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Phase and Correlation in `Random' Seismic Fields and the Reconstruction of the Green Function

机译：“随机”地震场的相位和相关性与绿色函数的重构

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We first present a summary of recent results on coda interpretation. We emphasize the observation of the stabilization of P to S energy ratio indicating the modal equipartition of the wavefield. This property clearly shows that the coda waves are in the regime of multiple scattering. Numerical solutions of the elastic radiative transfer equation are used to illustrate the evolution of the wave-field towards P-to-S energy stabilization, and asymptotically to complete isotropy. The energy properties of the coda have been widely studied but the phase properties have often been neglected. The recently observed coherent backscattering enhancement, an expression of the so-called `weak localization', demonstrates that interference effects still persist for multiple diffracted waves. Another manifestation of the persistence of the phase is the possibility to reconstruct the Green function between two stations by averaging the cross correlation of coda waves produced by distant earthquakes and recorded at those two stations. This reconstruction is directly related to the properties of reciprocity and time reversal of any wavefield. Using broadband seismic coda waves, we show that the dominant phases of the Green function in the band 2 s–10 s, namely fundamental mode Rayleigh and Love waves, are reconstructed. We analyze the time symmetry of the cross correlation and show how the level of symmetry evolves with the isotropization of the diffuse field with lapse time. Similarly we investigate the correlation in continuous ambient noise records. Whereas the randomness of the coda results from multiple scattering by randomly distributed scatterers, we assume that the seismic noise is random mostly because of the distribution of sources at the surface of the Earth. Surface waves can be extracted from long time series. The dispersion curves of Rayleigh waves are deduced from the correlations. On paths where measurements from earthquake data are also available, we show that they are in good agreement with those deduced from noise correlation. The measurement of velocities from correlation of noise along paths crossing different crustal structures opens the way for a `passive imaging' of the Earth's structure.
机译：我们首先介绍有关尾气分析的最新结果的摘要。我们强调观察到的P与S能量比稳定，表明波场的模态均分。该性质清楚地表明，尾波处于多重散射状态。弹性辐射传递方程的数值解用于说明波场向P-to-S能量稳定的演化，并渐近地表现出完全的各向同性。尾气的能量性质已被广泛研究，但相性质经常被忽略。最近观察到的相干后向散射增强，即所谓的“弱定位”，表明干涉效应对于多个衍射波仍然存在。该阶段持续性的另一个体现是，可以通过对遥远地震产生并记录在这两个站点的尾波的互相关求平均，从而在两个站点之间重建格林函数。这种重建与任何波场的互易性和时间反转特性直接相关。使用宽带地震尾波，我们显示了在2 s-10 s频段内格林函数的主导相位，即基本模态瑞利波和洛夫波，得以重构。我们分析了互相关的时间对称性，并显示了随着时间的推移，随着扩散场的各向同性，对称性水平如何演变。同样，我们研究连续环境噪声记录中的相关性。尾声的随机性是由随机分布的散射体的多次散射导致的，我们假设地震噪声是随机的，主要是由于地球表面源的分布。可以从长时间序列中提取表面波。由相关推导瑞利波的频散曲线。在可以从地震数据获得测量结果的路径上，我们表明它们与从噪声相关性推论得出的结果非常一致。通过沿着穿过不同地壳结构的路径的噪声相关性来测量速度，为地球结构的“被动成像”开辟了道路。

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