Modeling Small Earthquakes in Southern California with Calibrated High Frequency P waves

With the dense TriNet array in Southern California, the focal mechanism of a Mw ∼ 4.0 or larger event can be easily resolved using the full waveform data over relatively long periods (usually 5+ sec for Pnls and 10+ sec for surface waves), where imperfections of the velocity models are tolerated. However, the same strategy becomes less effective when applied to smaller events (Mw < 4.0) due to their poor signal to noise ratio (SNR). Better utilizing waveform data of these smaller events has to be pursued over much higher frequency bands for the sake of good SNR, where, however, any direct use of Green's functions is difficult since the complications caused by the path and site effects are far beyond the current model predictions. In this study, we first determine the focal mechanisms of more than 150 events with Mw ∼ 3.60 or larger since 1998 following our improved ``cut and paste'' method. With these well-resolved long-period solutions, we are able to study the un-modeled structural distortions on the waveform data over much higher frequency bands (up to 2 Hz), where the waveform data of an event as small as Mw ∼ 3.0 can survive the noise. We found that the azimuthal patterns of P wave amplitude ratios between different events (Mw from 3.60 to 4.50) within an event cluster well follow the differences in their various well-known focal mechanisms. This implies that whatever is causing the distortions on the amplitudes of P waves is relatively stationary and can be represented by a single ``Amplitude Amplification Factor'' (AAF) for the whole cluster at a large fraction of the stations. A detailed investigation is being conducted to learn more about the cause of the AAFs, however, the consistency of the ratios between the AAF on the radial component and that on the vertical component implies mainly a site effect. Taking advantage of these AAFs, we develop a new approach using short-period waveforms of P waves to determine the focal mechanisms of small events, as long as the events occur near well-determined bigger events, which can be used for calibration purposes. We test our new method and check the short-period solutions against the long-period solutions, which shows remarkable consistency.