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 mparameter from seismogram envelopes based on the maximum-likelihood (ML)method. CodaQis a parameter characterizing a smooth decay in seismic coda and is considered to reflect physical parameters in the Earth such as intrinsic absorption, scattering attenuation, and so on. The Nakagami-mparameter, denoted bym, is a shape parameter of the Nakagami mdistribution, which was originally proposed in the 1940s for the purpose of statistically characterizing the fading of short radio waves. 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 ML method for high-frequency seismic waves. From the data analysis of local earthquakes 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 the values are compatible with previously reported values. The m-parameter varies with events and is significantly different from 1 for some events. But mean values of m with 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 reciprocal of the scintillation index, which is used to express fluctuations in seismogram 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.