Fiber-optic vibration sensing—I: Rotation measurement technique and its seismological applications
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摘要: 地震波场可分解为三分量平动和三分量旋转运动. 旋转分量包含重要的波场梯度信息，是地震波场重建的关键要素，但过去由于缺乏稳定的高灵敏度旋转测量仪器，它在不同的地震学应用中常被忽略. 光纤旋转地震仪是率先打破测量仪器缺乏困境、最先实现商业化的旋转地震仪，也是目前最有发展前景的地震波旋转直接测量设备. 光纤旋转地震仪基于Sagnac效应，并依托成熟的光纤陀螺技术实现振动的旋转分量测量. 它具有纯光电传感不受平动影响的测量优势；并且能够在高灵敏度和宽频带旋转测量的基础下实现设备的小型化，有利于旋转测量的应用推广. 因此，光纤旋转地震仪和传统的地震仪将形成互补，实现旋转和平动六分量（6C）的观测，更好地提取地震波场特征，提高振动监测能力，有效改善震源过程反演、地下结构成像和地震破坏机理研究等应用. 本文主要介绍光纤旋转测量的基本原理、旋转地震学的应用及其潜在应用前景.Abstract: The seismic wavefield can be decomposed into three-component translational motions and three-component rotational motions. The rotation components contain important wavefield gradient information and are key elements of seismic wavefield reconstruction. Due to the lack of stable high-sensitivity rotational measuring instruments, the rotation component was often neglected in different seismological applications in the past. The fiber-optic rotational seismometer, breaking the dilemma of the lack of measuring instruments, is the first commercialized rotating seismometer. It is also the most promising device for direct seismic wave rotation measurement. The fiber-optic rotational seismometer is based on the Sagnac effect and relies on mature fiber-optic gyroscope technology to measure the rotation components of vibration. It has the advantage that pure photoelectric sensor unaffected by translational motions and can be made portable equipment based on high sensitivity and wideband rotation measurement, which is beneficial to the application and promotion of rotation measurement. Therefore, the fiber-optic rotational seismograph and the traditional seismograph will complement each other to observe the six-component (6C) rotational and translational motions, which can extract seismic wavefield characteristics better, and can improve the performance of vibration monitoring, as well as the researches or applications on the seismic source rupture inversion, underground structure imaging and seismic damage mechanism. This article mainly introduces the basic principles of fiber-optic rotation measurement, the application of rotational seismology and its potential prospects.
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图 1 不同类型的振动传感设备.（a）传统电容换能弹簧质量块平动地震仪；（b）Rotaphone六分量地震计原型（修改自http://rotaphone.eu/prototype.html）；（c）MEMS振动传感，左侧为旋转测量振荡器原型，右侧为一个国产6C MEMS芯片；（d）基于透射光相位变化的光纤振动传感示意图，小图表示波形相位相关（Marra et al., 2018）；（e）布拉格光栅传感换能弹簧质量块地震计；（f）基于光纤陀螺的旋转地震仪，左侧为Sagnac效应观测模型，右侧为BlueSeis-3A旋转地震仪内部示意图（修改自https://www.blueseis.com/blueseis）；（g）基于背向散射光的分布式光纤振动传感（DAS）示意图；（h）基于透射光极性变化的光纤振动传感示意图，小图表示光极性在传播中的变化（Zhan et al., 2021b）.（d）～（h）属于光纤振动传感
