A wide spectrum of processing schemes is commonly applied during the calculation of seismic noise correlations. This is intended to suppress large-amplitude transient and monochromatic signals, to accelerate convergence of the correlation process or to modify raw correlations into more plausible approximations of interstation Green’s functions. Many processing schemes, such as one-bit normalization or various other nonlinear normalizations, clearly break the linear physics of seismic wave propagation. This naturally raises the question: To what extent are the resulting noise correlations physically meaningful quantities? In this contribution, we demonstrate that commonly applied processing methods may indeed introduce an unphysical component into noise correlations. This affects not only noise correlation amplitudes but also, to a lesser extent, time-dependent phase information. The profound consequences are that most processed correlations cannot be entirely explained by any combination of Earth structure and noise sources, and that inversion results may thus be polluted. The positive component of our analysis is a new and easily applicable method that allows us to modify any existing processing such that it becomes optimal in the sense of (1) completely avoiding the unphysical component while (2) approximating the result of the original processing as closely as possible. The resulting optimal schemes can be derived purely on the basis of observed noise, without any knowledge of or assumptions on the nature of noise sources. In addition to the theoretical analysis, we present illustrative real-data examples from the Irish National Seismic Network and the Lost Hills array in Central California. We anticipate that optimal processing schemes may be most useful in applications that exploit complete correlation waveforms, amplitudes and weak arrivals, or small (time-dependent) phase shifts.

中文翻译：

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地震噪声相关性的最佳处理

在计算地震噪声相关性时，通常应用各种各样的处理方案。这旨在抑制大振幅瞬态和单色信号，以加快相关过程的收敛速度，或将原始相关修改为站间格林功能的更合理的近似值。许多处理方案，例如一位归一化或各种其他非线性归一化，显然破坏了地震波传播的线性物理学。这自然提出了一个问题：所产生的噪声关联在多大程度上具有物理意义？在此贡献中，我们证明了常用的处理方法确实可能将非物理成分引入噪声关联。这不仅会影响噪声相关幅度，还会在较小程度上影响噪声相关幅度。时间相关的阶段信息。深刻的后果是，大多数处理过的相关性无法完全由地球结构和噪声源的任何组合来解释，因此反演结果可能会受到污染。我们的分析的肯定成分是一种新的且易于应用的方法，它使我们能够修改任何现有的处理方法，使其在以下方面变得最佳：（1）完全避免非物理成分，而（2）近似原始处理结果为尽可能紧密地 所得的最佳方案可以完全基于观察到的噪声来导出，而无需任何有关噪声源性质的知识或假设。除了理论分析，我们提供了来自爱尔兰国家地震台网和加利福尼亚中部Lost Hills阵列的说明性真实数据示例。我们预计，最佳处理方案在利用完整的相关波形，幅度和弱到达或小的（随时间变化）相移的应用中可能最有用。