Magnitude and rupture duration from high frequency teleseismic P wave with projected landweber deconvolution

Earthquake magnitude and rupture duration are among the most important parameters characterizing an earthquake for the purpose of early tsunami warning. While they can be routinely determined from broadband P waveforms with iterative inversion procedures, the inversion procedures may fail when the rupture either lasts longer than the interval between P and later arrivals or requires too much time or human intervention. Little contaminated by later arrivals, high frequency P waves are useful for modeling earthquake source processes, though the envelope waveform is affected by strong scattering in lithosphere. With high frequency envelopes from aftershocks as Empirical Green's Function (EGF), the coda effects can be removed and more accurate relative source time function (RSTF) of the main shock can be obtained. Assuming that RSTFs cannot be negative, we use the projected Landweber deconvolution method (PLD) to obtain high frequency RSTFs because PLD method has the advantage of non-negativity, causality, and compactness (finite duration). We are able to determine rupture durations of four large earthquakes: the 2004 Sumatra-Andaman earthquake, the 2005 Nias event, the 2006 Java event, and the 2011 Tokuko earthquake. The rupture durations of the Sumatra-Andaman, Nias, and Tohuko events are found to be around 550, 110, and 120 s respectively, consistent with previous studies. The rupture duration of the Java event is about 130 s, supporting that the Java event is a tsunami earthquake. The magnitudes of these earthquakes are found to depend on both the amplitude and the duration of the deconvolved waveforms, and can be approximated by integrating these waveforms.