An areal distribution of sensors can be used for estimating the direction of incoming waves through beamforming. Beamforming may be implemented as a phase-shifting and stacking of data recorded on the different sensors (i.e., conventional beamforming). Alternatively, beamforming can be applied to cross-correlations between the waveforms on the different sensors. We derive a kernel for beamforming cross-correlated data and call it cross-correlation beamforming (CCBF). We point out that CCBF has slightly better resolution and aliasing characteristics than conventional beamforming. When auto-correlations are added to CCBF, the array response functions are the same as for conventional beamforming. We show numerically that CCBF is more resilient to non-coherent noise. Furthermore, we illustrate that with CCBF individual receiver-pairs can be removed to improve mapping to the slowness domain. An additional flexibility of CCBF is that cross-correlations can be time-windowed prior to beamforming, e.g., to remove the directionality of a scattered wavefield. The observations on synthetic data are confirmed with field data from the SPITS array (Svalbard). Both when beamforming an earthquake arrival and when beamforming ambient noise, CCBF focuses more of the energy to a central beam. Overall, the main advantage of CCBF is noise suppression and its flexibility to remove station pairs that deteriorate the signal-related beampower.

中文翻译：

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互相关波束成形。

传感器的面积分布可用于估计通过波束形成的入射波的方向。波束成形可以被实现为记录在不同传感器上的数据的相移和堆叠（即，常规波束成形）。备选地，可以将波束成形应用于不同传感器上的波形之间的互相关。我们推导了用于波束成形互相关数据的内核，并将其称为互相关波束成形（CCBF）。我们指出，CCBF的分辨率和混叠特性比常规波束成形稍好。将自相关添加到CCBF时，阵列响应函数与常规波束成形相同。我们用数字显示，CCBF对非相干噪声更具弹性。此外，我们说明了使用CCBF可以删除单个接收器对，以改善到慢速域的映射。CCBF的另一个灵活性是，可以在波束成形之前对互相关进行时间窗处理，例如，以消除散射波场的方向性。利用SPITS阵列（Svalbard）的现场数据证实了对合成数据的观察。在对地震到达进行波束成形和对环境噪声进行波束成形时，CCBF都会将更多的能量聚焦到中心波束上。总体而言，CCBF的主要优势在于噪声抑制以及其灵活性，可消除恶化信号相关波束功率的电台对。利用SPITS阵列（Svalbard）的现场数据证实了对合成数据的观察。在对地震到达进行波束成形和对环境噪声进行波束成形时，CCBF都会将更多的能量聚焦到中心波束上。总体而言，CCBF的主要优势在于噪声抑制以及其灵活性，可消除恶化信号相关波束功率的电台对。利用SPITS阵列（Svalbard）的现场数据证实了对合成数据的观察。在对地震到达进行波束成形和对环境噪声进行波束成形时，CCBF都会将更多的能量聚焦到中心波束上。总体而言，CCBF的主要优势在于噪声抑制以及其灵活性，可消除恶化信号相关波束功率的电台对。