Review of temporal variations of underground medium based on seismic waves
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摘要:
作为一颗充满活力的星球，地球存在着从秒（如地震破裂）到百万年（如地幔对流）跨越十几个时间数量级的动态演化过程. 利用地震波携带的信息，目前已经获得了从分钟到年尺度的地下介质动态变化. 本文较为系统地总结了基于地震波的地下介质随时间变化监测方法及应用. 首先介绍了一些传统的时变研究方法，包括波速比、剪切波分裂、尾波Q值和接收函数方法、以及时移成像新技术；之后重点介绍利用重复信号研究地下介质变化的新方法，这些信号主要来自主动源、重复地震及背景噪声互相关，基于尾波干涉测量技术，极大提高了波速测量的精度. 本文还综述了目前地震波时变监测的主要应用领域，包括火山喷发、地震、滑坡、工业活动、慢地震、内核差速旋转、降雨和地下水等环境因素相关的变化监测. 最后基于目前的研究方法和应用情况，从观测技术、数据处理方法和应用领域等方面对地震波速时变研究进行了展望.
Abstract:As a vibrant and ever-evolving planet, the Earth has a dynamic evolution process spanning more than a dozen orders of magnitude from seconds (e.g., seismic rupture) to millions of years (e.g., mantle convection). Dynamic changes in underground media, spanning from minute to year scales, have been captured and analyzed based on seismic wave. This paper systematically summarizes the methods and applications of monitoring temporal changes of underground media based on seismic waves. We introduce traditional temporal variation monitoring methods like VP/VS ratio, shear wave splitting, coda Q value, and receiver functions, along with novel time-lapse seismic tomography. The new method focuses on repeated signals from active sources, repeat earthquakes, and ambient noise correlation, enhancing seismic velocity measurement accuracy via coda interferometry for underground medium monitoring. This paper also reviews key applications of seismic temporal changes monitoring, encompassing volcanic eruptions, earthquakes, landslides, industrial activities, slow earthquakes, core differential rotation, rainfall, as well as changes associated with environmental factors such as rainfall and groundwater levels. Lastly, future prospects for temporal variations of seismic velocity researches are anticipated in observation technology, data processing, and application domains.
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0. 引 言
地球介质一直处在动态变化过程中，监测这些变化特性有助于深化对地球内部结构及演化的认识. 发生在地表的变化可以采用直接测量的方式进行，如全球定位系统（GPS）和干涉合成孔径雷达（InSAR），能以高时空分辨率测量地表变形，但不能很好地约束扰动的深度（Amos et al., 2014; Bawden et al., 2001; Borsa et al., 2014）. 地下介质应力状态和物性的变化不易直接测量，而地震波对这些变化极为敏感（Silver et al., 2007），因此，监测地震波相关参数的变化是研究地下介质变化的有效手段.
地震波传播特征与岩石本身的物理属性密切相关. 多种参数可以用来评估岩石的特性，包括动态模量，如剪切、体积和杨氏模量、共振等（Ostrovsky and Johnson, 2001; Riviere et al., 2014）. 通过测量应力扰动下岩石弹性模量的变化（例如，地震波速度的变化），可以研究岩石的非线性应力敏感性，进而判断岩样的原位物理条件（弹性特性、损伤或围压等）（Johnson and Jia, 2005; Ostrovsky and Johnson, 2001; Riviere et al., 2014）. 研究表明，岩石特性对应力扰动的敏感性会随着围压降低或介质破裂程度增加进一步增强（Riviere et al., 2014）；而孔隙压力的增加往往会降低有效围压，使岩石更容易破坏或破裂，促使地壳内部的裂缝密度升高，从而增加对应力扰动的敏感性（Taira et al., 2018）.
基于实验室岩石研究的理论基础，结合地震波传播特性，多种地下介质变化监测手段得以发展，如研究地震波的衰减、地震波传播各向异性及地震波波速变化等. 不同的监测手段均发展出了多种研究方法. 现今已有地下介质结构及变化相关的综述研究：王宝善等（2016）、孙庆山和李乐（2018）分别从人工震源、重复地震的角度进行介绍；杨微等（2021）回顾了气枪震源探测研究进展；肖卓和高原（2015）则针对尾波干涉法展开论述. 本文在现有研究上更为系统地介绍了基于地震波研究地下介质时变的多种研究方法，随后对各方法的主要应用领域进行了介绍，最后讨论了当前的研究热点问题和未来可能的发展方向.
