Yoritomo John Y, Weaver Richard L
Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA.
J Acoust Soc Am. 2016 Jul;140(1):702. doi: 10.1121/1.4959002.
Inasmuch as ambient noise fields are often not fully diffuse the question arises as to how, or whether, noise cross-correlations converge to Green's function in practice. Well-known theoretical estimates suggest that the quality of convergence scales with the square root of the product of integration time and bandwidth. However, correlations from natural environments often show random features too large to be consistent with fluctuations from insufficient integration time. Here it is argued that empirical seismic correlations suffer in practice from spurious arrivals due to scatterers, and not from insufficient integration time. Estimates are sought for differences by considering a related problem consisting of waves from a finite density of point sources. The resulting cross-correlations are analyzed for their mean and variance. The mean is, as expected, Green's function with amplitude dependent on noise strength. The variance is found to have support for all times up to its maximum at the main arrival. The signal-to-noise ratio there scales with the square root of source density. Numerical simulations support the theoretical estimates. The result permits estimates of spurious arrivals' impact on identification of cross-correlations with Green's function and indicates that spurious arrivals may affect estimates of amplitudes, complicating efforts to infer attenuation.
由于环境噪声场通常并非完全扩散，因此出现了这样一个问题：在实际中，噪声互相关如何或者是否会收敛到格林函数。著名的理论估计表明，收敛质量与积分时间和带宽乘积的平方根成比例。然而，来自自然环境的相关性往往显示出随机特征过大，无法与积分时间不足导致的波动相一致。本文认为，实际中的经验地震相关性受到散射体产生的虚假震相的影响，而不是积分时间不足。通过考虑一个由有限密度点源发出的波组成的相关问题来寻求差异估计。对由此产生的互相关进行均值和方差分析。均值正如预期的那样是格林函数，其振幅取决于噪声强度。发现方差在主震相之前的所有时间都有取值，直至其最大值。那里的信噪比与源密度的平方根成比例。数值模拟支持理论估计。该结果允许估计虚假震相对与格林函数互相关识别的影响，并表明虚假震相可能会影响振幅估计，使推断衰减的努力变得复杂。
