

Application to Chi-Chi, Taiwan Sequence

For this study, we selected 43 events ranging between $M_{w}$ 4.4 and 7.6 recorded by 9 stations of the Broadband Array in Taiwan (BATS) (Figure 2.67). Stable $M_{w}$s for all the events were obtained from a previous coda calibration. The coda ratio methodology is outlined in Mayeda et al. [2007], so we only give a brief processing description here. First, narrowband time-domain envelopes ranging between 0.03 and 8.0-Hz were made using the two horizontal components and log-averaged for additional stability and smoothed. Coda synthetic envelopes were then fit to the data for each station so that relative amplitudes could be measured using an L-1 fitting routine for each narrowband envelope. Then ratios were formed for all possible event pairs by subtracting the log10 amplitudes for each station that recorded the event pair. Observed ratios were then fit by theoretical ratios derived from a modified Brune source spectra outlined in Walter and Taylor, [2001]. Figure 2.68 shows corner frequency estimates along with $\pm$ 1 standard deviation, and their corresponding apparent stress drops are shown in Figure 2.67. As found in other studies, the coda-derived source ratios exhibited little scatter, and thus source parameters, such as corner frequency, are well constrained when we fit the observed data with theoretical source models. The averaging nature of coda waves has been shown to provide significantly lower amplitude variance than any traditional direct phase method. We have obtained stable source ratio estimates using broadband local and regional stations on Taiwan. We find the following: (1) For the mainshock and 7 of the larger aftershocks ($>M_{w}$ 5.5), apparent stress is tightly clustered around 6 bars ($\pm$ 2 bars); (2) In contrast, events below moment magnitude $\sim$$M_{w}$ 5.0 exhibit lower average apparent stress as well as larger scatter, ranging between $\sim$1.0 and 7.0 bars, and are spatially variable; 3) For this dataset, the Brune [1970] omega-square source model fits the spectral shape for events 4.5$<$$M_{w}$$<$7.6; however, a clear, step-wise break in self-similarity exists at around $M_{w}$5.0. We hypothesize that the larger events are subject to the average state-of-stress over a broader region, whereas the smaller aftershocks are more sensitive to the local state-of-stress resulting from stress-field redistribution following the mainshock.

Figure 2.68: Moment versus corner frequency is plotted for the Chi-Chi sequence with lines of constant apparent stress. In general, the mainshock and larger aftershocks above $M_{w}$ 5.5 have roughly the same scaling and apparent stress values, whereas for smaller events there is a clear shift and more scatter.
\begin{figure}\begin{center}
\epsfig{file=Mo_fc_Chi-Chi.ps, width=7.5cm} \end{center}\end{figure}

Acknowledgements

K. Mayeda was supported under Weston Geophysical subcontract No. GC19762NGD and AFRL contract No. FA8718-06-C-0024. Work by L. Malagnini was performed under the auspices of the Dipartimento della Protezione Civile, under contract S4, ProCiv-INGV (2004-06), project: "Stima dello scuotimento in tempo reale e quasi-reale per terremoti significativi in territorio nazionale".

References

Brune, J. N., Tectonic stress and spectra of seismic shear waves from earthquakes, J. Geophys. Res. 75, 4997-5009, 1970.

Hough, S.E., Empirical Greens function analysis: Taking the next step, J. Geophys. Res. 102, 5369-5384, 1997.

Izutani, Y., Radiated energy from the mid Niigata, Japan, earthquake of October 23, 2004 and its aftershocks, Geophys. Res. Lett. 32, L21313, doi:10.1029/2005GL024116, 2005.

Malagnini, L. and K. Mayeda, High-stress strike-slip faults in the Apennines: An example from the 2002 San Giuliano earthquakes (Southern Italy), Geophys. Res. Lett., doi:10.1029/2008GL034024, 2008.

Malagnini, L., L. Scognamiglio, A. Mercuri, A. Akinci, K. Mayeda, Source scaling for ground motion prediction in central Italy: Evidence for strong non-self-similar behavior, accepted Geophys. Res. Lett., 2008.

Mayeda, K., L. Malagnini, W.R. Walter, A new spectral ratio method using narrow band coda envelopes: Evidence for non-self-similarity in the Hector Mine sequence, Geophys. Res. Lett., doi:10.1029/2007GL030041, 2007.

Walter, W. R. and S. R. Taylor (2001). A revised magnitude and distance amplitude correction (MDAC2) procedure for regional seismic discriminants: theory and testing at NTS, Lawrence Livermore National Laboratory Report, UCRL-ID-146882, http://www.llnl.gov/tid/lof/documents/pdf/240563.pdf

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