A generic formulation for microtremor exploration methods using three‐component records from a circular array
A generic formulation for microtremor exploration methods using three‐component records from a circular array
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DOI：
10.1111/j.1365-246x.2006.02880.x
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发表时间：
2006-04
影响因子：
2.8
通讯作者：
I. Cho;Taku Tada;Y. Shinozaki
中科院分区：
文献类型：
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作者：
I. Cho;Taku Tada;Y. Shinozaki
总结我们提出了一个通用的配方，估计瑞利波和爱波的相速度的分析方法，通过中间量称为“频谱比”，使用三个组件的记录从一个圆形阵列的传感器的微震。在每一个时刻，记录的集合被展开成关于方位角的傅立叶级数，这样我们就得到了一组傅立叶系数，它们以复时程的形式表示。然后，我们估计这些傅立叶系数的功率和交叉谱密度。由此获得的谱密度通常包含关于瑞利波和Love波的各个模式的相速度、功率和到达方向的信息。通过取两种不同类型的谱密度的商，我们可以抵消关于它们的功率和到达方向的信息，并且仅提取关于它们的相速度的信息。在实践中，必须根据来自有限数量的地震传感器的记录来估计频谱比，这些地震传感器均匀地或不均匀地分布在圆周上。我们描述了一个一般的程序，他们的估计，并讨论了方向混淆的影响，有限数量的传感器和它们的配置上的估计的频谱比。我们还讨论了不相干噪声的存在所造成的频谱比的估计偏差。利用我们的方法，还可以估计地震动的中心到达方向，瑞利波的椭圆率，以及瑞利波是逆时针还是逆时针。
SUMMARY We present a generic formulation for analysis methods that estimate phase velocities of Rayleigh and Love waves, by way of intermediary quantities called ‘spectral ratios’, using three-component records of microtremors from a circular array of sensors. At each time instant, the set of records are expanded in a Fourier series with respect to azimuth, so that we obtain a set of Fourier coefficients that are represented in the form of complex time histories. We then estimate power- and cross-spectral densities of those Fourier coefficients. The spectral densities, thus obtained, generally contain information on the phase velocities, powers and arrival directions of individual modes of Rayleigh and Love waves. By taking the quotient of two different sorts of such spectral densities, we can cancel out information on their powers and arrival directions, and extract information on their phase velocities alone. The spectral ratios have to be estimated, in practice, on the basis of records from a finite number of seismic sensors that are either evenly or unevenly spaced around a circumference. We describe a general procedure for their estimation, and discuss the effects of directional aliasing that the finite number of sensors and their configuration have on the estimates of spectral ratios. We also discuss biases in the estimates of spectral ratios caused by the presence of incoherent noise. By using our method, it is also possible to estimate the central arrival direction of the microtremors, the ellipticity of the Rayleigh waves, and whether the Rayleigh waves are prograde or retrograde.