1. 利用地震波研究地下介质随时间变化的方法
地震学家提出多种方法研究地下介质结构随时间变化，基于不同研究方法测量原理，可以将其归为两大类：一类是利用非重复信号的传统方法，包括测量波速比、剪切波分裂、尾波Q值、接收函数以及时移成像；另一类是基于主动源、重复地震和背景噪声互相关等重复信号的测量方法.
1.1 传统方法
1.1.1 波速比
波速比（VP/VS）是日本地震学家Wadati和Oki（1933）提出的研究地下介质变化的地震学方法. 它利用台站记录的地震波资料，以和达法为基础，应用单台/多台记录的多次地震事件的纵波到时tP以及纵-横波到时差（tS − tP），再对此走时数据拟合分析得到波速比，即
$ {{{V_{\mathrm{P}}}} / {{V_{\mathrm{S}}}}} = {{\left( {{t_{\mathrm{S}}} - {t_{\mathrm{P}}}} \right)} / {{t_{\mathrm{P}}}}} + 1 $ ，进而得到该台站记录的多次地震发生时段内地震至台站间介质的平均波速比特征（傅征祥和程燕，1988）. 许多研究观察到地震前的波速比异常特征（冯德益, 1975; Whitcomb et al., 1973），但也有研究工作发现震前并未出现明显的波速比异常（Kanamori and Hadley, 1975; McGarr, 1974），他们认为这些异常信号可能只是震源的深度和震级差异引起的，与任何前兆物质性质变化无关（Lindh et al., 1978）.1.1.2 剪切波分裂
剪切波分裂是用来研究地下介质时变的重要方法. 当剪切波在各向异性介质中传播时，入射波分裂成两个以不同速度传播的波，即快波和慢波，而快波偏振方向和慢波延迟时间对地下介质各向异性的强度和应力场的变化敏感（Crampin, 1984; Crampin and Peacock, 2005; Gao and Crampin, 2004）. 常用的剪切波分裂分析方法主要有偏振分析法（Crampin, 1978）、相关函数分析法（高原和郑斯华，1994）.
偏振分析法是最早用于获得剪切波分裂参数快波偏振方向和慢波延迟时间的方法. 它通过分析单个地震事件在两个水平分量的剪切波质点振动图来确定快、慢波的到时，进而得到快、慢波到时差. 该到时差反映了震源到台站整个射线路径下慢剪切波相对于快剪切波的到时差（Crampin, 1978）.
相关函数分析法即通过相关分析判断经过重新投影而分解的两个波列是否为剪切波分裂而产生的快波和慢波（高原和郑斯华，1994）. 它分别计算不同方位上不同时间延迟的两个水平方向波列（重投影产生）的相关函数，假设快波偏振方向与正北方向的夹角为α，慢波相对于快波的时间延迟为τ，随后计算每个α上不同τ的快慢波间的相关函数，其最大值对应的α和τ即为所求的快波偏振方向和慢波时间延迟（高原和郑斯华，1994）.
剪切波分裂的变化已被用于监测地震相关的应力积累与释放过程（Crampin, 1994; Gao and Crampin, 2004）. 而地震学家对于地震相关的剪切波分裂时间延迟变化的原因也存在分歧，慢剪切波时间延迟变化可能是由于地震活动性的变化引起的射线传播路径的空间变化，而不是各向异性介质的性质随时间的变化（Peng and Ben-Zion, 2005）.
1.1.3 尾波Q值
Aki和Chouet（1975）在单次散射的假设下提出了尾波Q值的概念，发现尾波Q值与构造活动性强度相关. Sato（1977）对其计算方法进行了修正，提出了更普遍的适用于源台分离情况下的Qc值计算方法. 根据Sato模型，在一定的频率下尾波振幅可以表示为：
$$ F\left( t \right) = {\log _{10}}{\left[ {\frac{{{A_{\mathrm{C}}}\left( t \right)}}{{{A_{\mathrm{S}}}}}} \right]^2}{K^{ - 1}}\left( a \right) = C\left( f \right) - b\left( {t - {t_{\mathrm{S}}}} \right) $$ (1) 式中，AS为S波最大振幅，AC(t) 为流逝时间t附近尾波均方根振幅，K为依赖于时间的传播因子，C(f)为与频率有关的影响因子. 在相同地震、相同频率下，C(f)为常数，随后拟合F(t)与 t − tS 间的线性关系即可获得b值，再利用b与Qc间的关系
$ b = 2 \text{π} f\lg {e / {{Q_{\mathrm{c}}}}} $ 即可得到该频率对应的Qc值.尾波Q值被广泛应用于不同区域的研究工作，许多研究观察到与地震相关的尾波Q值的异常变化（Jin and Aki, 1986; Peng et al., 1987）. 进一步的研究发现，尾波Q−1也与地震活动性相关（马宏生等, 2005; Sato, 1986）. 地震活动使地下介质改变（如裂隙的张开/闭合、流体的渗入等），导致地震波的衰减程度变化，进而影响尾波Q值，但对于不同区域，震前尾波Q值变化存在差异（啜永清等, 2004; 荣代潞等, 2006; Sato, 1988）.
