A New Method for Determining Small Earthquake Source Parameters Using Short-Period P Waves

Abstract

We developed a new technique of inverting short-period (0.5-2 Hz) P waveforms for determining small earthquake (M Ͻ3.5) focal mechanisms and moments, where magnitude ϳ4 events with known source mechanisms are used to calibrate the "unmodeled" structural effect. The calibration is based on a waveform cluster analysis, where we show that clustered events of different sizes, for example, M ϳ4 versus M ϳ2, display similar signals in the short-period (SP, 0.5-2 Hz) frequency band, implying propagational stability. Since both M ϳ4 and M ϳ2 events have corner frequencies higher than 2 Hz, they can be treated as point sources, and the "unmodeled" structural effect on the SP P waves can be derived from the magnitude 4 events with known source mechanisms. Similarly, well-determined magnitude 2's can provide calibration for studying even smaller events at higher frequencies, for example, 2-8 Hz. In particular, we find that the "unmodeled" structural effect on SP P waves is mainly an amplitude discrepancy between data and 1D synthetics. The simple function of "amplitude amplification factor" (AAF) defined as the amplitude ratio between data and synthetics provides useful calibration, in that the AAFs derived from different clustered events appear consistent, hence stable and mechanism independent. We take a grid-search approach to determine source mechanisms by minimizing the misfit error between corrected data and synthetics of SP P waves. The validation tests with calibration events demonstrate the importance and usefulness of the AAF corrections in recovering reliable results. We introduce the method with the 2003 Big Bear sequence. However, it applies equally well to other source regions in southern California, because we have shown that the mechanism independence and stability of the AAFs for source regions of 10 km by 10 km are typical. By definition, the AAFs contain the effects from the station site, the path, and crustal scattering. Although isolating their contributions proves difficult, the mechanism independence and stability of the AAFs suggest that they are mainly controlled by the near-receiver structure. Moreover, the ratios between the AAFs for the vertical and radial components from various events at different locations appear consistent, suggesting that these AAF(v)/AAF(r) ratios might be simple functions of site conditions. In this study, we obtained the focal mechanisms and moments for 92 Big Bear events with M L down to 2.0. The focal planes correlate well with the seismicity patterns, while containing abundant finer-scale fault complexity. We find a linear relationship between log(M 0 ) and M L , that is, log(M 0 ) ‫ס‬ 1.12M L ‫ם‬ 17.29, which explains all the data points spanning three orders of magnitude (2.0 Ͻ M L Ͻ 5.5).

Source Mechanism and Rupture Directivity of the 18 May 2009 MW 4.6 Inglewood, California, Earthquake

“…The synthetics are computed with source parameters obtained from long-period CAP inversion, then both synthetic and observed P waves are filtered between 0.5 and 2 Hz. Obviously for many of stations, the synthetic P waves are either too large or too small, which is consistent with the study by Tan and Helmberger (2007). However, after we scale the synthetic P waves to the observed ones with a constant (also called an amplitude adjustment factor, AAF), the synthetic and observed P waves match well (Fig.…”

“…Because the rupture velocity is inferred from P waves, S waves would provide independent data to verify the rupture directivity. More importantly, the S wave is a better seismic phase for studying rupture velocity because the smaller propagation speed of S waves and the radiation pattern are more favorable than for P waves (Tan and Helmberger, 2007). For the Inglewood earthquake, we choose two stations STS and SMS, which are situated toward and against the rupture direction, respectively (see Fig.…”

“…With better 3D models available, it can be expected that both the direct and secondary body waves can be well modeled at short-period frequency or at higher frequency (say, 4 Hz or higher). Thereafter, source parameters of even smaller events (M 1) can be modeled with waveforms at those higher frequencies as discussed by Tan and Helmberger (2007).…”

“…However, for weaker events (M 2-3), only short-period body waves are strong enough to escape the noise. Though Ebel and Bonjer (1990) demonstrated that short-period P and S waves can be used to constrain focal mechanism, the accuracy of the solution depends on the adequacy of the velocity model; for example, Tan and Helmberger (2007) find that the amplitude of observed short-period P waves can be different from synthetics by a factor of 5. Although directly modeling the short-period P waves is difficult without a detailed velocity model, Tan and Helmberger (2007) demonstrate the amplitude anomaly can be calibrated with well-known events and then corrected in studying smaller events nearby.…”

“…The corresponding values for τ c show large azimuthal variation with a clear minimum near 147°. We follow the same procedure as Tan and Helmberger (2007) for estimating the rupture propagation direction φ, fault length fl, and rupture speed V r . The obtained φ nearly coincides with the strike of the southeast fault plane of the focal mechanism solution, as well as the NIF.…”