Microtremor surveys based on rotational seismology: theoretical analysis with focus on separation of Rayleigh and Love waves in general wavefield of microtremors
Microtremor surveys based on rotational seismology: theoretical analysis with focus on separation of Rayleigh and Love waves in general wavefield of microtremors
复制标题
基于旋转地震学的微震勘测：微震一般波场中瑞利波与拉夫波分离的理论分析
DOI：
10.1093/gji/ggab358
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发表时间：
2022
影响因子：
2.8
通讯作者：
Uebayashi H
中科院分区：
文献类型：
--
作者：
Cho I;Yoshida K;Uebayashi H
基于二维波场的随机过程模型，从理论上论证了旋转地震学对一般微震波场的适用性。在同时从不同方向、不同强度的波到达的波场中，我们展示了利用微动波形的旋转(即空间微分)来分离瑞利波和乐夫波的有效性。这意味着，基于旋转地震学的方法(旋转法)能够分离瑞利波和乐夫波，而不采用特定的阵列几何或对微动波场施加特定的假设。这是旋转方法的一个重要特征，因为空间自相关(SPAC)方法是在微动阵列测量中确定相速度的传统方法，它需要使用圆形阵列或假设各向同性波场(即需要对相关性进行方位平均)。SPAC方法的导数还需要假设瑞利波和乐夫波是不相关的。我们还表明，基于由平移(即普通)三分量传感器组成的简单三点微动阵列，应用旋转方法来确定Love波的特征是可能的。在后面的章节中，我们假设对带有平移传感器的微动阵列进行现实的数据处理，以构建一个理论模型来评估有限差分近似空间差异(即阵列衍生旋转，ADR)的影响以及非相干噪声对分析结果的影响。利用该模型表明，在短波长范围内，相对于有限差分的距离(例如，其中分别是有限差分的波长和距离)，不需要的波分量的泄漏可以决定分析极限。在长波长范围内(例如)，信号强度逐渐降低，因此非相干噪声的影响增加(即信噪比、信噪比降低)，并决定了分析极限。推导了信噪比与波长的关系。虽然分析结果在数量上取决于用于有限差分的阵列几何，但具有物理上明确含义的数学表达式所支持的定性理解可以作为处理从ADR获得的数据的指导方针。
The applicability of rotational seismology to the general wavefield of microtremors is theoretically demonstrated based on a random process model of a 2-D wavefield. We show the effectiveness of taking the rotations (i.e. spatial differentiation) of microtremor waveforms in separating the Rayleigh and Love waves in a wavefield where waves are simultaneously arriving from various directions with different intensities. This means that a method based on rotational seismology (a rotational method) is capable of separating Rayleigh and Love waves without adopting a specific array geometry or imposing a specific assumption on the microtremor wavefield. This is an important feature of a rotational method because the spatial autocorrelation (SPAC) method, a conventional approach for determining phase velocities in microtremor array surveys, requires either the use of a circular array or the assumption of an isotropic wavefield (i.e. azimuthal averaging of correlations is required). Derivatives of the SPAC method additionally require the assumption that Rayleigh and Love waves are uncorrelated. We also show that it is possible to apply a rotational method to determine the characteristics of Love waves based on a simple three-point microtremor array that consists of translational (i.e. ordinary) three-component sensors. In later sections, we assume realistic data processing for microtremor arrays with translational sensors to construct a theoretical model to evaluate the effects of approximating spatial differentiation via finite differencing (i.e. array-derived rotation, ADR) and the effects of incoherent noise on analysis results. Using this model, it is shown that in a short-wavelength range compared to the distance for finite differencing (e.g., whereandare the wavelength and distance for finite differencing, respectively), the leakage of unwanted wave components can determine the analysis limit. It is also shown that in a long-wavelength range (e.g.), the signal intensity gradually decreases, and thus the effects of incoherent noise increase (i.e. the signal-to-noise ratio, SNR decreases) and determine the analysis limit. We derive the relation between the SNR and wavelength. Although the analysis results quantitatively depend on the array geometry used for finite differencing, the qualitative understanding supported by mathematical expressions with a physically clear meaning can serve as a guideline for the treatment of data obtained from ADR.