Maximum-Likelihood Method for Estimating Coda Q and the Nakagami-m Parameter

We propose a new method to simultaneously estimate coda Q and the Nakagami-mparameterfromseismogramenvelopesbasedonthemaximum-likelihood (ML)method.CodaQisaparametercharacterizingasmoothdecayinseismiccodaand is considered to reflect physical parameters in the Earth such as intrinsic absorption, scattering attenuation, and soon.TheNakagami-mparameter,denoted bym,is ashape parameter oftheNakagami-mdistribution,whichwasoriginally proposedinthe1940s for the purpose of statistically characterizing the fading of short radiowaves. Recently, it was found that the statistics of high-frequency seismogram envelopes also obey the Nakagami-m distribution. An ML estimation of coda Q was so far proposed assuming Rayleigh distribution, which is equivalent to the Nakagami-m distribution for m 1. This study extends the previous method for estimating coda Q to the values of m different from 1. Concerning the estimation of m, this study may be the first to propose an MLmethod for high-frequency seismic waves. From thedata analysis oflocal earth- quakes in the frequency range from 1 to 32 Hz, we find that coda Q ranges from 100 at 1-2 Hz to 2000 at 16-32 Hz increasing with frequencies increasing. And thevalues are compatiblewith previously reported values. The m-parameter varies with events and is significantly different from 1 for some events. But meanvalues ofmwith respect to the events are close to 1 irrespective of components and frequencies. Variations in m are found to be larger for lower frequencies. The m-parameter is exactly equal to a reciprocalofthescintillationindex,whichisusedtoexpressfluctuationsinseismogram envelopes. Introduction of the m-parameter into seismology will help investigate statistical characteristics of small-scale fluctuations in seismic velocity structure in the Earth from fluctuations in seismogram envelopes.