1.1.4 接收函数
接收函数（RF）方法是目前研究地球内部圈层精细结构的最有效和较常用方法之一，它主要利用远震波入射到台站下方界面上产生的Ps或Sp转换波来探测台站下方间断面形态. 该方法能有效提取地球圈层界面结构，具有良好的垂向分辨率（Kind et al., 1996）. Audet（2010）最早利用接收函数研究地下介质时间变化. 在接收函数处理之前，先将地震记录旋转到P、SV（径向）和SH（横向）波分量（Bostock, 1998），再采用P波波形作为震源时间函数，对SV和SH分量进行反卷积，从而形成P波接收函数（PRF）. 现阶段使用的反卷积方法包括迭代时域反卷积（Ligorría and Ammon, 1999）、频域阻尼维纳反卷积（Audet, 2010）. 对获取的RF进行进一步的分析可获取台站下方介质结构时间变化特性. 例如，Audet（2010）对Parkfield邻近区域每个未滤波的RF计算功率谱密度（PSD），观察到PSD强度在2004年Parkfield地震后显著降低. Porritt和Yoshioka（2017）利用P波接收函数方法对日本东北地区进行了分析，发现研究区基于PRF的PSD水平无显著变化，但观察到PRF波形随时间的显著变化，并推断这种变化主要是由于大地震后火山区域的流体迁移和剪应力/强度重组. 同时，地震学家也采用了多种方法相结合的手段来研究浅地表地下介质的变化，分析表明地下水位的激增伴随着接收函数功率谱和背景噪声自相关的变化，且地下水位的变化对P波速度影响比S波更大（Kim and Lekic, 2019）.
1.1.5 时移成像
地震层析成像是研究地下结构最重要的手段之一. 通过采用对同一地区不同时间段反演获得的速度模型相减的方式，可以获得地下结构速度的时间变化特征（Chiarabba et al., 2009）. 然而，由于地震射线分布的变化及反演计算中的随机误差的存在，这种变化结果的可靠性不高（Julian and Foulger, 2010）. 传统的时移层析成像的方法通过最小化模型差异和不同时段的到时差来同时反演多个数据集，这在一定程度上受到不同时间段数据分布不均匀的影响（Julian and Foulger, 2010）. Qian等（2018）提出了基于双差层析成像（Zhang and Thurber, 2003）的时移层析成像方法. 它首先基于双差层析成像方法使用第一个时间段的到时数据来反演速度模型，然后构建第二个时间段相对于第一个时间段的到时差，再利用前面所获得的速度模型来反演到时差对应的速度变化. 基于这一方法，曹颖等（2021）使用云南地震区域台网所记录到的P波绝对到时及相对到时数据，在震源区观察到2014年鲁甸MS6.5地震相关的同震及震后P波速度变化. Pei等（2019）提出了上地壳脆性层四维成像新方法，并应用于龙门山断裂带研究，揭示了断裂带在大地震中的同震变化和震后恢复的演化过程.
1.2 基于重复信号的方法
1.2.1 三类重复信号
监测地震波速度的变化是现今颇为可靠的研究地下介质时变性质的方法. 地震波的速度取决于地下介质的物理特性，可以使用地震波速度的重复测量来推测物理属性和应力状态变化. 这些几乎相同的地震波形通常来自于重复的地震（Poupinet et al., 1984）、人工震源（Yamamura et al., 2003）或背景噪声互相关波形（Brenguier et al., 2008a）. 这三种方法下重复信号的提取方式略有差别，但测量时变时的方法近乎一致. 利用非重复信号进行地下介质时变研究的可用数据量较多、且监测方法多样，它可以提供多个物理参数下的介质属性；基于重复信号的地下介质时变监测对数据质量要求更高，导致可用数据量偏少，但因为使用了高度相似的地震波形，获得的时变结果可靠性和精确性大大提升.
