Power-law decay characteristic of coda envelopes revealed from the analysis of regional earthquakes

So far, coda envelopes for wide frequency bands with long lapse time range have been described by bending curves which have several systematic changes in decay rate with lapse time. However, for NS component seismograms of regional earthquakes, applying the Hilbert Transform to make envelope curves and taking regression analysis on the envelopes in period bands from 24 s to 1/6 s for a wide lapse time range up to 4,000 s instead of measuring the peak amplitudes of the coda used previously, we found coda envelopes show the feature of ``power-law'' decay and there is no systematic change of decay gradient except for once occurring around ScS arrival with lapse time. 157 seismic events recorded by 11 IRIS broadband seismic network stations during the period from 1988 to 2005 with focal depths shallower than 50 km (shallow events) and deeper than 150 km (deep events) and with epicentral distance less than 1,000 km from individual seismic station were collected in this study. The moment magnitude of selected events ranges from 4.7 to 7.8. The ``power-law'' decay characteristic of seismic envelopes indicates that the power spectrum of seismic coda could be simply expressed as of the form P( T, t) ~ t - α, where t is lapse time and T is central period. We find that α = 1.6-6.2 for before ScS arrival in all period bands and 0.6-5.3 for after ScS arrival ranging from 24 s to 3/2 s periods. The coda decay gradient at short periods is steeper than that at longer periods for both cases of before and after ScS arrival. In particular, a clear offset of coda amplitude associated with ScS arrival appears in Turkey, Kyrgyzstan and Bolivia at 4-8 s and 8-16 s period bands. These coda decay gradient change and offset behavior in coda envelopes around ScS arrival are not clear in seismograms of shallow events. The simple and distinct characteristics of seismic coda envelopes could provide reliable information to determine physical values such as seismic source parameters and to identify the regional difference of medium heterogeneity in the deep Earth.