﻿ 不同台阵形式对微动探测结果的影响
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 大地测量与地球动力学  2020, Vol. 40 Issue (1): 98-103  DOI: 10.14075/j.jgg.2020.01.019

### 引用本文

LI Jinggang, XIE Peng, WANG Qiuliang, et al. Influence of Different Array Type on the Results of Microtremor Survey[J]. Journal of Geodesy and Geodynamics, 2020, 40(1): 98-103.

### Foundation support

National Natural Science Foundation of China, No. 41572354.

### Corresponding author

XIE Peng, postgraduate, majors in theory and applications of microtremor survey, E-mail: xipa813@126.com.

### 第一作者简介

LI Jinggang, assistant researcher, majors in theory and applications of microtremor survey, E-mail:21263823@qq.com.

### 文章历史

1. 中国地震局地震研究所地震大地测量重点实验室，武汉市洪山侧路40号，430071;
2. 厦门市万科房地产有限公司，厦门市莲前西路859号，361000

1 微动与微动探测方法 1.1 空间自相关法

 $S\left( {t, \mathit{\boldsymbol{\eta }}, \mathit{\boldsymbol{\xi }}} \right) = E\left[ {{X^ * }\left( {t, \mathit{\boldsymbol{\eta }}} \right)X\left( {t, \mathit{\boldsymbol{\eta }} + \mathit{\boldsymbol{\xi }}} \right)} \right]$ (1)

 $S\left( {\bf{ \pmb{\mathsf{ ξ}} }} \right) = \int {\int {\int_{ - \infty }^{ + \infty } {\exp ik\mathit{\boldsymbol{\xi }}} \cdot E\left[ {{{\left| {{\rm{d}}z\left( {\omega ,k} \right)} \right|}^2}} \right]} }$ (2)

 $\begin{array}{*{20}{l}} {\;\;\;\;S\left( {r, \theta } \right) = }\\ {\int_{ - \infty }^{ + \infty } {\int_0^{2\pi } {\left[ {\exp \left( {ikr\cos \left( {\theta - \varphi } \right)} \right)h\left( {\omega , \varphi } \right){\rm{d}}\varphi } \right]} } {\rm{d}}\omega } \end{array}$ (3)

 $\begin{array}{l} \;\;\;\;\;\;\;\;\;g\left( {\omega , r, \theta } \right) = \\ \int_0^{2\pi } {\exp \left( {ikr\cos \left( {\theta - \varphi } \right)} \right)h\left( {\omega , \varphi } \right){\rm{d}}\varphi } \end{array}$ (4)

 $S\left( {r, \theta } \right) = \int_{ - \infty }^{ + \infty } {g\left( {\omega , r, \theta } \right)} {\rm{d}}\omega$ (5)
1.2 台阵选取

2 数据采集和分析 2.1 实验场地

 图 1 浩口中学GPS卫星图 Fig. 1 GPS satellite map of Haokou middle school
2.2 观测仪器

 图 2 仪器一致性测试波形记录 Fig. 2 Waveform records of instrument's conformance test

 图 3 仪器功率谱测试结果 Fig. 3 Test results of instrument's power spectrum
2.3 3种台阵形式以及场地条件介绍

 图 4 台阵测点布局 Fig. 4 The layout of arrays

2.4 数据处理流程

 图 5 反演S波速度结构的流程 Fig. 5 Flow of inversion of S-wave velocity structure

 图 6 三重圆形台阵的频散图谱 Fig. 6 Dispersion spectrum of nested equilateral triangles array

 图 7 T形台阵的频散图谱 Fig. 7 Dispersion spectrum of T-shape array

 图 8 L形台阵的频散图谱 Fig. 8 Dispersion spectrum of L-shape array

 图 9 3种台阵频散曲线 Fig. 9 Dispersion curves for three arrays

3组频散曲线拟合结果如图 10所示。整体来看，模型与3条频散曲线的拟合效果较好，残差值小于0.03。相比于低频段，高频段的拟合效果更好一些。

 图 10 频散曲线拟合效果 Fig. 10 Dispersion curves for three arrays
2.5 数据处理结果

 图 11 反演S波速度结构 Fig. 11 Inversion of S-wave velocity structure

3 结果和讨论

 图 12 微动探测结果与钻孔岩芯对比 Fig. 12 Microtremor survey results compared with borehole core

1) 从3组台阵都提取到了1.2~4.6 Hz内的频散曲线，且结果基本一致。

2) 频散图谱能量集中度具有明显的差异，三重圆形台阵频散图谱能量集中度最高，L形、T形台阵在2.0~4.6 Hz频段范围内集中度也较高，而在1.2~2.0 Hz频段范围内较分散。

3) 相比T形和L形台阵，三重圆形台阵在地层分界面处波速突变更明显，即三重圆形台阵比其他两种台阵形式的准确性及可靠性更高。

4 结语

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Influence of Different Array Type on the Results of Microtremor Survey
LI Jinggang1     XIE Peng1     WANG Qiuliang1     YU Jinxin1     SHEN Yuyi1,2
1. Key Laboratory of Earthquake Geodesy, Institute of Seismology, CEA, 40 Hongshance Road, Wuhan 430071, China;
2. Xiamen Vanke Co Ltd, 859 West-Lianqian Road, Xiamen 361000, China
Abstract: In the same site of Jianghan basin, three different array forms: triple circular, T-shaped and L-shaped, are used for observation and comparison experiments. The results show that the dispersion curves of the three arrays are basically the same; the energy concentration degree of the three arrays is obviously different. The energy concentration degree of the triple circular arrays is the highest, and the concentration degree of the L-shaped and T-shaped arrays is also higher in the range of 2.0-4.6 Hz. Compared with the T-shaped and L-shaped arrays, the wave velocity contrast of the triple circular arrays near the stratigraphic interface is more obvious; that is, the triple circular arrays is more reliable and accurate than the other two array forms.
Key words: microtremor survey; SPAC; array type; stratigraphic structure; Jianghan basin