To examine the upper limit of the analyzable wavelength ranges (upper limit wavelength, ULW) of the spatial autocorrelation (SPAC) method in microtremor surveys, we have derived a formula evaluating stochastic errors of a phase velocity estimate obtained by the SPAC method. We then followed our previous paper to evaluate biases generated in a phase velocity estimate that come from the presence of the incoherent noise so that we could discuss which is the crucial factor determining the ULW. As a result, the incoherent noise is considered as the crucial factor. In the consequence, we proposed a formula to evaluate signal‐to‐noise ratio (SNR) and to determine phase velocity with the effects of the incoherent noise compensated. We used observed data to validate the above theory. Through the validation procedure, we obtained an approximation equation , where NULW means ULW normalized by array radius and A is a constant. The parameter A took a value from about 1/2 to 2 in the cases of this study. Finally, an additional and simple analysis was executed, which indicates that the incoherent noise not only limits the SPAC analysis but also can provide benefits: they are possibly used for evaluating the attenuation of soils. A microtremor array survey with the traditional SPAC method of Okada (2003, https://doi.org/10.1190/1.9781560801740) can be a mobile tool for evaluating the very local attenuation at a site of interest (i.e., gaining a high spatial resolution), in frequency ranges suited for earthquake engineering and by using simple seismic arrays with short time observations.

中文翻译：

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非相干噪声引起的空间自相关微颤动阵列方法的局限性和优势，特别是对长波长范围的分析

为了检查微震勘测中空间自相关（SPAC）方法的可分析波长范围的上限（上限波长，ULW），我们导出了一个公式，用于评估通过SPAC方法获得的相速度估计的随机误差。然后，我们按照之前的论文来评估在相速度估计中由于不相干噪声的存在而产生的偏差，因此我们可以讨论哪个是确定超低周波的关键因素。结果，非相干噪声被认为是关键因素。结果，我们提出了一个公式来评估信噪比（SNR），并在补偿了非相干噪声的情况下确定相速度。我们使用观察到的数据来验证上述理论。通过验证过程，我们获得了一个近似方程，其中NULW表示通过阵列半径归一化的ULW，而A为常数。在本研究的案例中，参数A的取值约为1/2到2。最后，进行了另外的简单分析，这表明非相干噪声不仅限制了SPAC分析，而且还可以带来好处：它们可能被用于评估土壤的衰减。使用Okada的传统SPAC方法进行的微震阵列调查（2003，https://doi.org/10.1190/1.9781560801740）可以作为一种移动工具来评估感兴趣部位的局部衰减（即获得高空间分辨率） ），在适用于地震工程的频率范围内，并使用具有短时间观测结果的简单地震阵列。