重复地震发生在地下介质的相同位置，且地震波传播路径相同，因而相同台站记录到的地震信号具有高度相似性（Nadeau et al., 1995）. 通过对原始地震资料中记录的地震事件进行扫描截取，随后对截取的地震波形计算相关系数，再设定较高的相关系数阈值（如0.8以上），即可以获得初步认定的重复地震簇，早期研究工作大多是在初步的重复地震基础上研究分析，而仅仅依靠波形相似度是不足以判断这一系列事件是否为重复地震，因此可以对检测到的相似地震簇进行相对位置检测约束，进而确定更为准确的重复地震（Schaff and Beroza, 2004; Waldhauser and Ellsworth, 2000）.
人工震源激发的信号高度可控，其发震时刻精确已知，可以产生更确切的重复信号（Poupinet et al., 1984; Snieder et al., 2002）. 为提取人工震源产生的重复信号，我们同样在原始地震资料中截取人工震源激发产生的信号. 由于人工震源的高度重复性，往往对同一台站在一定的时间区间内记录的震源信号进行叠加，以获取更为稳定的重复的人工地震信号（Silver et al., 2007; Wang et al., 2020）.
若噪声源分布稳定且持续，同时台站位置固定，且基于背景噪声的互相关波形与格林函数近似（Shapiro and Campillo, 2004），因而可获得连续、稳定的重复信号. 为了获取重复的背景噪声互相关波形，首先对获得的原始地震资料进行预处理（Liu et al., 2014），进而获得背景噪声记录，随后对其计算互相关，即可获得重复的背景噪声互相关波形，再对一定时间内的互相关波形进行叠加以获取更为稳健的波形记录.
1.2.2 基于重复信号的波速时变测量方法
早期进行波速时变监测使用重复信号的直达波部分（Reasenberg and Aki, 1974; Vidale and Li, 2003），但难以获得可靠的结果. 进一步研究发现，地震尾波也包含地下介质的信息，且相比直达波对波速变化更为敏感.
基于尾波的地震波速变化监测方法称为尾波干涉法. 它最早由Poupinet等（1984）提出，通过测量地震对波形间的相移来监测波速变化. Snieder等（2002）后来提出了类似的概念，利用不同的走时移动窗口来测量时间变化，再通过线性拟合来评估相对地震波速度变化. 该方法假设地下介质变化是均匀的，则相对走时变化（dt/t）与相对波速变化（dv/v）相反，即
$ {{{\mathrm{d}}v} / v} = - {{{\mathrm{d}}t} / t} $ .基于尾波的走时变化测量方法主要有五种：移动窗互相关法（WCC）、压缩拉伸法（TS）、动态时间扭曲（DTW）、移动窗互谱法（MWCS）、小波互谱法（WCS）.
移动窗互相关法是尾波干涉测量中的常用方法（Grêt et al., 2006; Mikesell et al., 2015; Snieder, 2006）. 依据尾波干涉法，两个时间序列之间的互相关函数的最大值发生在走时偏移dt处，该走时偏移dt使两个时间序列之间的相似度最大化. 因此，WCC通过对波形中的滑动窗口在不同流逝时间t处测量走时偏移dt，随后利用线性拟合测量相对走时偏移dt/t，进而获得dv/v.
压缩拉伸法依赖于走时偏移dt随流逝时间线性增加的假设. 该方法通过沿着流逝时间轴线性拉伸一个波形，从而使其与参考波形的相关性最大化，其最大相关系数对应的拉伸系数ɛ即为速度变化值，即
$ \varepsilon = - {{{\mathrm{d}}t} / t} = {{{\mathrm{d}}v} / v} $ （Wegler and Sens-Schönfelder, 2007）.Mikesell等（2015）引入了用于尾波干涉测量的DTW. 它遵循类似于TS的概念，但不是采用恒定的拉伸因子，而是允许在每个流逝时间处使用可变拉伸因子，然后通过最短的弯曲路径找到走时偏移dt.
MWCS最初是由Poupinet等（1984）提出的，用于测量一对重复地震波形的速度扰动. 该方法在理论上是将WCC扩展到频域. 它测量特定频带下的时移，与WCC相比，每个走时偏移都是在频域而不是时域计算的，因而可以改进频率分辨率.
