Maximum-Likelihood Method for Estimating Coda Q and the Nakagami-m Parameter
Maximum-Likelihood Method for Estimating Coda Q and the Nakagami-m Parameter
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DOI：
10.1785/0120100030
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发表时间：
2010-12
影响因子：
3
通讯作者：
H. Nakahara;E. Carcolé
中科院分区：
文献类型：
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作者：
H. Nakahara;E. Carcolé
我们提出了一种同时估计尾波Q的新方法，Nakagami-mparameterfromseismogramenvelopesbasedonthemaximum-likelihood(ML)method.CodaQisaparametercharacterizingasmoothdecayinseismiccodaand被认为反映了地球上的物理参数，如本征吸收、散射衰减和速度。Nakagami参数，记为m，是Nakagami-m分布的形状参数，最初是在20世纪40年代提出的，目的是统计描述短无线电波的衰落。最近，人们发现高频地震记录包络的统计也服从Nakagami-m分布。到目前为止，已提出了一种基于瑞利分布的尾波Q的最大似然估计方法，该分布等价于m-�1的Nakagami-m分布。本研究将以往的尾波Q估计方法推广到不同于1的m值。关于m的估计，本研究可能是首次提出高频地震波的最大似然估计方法。对1-32赫兹近震资料的分析表明，1-2赫兹的尾波Q值为100，16-32赫兹的尾波Q值为2000，随频率的增加而增加。这些值与之前报道的值是一致的。M参数随事件而变化，某些事件的m参数明显不同于1。但是，无论分量和频率如何，M相对于事件的平均值都接近于1。研究发现，频率越低，m的变化越大。M参数正好等于闪烁指数的倒数，该指数用来表示地震记录包络中的波动。将m参数引入地震学将有助于从地震记录包络的波动中研究地球上地震速度结构的小尺度波动的统计特征。
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.