Figure 1. Different types of vibration sensing devices. (a) Traditional mass-spring translational seismometer with capacity transducer; (b) Rotaphone six-component seismometer (modified from http://rotaphone.eu/prototype.html); (c) MEMS vibration sensing, the left is rotation measure, and the right is a 6C MEMS chip made in China; (d) Schematic diagram of optical phase based on vibration sensing with frequency metrology technique (Marra et al., 2018); (e) Mass-spring seismometer with optical Bragg grating; (f) Rotation seismometer based on fiber optic Gyroscope, the left is the scheme of Sagnac effect, and the right is inner scheme of BlueSeis-3A (modified from https://www.blueseis.com/blueseis); (g) Diagram of fiber distributed acoustic sensing (DAS); (h) Diagram of optical polarity based vibration sensing (Zhan et al., 2021b). (d)～(h) belong to fiber vibration sensing
图 2 （a）单点运动的平动和旋转六分量；（b）ADR旋转测量示意：双点平动空间微分获得一个旋转分量
Figure 2. (a) Six components including translation and rotation motions in a site; (b) Diagram of ADR: derived one rotation by spatial derivation of translation motions in two sites
图 3 目前不同陀螺技术所处的发展阶段（修改自薛连莉等，2020）
Figure 3. The current development stage of different gyro technologies (modified from Xue et al., 2020)
图 4 Sagnac效应.（a）没有旋转时同时发射相向传播的两束光（绿色和红色虚线）的走时差为0；（b）旋转后，两束光出现走时差. 黑线为光纤环，A为面积，M和M'为旋转前后激光入口位置
Figure 4. Sagnac effect. (a) Zero time difference for two lights (red and green dot lines) traveling in opposite directions; (b) Time difference after rotation. Where black line is fiber optical loop, and A is the area in the loop. M and M' are the position of laser source before and after rotation
图 5 从多事件纠缠6C和3C波形记录中提取地震波参数（修改自Sollberger et al., 2017）.（a）两个不同角度、相同速度入射的P波在自由表面记录的6C波形；（b）3C平动波形，即图（a）中前三道；（c）基于6C MUSIC算法获得的波矢量参数，以能量团表示结果误差范围，红点为真实参数；方位角和本地速度都获得准确的估计；（d）由平动3C数据提取的波矢量参数，由于两列波纠缠在一起无法仅从平动数据中获得准确的参数（红点）
Figure 5. Demonstration of the retrieval of wave parameters for multiple interfering events using the proposed 6-C and 3-C MUSIC algorithm (modified from Sollberger et al., 2017). (a) 6-C seismograms of two interfering P-waves recorded at the free surface. Two waves arrive at a recording station at the same time; (b) 3-C translational seismograms (correspond to the first three components in panel a); (c) Result of the 6-C MUSIC algorithm, zoomed in into the region of interest. The parameters of both events (direction angles and local velocities) are accurately retrieved. The true parameters are marked by a red dot; (d) Result obtained using pure translational 3-C data. The interference of the two waves causes the analysis to break down. The true parameters (red dots) cannot be recovered using translational data only
图 6 韩国2016年Gyeongju的MW5.4地震合成数据（0.02～0.16 Hz）矩张量反演结果的后验概率密度函数（kde：核密度估算，值越高越好）. 各小图对应独立分量的矩张量和质心深度，竖线为真实值. 沙滩球从左至右分别对应从平动三分量（3C）1D速度结构至六分量（6C）3D速度结构（对应总信息增益顺序）的反演结果（修改自Donner et al., 2020）
Figure 6. Inversion results for the synthetic experiment on the 2016 MW5.4 Gyeongju, ROK, earthquake in the frequency band of 0.02～0.16 Hz as posterior probability density functions (kde—kernel density estimation). Subplots show individual components of the moment tensor and the centroid depth. Blue and red curves show the outcomes of inverting three and six components (synthetic) data, respectively. Dashed and solid lines represent the cases of 1-D and 3-D GFs, respectively. Boxes within subplots give the information gain for each case and parameter, while the legend gives the sum of information gain over all parameters. Beachballs show the corresponding full MT solutions according the peak values of the distributions: light and dark colours correlate to 1-D and 3-D cases; blue and red to 3C and 6C cases, respectively (modified from Donner et al., 2020)
