Direct estimation method to extract phase velocities of Rayleigh waves in microtremors using arbitrary geometry array

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  • 任意形状アレーを用いた微動探査における位相速度の直接同定法
  • ニンイ ケイジョウ アレー オ モチイタ ビドウ タンサ ニ オケル イソウ ソクド ノ チョクセツ ドウテイホウ

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Abstract

 Both SAPC method and F-K method are mainly used for the estimation of phase velocities in the microtremor survey method (MSM). However, these conventional techniques have some problems. That is, as for SPAC method, the array geometry is restricted to circular arrays and sensors on the circle have to be installed at even intervals (Minimum configuration requires four sensors). By this restriction, sensors can not be installed in some cases because of obstacles such as dense houses or intricate roads. On the other hand, F-K method has less restriction on the array configuration. However, this method takes much work for array deployment, because about ten sensors are necessary for the observation.<br>  To break down these problems, authors have derived a new estimation technique for the Rayleigh wave phase velocities. We call this technique direct estimation method (DEM). DEM does not require any restriction for the array geometry, and phase velocities can be estimated by even a few sensors (Minimum configuration requires three sensors). In the DEM, the outputs of arrays are expressed by complex coherence functions (CCFs) and the phase velocities are estimated by the least square approach which minimizes the residuals between the theoretical CCFs and observed CCFs. In this article, the theory of DEM for arbitrary geometry arrays is illustrated and the results of both numerical experiments and verification test are presented. They are implemented to illuminate the basic characteristics of the DEM and to confirm the validity of this technique. The numerical experiments are examined on the following matter. 1) Since the CCF is an infinite series, the CCFs have to be approximated by some finite terms to perform the least square approach. Therefore, some examinations for deriving a measure of approximation are performed, 2) An examination about restrict conditions using source parameters contained in the CCF is performed, 3) The relationship between the estimated phase velocities and the incident angles, 4) The relationship between the estimated phase velocities and the number of sensors. In the verification test, it was confirmed that the phase velocities obtained by the DEM are well agreement with those obtained by the conventional method with satisfactory accuracy. The DEM for arbitrary geometry arrays enables us to estimate the phase velocities with the least three sensors and it can be applied to the records of existing observation networks. Therefore, the DEM is useful to extend the applicability of the MSM.<br>

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