一般认为，不同频带的波速变化对应不同的变化深度的范围. 由于傅里叶变换的时频分辨率低，Mao等（2019）提出了一种基于小波互谱分析（MCS）的新方法，即连续小波变换. MCS是一个混合时频场，其相位
$ \varphi \left( {f,t} \right) $ 取决于频率f和相位滞后t，即走时偏移$ {\mathrm{d}}t\left( {f,t} \right) = {{\varphi \left( {f,t} \right)} / {\left( {2 \text{π} f} \right)}} $ . 与其它方法类似，通过$ {{ - {\mathrm{d}}t\left( {f,t} \right)} / t} $ 的线性拟合得到频率相关的速度变化测量$ {{{\mathrm{d}}v} / v}\left( f \right) $ . 该方法提供了最佳的时频联合分辨率与全流逝时间测量，具有强大的多频带计算优势，可实现对变化深度的分析.不同的方法各具特色，TS和DTW方法计算便捷，计算参数相对简单，但会污染噪声源的频率谱，且受季节性变化影响较大，容易掩盖地下介质真实响应；移动窗方法参数繁多，但计算结果误差相对更小，对于变化的深度可以提供更好的约束，同时可以更好地避免钟差的影响；MCS则较好地结合了两者的优势，计算参数相对简化，计算速度更为便捷，易于区分不同频率的变化.
2. 基于地震波的地下介质时变的应用研究
利用地震波研究地下介质变化已经取得了大量的研究成果，在近二十年内，利用重复信号的地震波速度变化研究倍受关注. 依据地下介质时间变化的物理机制，可以将变化分为“突变”和“长期变化”. 典型的“突变”包括火山喷发、地震、滑坡、工业活动等，常见的“长期变化”则包含慢地震、内核差速旋转、地下水及其它环境因素等. 两种变化类型往往并存于不同场景之下，例如在研究火山喷发或者中/大地震时，在特定的时间（喷发期、同震阶段）可以观察到显著的“突变”，而在其它时间（平静期、无震期）可以观察到“长期变化”. 为了避免重复，我们对火山喷发、地震、滑坡、工业活动仅介绍“突变”相关研究，其它场景则介绍“长期变化”的应用研究.
2.1 与火山喷发相关的地下介质时变研究
几十年来，科学家们一直在寻找提高火山喷发预测准确性和可靠性的方法. 他们利用来自不同学科的大量技术进行了研究分析. 例如，卫星技术（Mania et al., 2019; Massonnet et al., 1995）或倾斜仪（Fontaine et al., 2014; Peltier et al., 2005）可以用来探测火山膨胀引起的地形变化. 在许多情况下，地震活动性的增加也发生在火山爆发之前（Chouet, 1996; Soubestre et al., 2021）. 然而，不同火山的各种前兆的特征不同，甚至可能根本不存在（Biggs et al., 2014; Chaussard et al., 2013; Ebmeier et al., 2013），这就突显了探索其它类型前兆的必要性（Brenguier et al., 2008b, 2016）.
2.1.1 基于地震波速变化研究
受限于获取重复信号的源的性质，基于主动源和重复地震直接研究火山喷发相关的波速变化工作相对较少. Maeda等（2015）利用主动源研究日本Sakurajima火山结构变化，观察到喷发期格林函数的时间变化；Hirose等（2017）则同时采用尾波干涉法与地震干涉法对该地区进行了研究，发现两种方法观测结果基本一致. 噪声互相关比主动源更经济，比重复地震更为连续，倍受地震学者喜爱. 基于噪声互相关的最经典和最具代表性的例子之一是Piton de la Fournaise火山观测到的喷发前的前兆地震速度下降（~0.05%，图1a）（Brenguier et al., 2008b），Takano等（2020）也将噪声互相关的直达波应用于Piton de la Fournaise火山监测研究，发现速度变化可能是浅层岩浆储层膨胀的结果. 类似的火山过程相关观测不断涌现，如火山喷发（Mordret et al., 2010; Obermann et al., 2013; Olivier et al., 2019）、火山形变（Takano et al., 2017）、火山口崩塌（Wu et al., 2020）、火山震颤（Donaldson et al., 2017）、岩浆扰动与运移（Hirose et al., 2017; Nishida et al., 2020），揭示了速度变化与火山系统的扩张或压缩密切相关性. 然而，不均匀的空间应力分布可能导致同一火山活动的地震速度响应相反，如Liu等（2019）对Kilauea火山区收集的噪声资料采用压缩拉伸法进行了分析，结果表明在2018年喷发之前存在两个阶段的波速变化特征（先增加，后降低），分别对应岩浆的上涌阶段和岩浆的注入阶段. Hotovec-Ellis等（2022）则利用重复地震研究了与此次喷发活动相关的火山口崩塌事件，发现在每次崩塌事件后地震速度突然增加后缓慢下降. 然而，火山活动导致的变化往往也会受环境因素削弱甚至覆盖，如2014年Piton de la Fournaise火山喷发的前兆信号因受降雨的影响并不显著（Rivet et al., 2015），因而分离这些因素的影响将有助于更好地识别地下介质真实的变化，下文将对环境因素进行更为细致的说明.
