Equipartitioning is not sufficient for Green’s function extraction
Equipartitioning is not sufficient for Green’s function extraction
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均分不足以进行格林函数提取
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
K. Wapenaar
中科院分区：
文献类型：
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作者：
R. Snieder;Yuanzhong Fan;E. Slob;K. Wapenaar
从磁场波动中提取地球的绿色函数是一个快速发展的研究领域。绿色函数提取的原理往往与均分要求有关，均分要求场涨落的能量在某种意义上均匀分布。我们展示了各种不同的配方绿色的功能检索均分的意义。我们表明，均分不是一个充分条件，并提供了几个例子来说明这一点。我们讨论了地震学中重建绿色函数的各种方案缺乏均分的影响。用于绿色函数提取的理论通常基于依赖于系综平均的统计理论。由于只有一个地球，人们通常用时间平均来代替集合平均。我们表明，这样的替换只有考虑到衰减时才有意义，并显示如何振荡系统的绿色函数提取的理论可以扩展到将衰减。
The extraction of the Earth’s Green’s function from field fluctuations is a rapidly growing area of research. The principle of Green’s function extraction is often related to the requirement of equipartitioning, which stipulates that the energy of field fluctuations is distributed evenly in some sense. We show the meaning of equipartitioning for a variety of different formulations for Green’s function retrieval. We show that equipartitioning is not a sufficient condition, and provide several examples that illustrate this point. We discuss the implications of lack of equipartitioning for various schemes for the reconstruction of the Green’s function in seismology. The theory for Green’s function extraction is usually based on a statistical theory that relies on ensemble averages. Since there is only one Earth, one usually replaces the ensemble average with a time average. We show that such a replacement only makes sense when attenuation is taken into account, and show how the theory for Green’s function extraction for oscillating systems can be extended to incorporate attenuation.