Abstract Body waves may affect phase velocity obtained from microtremor array surveys in some rare cases. Fitting theoretical phase velocities based on a surface-wave theory to observed phase velocities affected by body waves would therefore result in distorted images of subsurface S-wave velocity structure. In this study, we present a method for the theoretical calculation of phase velocities in which the full-wave field (i.e. a wavefield including not only surface waves but also body waves) is taken into account. In numerical experiments conducted in this study, in which we considered the full-wave field, we generated synthetic microtremors by randomly distributing point vibration sources on the surface of a horizontally stratified velocity model. We then determined the phase velocities by applying the spatial autocorrelation (SPAC) method to the synthetic vertical-component wave data. The phase-velocity dispersion curve thus obtained exhibited a shape with a clear peak, with a peak value (peak phase velocity) exceeding the S-wave velocity of a bedrock in the model, which was not explainable with a surface-wave (Rayleigh-wave) theory. We conducted systematic numerical experiments and clarified the following two features of the peak phase velocity: (1) the peak phase velocity becomes large as the contrast of the S-wave velocities between the surface layer and the bedrock, or the P-to-S-wave velocity ratio (related to the Poisson’s ratio) in the surface layer gets large, and (2) the frequency at which peak phase velocity occurs (peak frequency) lies in the vicinity of the S-wave resonance frequency of the ground. Both the peak phase velocity and the peak frequency were theoretically reproduced by the calculation method that we propose in this study, based on a SPAC method modified to consider the full-wave field. These results imply the possible improvement in the accuracy of microtremor array survey analysis for velocity-structure inference, by applying a full-wave theory to the peak phase velocity.

中文翻译：

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体波对由空间自相关 (SPAC) 方法确定的相速度的影响，使用全波建模进行评估

摘要 在极少数情况下，体波可能会影响从微震阵列调查中获得的相速度。因此，将基于表面波理论的理论相速度拟合到受体波影响的观测相速度将导致地下 S 波速度结构的失真图像。在这项研究中，我们提出了一种理论计算相速度的方法，其中考虑了全波场（即不仅包括面波还包括体波的波场）。在本研究中进行的数值实验中，我们考虑了全波场，我们通过在水平分层速度模型的表面上随机分布点振动源来生成合成微震。然后，我们通过将空间自相关 (SPAC) 方法应用于合成垂直分量波数据来确定相速度。这样得到的相速度频散曲线呈现出一个清晰的峰值形状，峰值（峰值相速度）超过了模型中基岩的 S 波速度，这是表面波无法解释的（Rayleigh-波）理论。我们进行了系统的数值实验，阐明了峰值相速度的以下两个特征：(1) 峰值相速度随着表层和基岩之间的 S 波速度或 P-to-S 之间的对比而变大。 - 表层的波速比（与泊松比有关）变大，(2)出现峰值相速度的频率(峰值频率)位于地面横波共振频率附近。峰值相速度和峰值频率均通过我们在本研究中提出的计算方法在理论上再现，基于修改为考虑全波场的 SPAC 方法。这些结果意味着通过将全波理论应用于峰值相速度，可能会提高微震阵列调查分析的速度 - 结构推断的准确性。