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图 1 （a）Piton de la Fournaise火山喷发前地震波速的降低及地震能量的时间变化，地震能量是通过记录到的连续地震信号的日平均均方根（RMS）值计算得到，阴影区域表示喷发期（引自Brenguier et al., 2008b）；（b）新西兰Ruapehu火山在1995—1996年的一次喷发前后地震各向异性快波方向变化，白色箭头表示区域应力场方向，黑色箭头表示局部应力场方向（引自Gerst and Savage, 2004）Figure 1. (a) Reduction of seismic velocity and temporal change of seismic energy before the eruption of Piton de la Fournaise volcano. Seismic energy is calculated from the daily average root-mean-square (RMS) value of the recorded continuous seismic signals, and shadow areas represent the eruption period (from Brenguier et al., 2008b). (b) The fast anisotropic direction changed before and after an eruption in 1995-1996 at Ruapehu volcano, New Zealand. The white arrows indicate the direction of the regional stress field, and the black arrows indicate the direction of the local stress field (from Gerst and Savage, 2004)2.1.2 基于各向异性变化研究
研究地震各向异性也是火山前兆性研究的重要参数，图1b展示了新西兰Ruapehu火山在1995—1996年的一次喷发前后地震各向异性快波方向显著变化特征（Gerst and Savage, 2004）. 目前，许多研究观测到与火山活动相关的各向异性的变化（Savage et al., 2010, 2015），他们将这种变化归因于裂缝的空间分布和方向因喷发前应力场的作用而改变. Illsley-Kemp等（2018）对2009年10月至2010年10月期间Dabbahu裂谷段的地壳地震各向异性进行了详细的研究，观察到岩脉侵入前的地震各向异性的变化，并提出地震各向异性可用于监测岩浆通道系统变形过程. 最近，Mengesha等（2024）采用剪切波分裂来研究2018年至2020年期间Whakaari/White 火山各向异性的变化，结果表明这种变化可能源于各向异性随时间的变化而不是地震路径在空间上的变化，并将其解释为由应力或流体含量的变化引起的裂缝排列的变化.
2.1.3 基于地震衰减变化研究
在火山区也有地震衰减变化的研究（Titzschkau et al., 2010）. 例如，Caudron等（2019） 利用活动火山口附近记录的地震信号研究Kawah Ijen（印度尼西亚）、Ruapehu和Tongariro（新西兰）火山活动，发现在喷发之前地震衰减显著增加，并表示可以利用地震衰减预测无前兆的气体驱动的火山爆发. Ardid等（2022）对此再次分析，提出了热液封闭的形成使得浅层地下水快速加压的机制解释，并将这一模型成功应用于2019 年Whakaari喷发的前兆分析. 最近，Caudron等（2021）利用背景噪声和基于震颤的方法对Whakaari/White 岛火山进行了回顾性研究，其多参数（地震衰减、相对地震速度、去相干等）分析结果揭示了火山活动不同时期（平静期、增压期、喷发期）的特征.
