4 Quantitative Analysis of Coda Window Length: How Much Length of Coda is Enough for Stable Amplitudes?

In earthquake source estimation, coda-derived source methods provide more stable source parameters than methods using direct waves due to the inherent averaging nature of coda waves (Mayeda and Walter, 1996; Mayeda et al., 2007). Unlike conventional direct-phase regional measurements (e.g., Pg or Lg), which take peak amplitude at the specific arrival time, the coda amplitude measurement through a relatively long time window can dramatically reduce the inter-station scattering by smoothing out 3-D path variability, source radiation pattern, and directivity effects (Mayeda and Malagnini, 2010). Although a number of studies have shown this stability of the coda measurement, it is still unclear how much length of coda is enough for accurate measurements of coda amplitudes. Inappropriate short window measurement can not only lead to higher inter-station scatter of coda amplitudes, but can also give a distorted amplitude by using only earlier parts of a coda envelope, which shows a radical change in energy density with increasing lapse time. But long-lasting coda, which guarantee a stable measurement, are not always easy to obtain, because of small magnitude, low signal to noise ratio, and interfering aftershocks. In this study, to address this unsettled question and quantify the optimum window length for accurate coda measurements, we analyze inter-station standard deviation of the coda ratios as a function of the time window length using an earthquake sequence data set that was well-recorded by a dense broadband seismic array. This allows us an in-depth look at the effects of coda on averaging over source radiation pattern and directivity and can help serve as a guide to future coda-based studies regarding how much window length is needed to get good measurements.