The horizontal-to-vertical spectral ratio (HVSR) of ambient noise is commonly used to infer a site's resonance frequency (⁠|${f_{0,site}}$|⁠). HVSR calculations are performed most commonly using the Fourier amplitude spectrum obtained from a single merged horizontal component (e.g. the geometric mean component) from a three-component sensor. However, the use of a single merged horizontal component implicitly relies on the assumptions of azimuthally isotropic seismic noise and 1-D surface and subsurface conditions. These assumptions may not be justified at many sites, leading to azimuthal variability in HVSR measurements that cannot be accounted for using a single merged component. This paper proposes a new statistical method to account for azimuthal variability in the peak frequency of HVSR curves (⁠|${f_{0,HVSR}}$|⁠). The method uses rotated horizontal components at evenly distributed azimuthal intervals to investigate and quantify azimuthal variability. To ensure unbiased statistics for |${f_{0,HVSR}}$| are obtained, a frequency-domain window-rejection algorithm is applied at each azimuth to automatically remove contaminated time windows in which the |${f_{0,HVSR}}$| values are statistical outliers relative to those obtained from the majority of windows at that azimuth. Then, a weighting scheme is used to account for different numbers of accepted time windows at each azimuth. The new method is applied to a data set of 114 HVSR measurements with significant azimuthal variability in |${f_{0,HVSR}}$|⁠, and is shown to reliably account for this variability. The methodology is also extended to the estimation of a complete lognormal-median HVSR curve that accounts for azimuthal variability. To encourage the adoption of this statistical approach to accounting for azimuthal variability in single-station HVSR measurements, the methods presented in this paper have been incorporated into hvsrpy, an open-source Python package for HVSR processing.

中文翻译：

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一种用于统计单站HVSR测量中方位角变异性的统计方法

环境噪声的水平与垂直频谱之比（HVSR）通常用于推断站点的共振频率（⁠| $ {f_ {0，site}} $ |⁠）。HVSR计算通常是使用从三分量传感器的单个合并水平分量（例如，几何平均分量）获得的傅立叶振幅谱来执行的。但是，使用单个合并的水平分量隐式依赖于方位各向同性地震噪声以及一维地表和地下条件的假设。这些假设可能在许多地点都没有根据，导致HVSR测量中的方位角变化，无法使用单个合并的分量进行解释。本文提出了一种新的统计方法来说明HVSR曲线峰值频率中的方位角变化（⁠| $ {f_ {0，HVSR}} $ |⁠）。该方法使用均匀分布的方位角间隔的旋转水平分量来研究和量化方位角变化性。确保| $ {f_ {0，HVSR}} $ |的统计信息无偏 获得后，将在每个方位角上应用频域窗口拒绝算法，以自动删除其中的| $ {f_ {0，HVSR}} $ |的受污染时间窗口。相对于从该方位的大多数窗口获得的统计离群值。然后，使用加权方案来说明每个方位角上不同数量的接受时间窗口。新方法应用于| $ {f_ {0，HVSR}} $ |⁠中114个HVSR测量的数据集，这些数据具有明显的方位角变化，并且可以可靠地说明这种差异。该方法还扩展到估计方位角变异性的完整对数正态中值HVSR曲线的估计。为了鼓励采用这种统计方法来说明单站HVSR测量中的方位角变异性，本文介绍的方法已合并到hvsrpy中，hvsrpy是用于HVSR处理的开源Python软件包。