2.2 与地震相关的地下介质时变研究
2.2.1 基于地震波速变化研究
研究地壳对大地震的力学反应可以为我们提供对深部应力积累和释放过程的独特见解（Bürgmann and Dresen, 2008）. 地震破裂过程和大地震引起的强烈震动对地球浅层地壳内的局部地震速度产生永久和短暂的影响. 在圣安德烈斯断裂带的基于噪声互相关的经典研究表明（Brenguier et al., 2008a; 图2），观测到的地震速度变化（−0.08%）应来自于浅层同震损伤和断裂带内深部同震应力改变和震后应力松弛. 基于重复地震的观测结果表明这种变化与频率密切相关，同震波速降主要集中在浅部介质（Sheng et al., 2021）. Okubo等（2024）监测了2002年至2022年Parkfield地区的速度变化，以调查整个地震期间圣安德烈斯Parkfield地区附近断层物理状态的时间变化. 在大多数情况下，地震速度在地震过程中下降，并随着时间的推移逐渐恢复（安艳茹等, 2023; Brenguier et al., 2008a; Hong et al., 2017; Illien et al., 2023; Liu et al., 2014, 2018; Meng et al., 2024; Poli et al., 2020; Sawazaki et al., 2009; 王俊等, 2020; Wang et al., 2019; 温扬茂等, 2019），导致地震速度变化的机制可能是由于强震引起的动态应力/应变变化（Brenguier et al., 2008a, 2014; Minato et al., 2012; Schaff and Beroza, 2004; Wang and Shearer, 2019）、静态应变变化（Wang and Shearer, 2019）和增压流体（Brenguier et al., 2014; Nimiya et al., 2017）. 这种非线性弹性行为，在实验和数值上都得到了解释（Johnson and Sutin, 2005; Lyakhovsky et al., 1997; Sens-Schönfelder et al., 2019）. 在最近的研究中，Boschelli等（2021）利用地震背景噪声数据的高频自相关，研究了与2019年Ridgecrest地震序列相关的地震速度变化，发现地震速度变化很大程度上是由浅层地壳物性的改变导致. Çubuk-Sabuncu等（2024）则首次将地震波速变化与地壳形变、地震活动性及同震体积应力变化联合分析，同时对比了小波变换和压缩拉伸法的观测结果，发现两种方法下的波速测量结果基本相同，不同频带下波速变化差异显著，分析表明与强震动相关的破坏可能是同震波速降低的主要原因. 相比之下，采用人工震源实验，可以以更好的分辨率识别同震速度变化（Ikuta et al., 2002; Tsuji et al., 2018; Yang et al., 2014），以及尾波特性的时间变化（Nishimura et al., 2000; Wegler et al., 2006），但大大受限于研究经费. 由于基于重复地震监测地球的时间变化受到不规则时间采样的限制，近些年利用重复地震的地震相关研究工作相对较少. 这些研究也观察到与地震相关的同震（Sheng et al., 2021; Zhou et al., 2023）及震后变化（Li et al., 2017）. Merrill等（2023）联合重复地震和背景噪声方法研究Haida Gwaii MW7.8地震，基于重复地震的S波速度在地震后下降量高达0.16%，基于背景噪声的速度下降0.26%～0.39%，他们将其解释为变化发生在最上层的地壳中，因而更为显著.
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图 2 加利福尼亚州帕克菲尔德地区地震波速变化、地表位移及地震活动性. 曲线表示由GPS站测量的沿圣安德烈斯断层的地震后断层平行位移（引自Brenguier et al., 2008a）Figure 2. Seismic velocity variations, surface displacements, and tremor activity near Parkfield, California. The curve represents post-seismic fault-parallel displacements along the San Andres Fault measured by GPS stations (from Brenguier et al., 2008a)2.2.2 基于地震衰减变化研究
先前的研究报道了与大/中地震相关的地震衰减特性的变化（Chun et al., 2004; Hirose et al., 2020; Kelly et al., 2013; 李发等, 2013; Obermann et al., 2014; Sato, 1986）. Yamamura等（2003）使用压电器产生恒定振幅的地震信号，以揭示与固体潮相关的衰减的周期性变化. 尽管使用了高分辨率的震源，但在实验过程中没有发生显著的地震，没有检测到与同震相关的衰减变化. 陈海潮等（2012）利用电动落锤进行的震源实验探测到与大气压相关的衰减变化，并同时观测到汶川地震后强余震相关的衰减变化. Tsuji等（2022）发展了一种检测由精确控制的人工震源激发的地震波传播过程中的衰减变化的方法，并将其应用于监测2000年至2001年在日本Awaji岛实验中获得的数据集的时间变化，观察到同震振幅降低，结合各向异性特征，发现速度降低沿主轴方向的减小更大.
2.2.3 基于地震各向异性变化研究
地震各向异性是观测断裂带局部应力场及其时间演化的有效工具，是地震波以不同的速度传播的一种现象. 地震速度随方向的变化可能是由于岩石固有特性（Johnston and Christensen, 1995）或应力引起（Boness and Zoback, 2004; Hung et al., 2009; Zatsepin and Crampin, 1997）. 基于剪切波分裂，许多研究工作中观察到了与同震（Ikuta and Yamaoka, 2004; Nakata and Snieder, 2012; Peng and Ben-Zion, 2005; Sawazaki et al., 2018; Takagi and Okada, 2012）以及与震后愈合（Hung et al., 2022; Kaproth and Marone, 2014）相关的地震各向异性的变化. Durand等（2011）利用台站间的地震背景噪声互相关研究2004年9月28日MW6.0 Parkfield地震前后面波极化特征，结果表明面波极化对裂纹分布方向的变化非常敏感. Saadé等（2017）利用被动成像干涉法研究了2008年6月13日日本Iwate-Miyagi地震前后面波极化的时间变化，发现其在地震前一个半月剧烈变化，可能与裂纹方向的分布变化有关.