图 7 德国慕尼黑Fürstenfeldbruck地球物理观测站6自由度点观测获得的交通振动噪声（近1小时）记录及提取的背方位角（BAZ）信息（修改自Yuan et al., 2021）；（a）观测场地，红三角是STS-2地震仪和一个环状激光陀螺组成的6自由度点观测. 蓝线是高速公路.（b）从上往下分别是：南北和东西分量的加速度、垂直旋转速率和从上面三道记录提取的背方位角信息. 黑点是滑动时窗估算的、相关系数大于0.40的背方位角.（c）局部放大图
Figure 7. Site map at the Geophysical Observatory Fürstenfeldbruck near Munich, Germany and estimated back azimuth (BAZ) of the traffic-induced seismic noise (nearly one-hour continuous data) from 6-DOF point measurement (modified from Yuan et al., 2021). (a) The red triangle indicates the position where a STS-2 seismometer and a ring laser gyroscope are collocated. The blue curve denotes the highway next to the observatory. (b) From top to bottom: the north-south and east-west components of acceleration, the vertical rotational rate and the estimated BAZ from above three components. Black dots represent the estimated BAZ for the sliding window, with the cross-correlation (CC) coefficient being higher than 0.40. The dotted and dashed lines indicate the expected range of the BAZ variation for the inbound and outbound moving cars. (c) The zoom-in plot of (b) within the two solid red lines
图 8 采用单台6C记录极性分析方法估计2018年Alaska海湾地震的瑞利波波场参数（修改自Sollberger et al., 2020）.（a）南北平动分量；（b）S变换谱分析；（c）瑞利波相速度；（d）瑞利波背方位角;（e）瑞利波椭圆度角
Figure 8. Single-station wave parameter estimation using 6-C polarization analysis on the example of the 2018 gulf of Alaska earthquake (modified from Sollberger et al., 2020). The North component of translational motions is displayed in (a) with the corresponding S-transform in (b). Shown below is the estimation of frequency- and time-dependent Rayleigh wave parameters: (c) phase velocity, (d) back azimuth, and (e) ellipticity angle
表 1 几种激光/光纤旋转地震仪的主要参数对比（修改自Jaroszewicz et al., 2016; BlueSeis-3A根据https://www.blueseis.com/product-page/blueseis-3a网站列出的参数进行了修改; RotSensor3C参数来自Cao et al., 2021）
Table 1. Comparison of main parameters of several ring laser/Fiber-optic rotational seismometers (mainly modified from Jaroszewicz et al., 2016; the parameters for BlueSeis-3A are modified from https://www.blueseis.com/product-page/blueseis-3a; and for RotSensor3C from Cao et al., 2021)
参数 G-Ring μFORS-1 LCG AFORS-1 BlueSeis-3A RotSensor3C 设备研发国家 德国 德国 德国 波兰 法国 中国 分量 单分量 单分量 三分量 单分量 三分量 三分量 自噪声/（rad·s−1·Hz−1/2） 9 × 10−11 3 × 10−5 6.3 × 10−7 4 × 10−9 2 × 10−8 1.2 × 10−7 最大量程/(rad·s−1) 1 17.5 无数据 6.4 × 10−3 0.5 无数据 动态范围/dB 280 115 无数据 124 125 152 频段/Hz 0.003~10 无数据 DC~100 0.83~106.15 DC~50 0.005~125 标度因子误差/(%·℃−1) 无观测 ≤0.05(1σ) 无观测 无数据 <0.01 <0.01 工作温度/℃ 恒温 −40~77 无数据 −10~50 −10~50 无数据 标定 需要 无数据 不需要 远程 不需要 无数据 工作电压/V 高 ±5, 3.3 24 12 12 无数据 功耗/W 高 2.5 25 <24 19 无数据 重量/kg 无数据 0.137 2.7 18 20 4.5 尺寸(长宽高)/mm 面积16 m2 22 × 73 × 58 278×102×128 700(直径)×160 318(直径)×335 190×190×165 采样率/Hz 4 5~1000 200 212 200 无数据 
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