We propose a new method to simultaneously estimate coda Q and the Nakagami-m parameter from seismogram envelopes based on the maximum-likelihood (ML) method. Coda Q is 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-m parameter, denoted by m, is a shape parameter of the Nakagami-m distribution, 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.

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