2.3 与滑坡相关的地下介质时变监测研究
滑坡灾害遍布全球，属于发生频次最高、造成损失最严重的自然灾害之一，因此对滑坡实现前兆性动态监测意义显著. 目前已有多个研究监测到与滑坡相关的前兆信号，例如，基于微震检测发现与滑坡滑移速率相关的微震率的变化（Amitrano et al., 2007; Tonnellier et al., 2013; Walter et al., 2013）；使用背景噪声互相关方法对长期监测数据进行分析，发现在滑坡事件前几小时或几天就有明确的预测信号（Larose et al., 2015），如地震波速度降低（Mainsant et al., 2012a）、互相关波形相关系数的降低（Fiolleau et al., 2020; 图3），并将这一前兆信号解释为孔隙饱和度的增加导致黏土中剪切波速度下降. 这种机制在理论上也得到了证明（Carrière et al., 2018; Dong and Lu, 2016; Mainsant et al., 2012b, 2015）. 然而，采用相同的方法，部分研究区并未观察到类似的前兆现象（Bontemps et al., 2020; Voisin et al., 2016）.
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图 3 HAR0-HAR1台站对每天互相关分析. （a）在1～12 Hz的瑞利波速度变化；（b）互相关系数（CC）变化；（c）累计降雨量（蓝色）和空气温度变化（红色）（引自Fiolleau et al., 2020）Figure 3. Daily cross-correlation analysis for HAR0-HAR1 stations. (a) Rayleigh wave velocity changes between 1 and 12 Hz; (b) Cross-correlation (CC) coefficient changes; (c) Cumulative rainfall (blue) and air temperature changes (red) (from Fiolleau et al., 2020)2.4 与工业活动相关的地下介质时变研究
随着人类生产力的发展，许多生产活动都会对地下介质产生短期或长期的影响. 例如，矿山活动（Olivier et al., 2015）和地热田流体注入（Hillers et al., 2015a; Obermann et al., 2015）导致的地震波形中速度和退相干的变化或者地震活动性的变化（Li et al., 2023）；油气田生产相关的裂缝连通性的变化致使剪切波分裂极化的时间变化（Baird et al., 2013; Teanby et al., 2004; Zuo et al., 2018）；在与二氧化碳注入相关的地质二氧化碳存储试验场中检测到初至P波到时的地震衰减的变化（Zhu et al., 2017）. 这些工作验证了在小规模应用中基于地震波方法跟踪内部变形和压力状态的潜力，例如在水坝和水库中，监测小型水库应力状态的演变对防灾减灾具有重要意义. Planès等（2016）和Olivier等（2017）成功地观察到由于地下水位和介质孔隙度的变化导致大坝应力场的变化，进而导致地震波速度的变化.
2.5 与慢地震相关的地下介质时变研究
研究表明，从俯冲板块向上覆大陆板块（上板块）的流体供应可能引发地壳和地幔楔的地震（Halpaap et al., 2019; Nakajima and Hasegawa, 2016）. 此外，在某些俯冲带也观察到上板块的构造变化. 例如，在Hikurangi俯冲带北部浅层慢滑移事件（SSE）发生后，上板块地震活动增加（Shaddox and Schwartz, 2019），这与上板块地震速度和各向异性的变化是同步的（Wang et al., 2022; Zal et al., 2020）；在Cascadia俯冲带前弧则观测到ETS事件前后均出现RF变化（Gosselin et al., 2020）. 解释地震活动性增强与上板块构造变化耦合过程的一个可能原因是：由于沿板块界面的不透水的密封状态被破坏而产生的SSE排水（Wang et al., 2022）. Nakajima和Uchida（2018）报告了上板地震活动性与日本关东地区俯冲菲律宾海板块界面沿线重复地震活动之间的长期时空相关性，研究了上板P波和S波衰减相关的时间变化，结果表明，在大约一年的时间间隔内，板块界面的排水会反复发生，以响应SSE（Ito and Nakajima, 2023; Nakajima and Uchida, 2018）. Ito和Nakajima（2024）利用剪切波分裂对日本Kanto地区S波极化各向异性分析表明，延迟时间在SSE之后增强，板块界面上方的平均裂缝密度增加，但平均裂缝半径随时间变化很小. 最近Sheng等（2022）进行的一项研究利用地震波速度变化测量监测到未识别的慢滑移事件相关的变化（图4），而该变化因超出了大地测量方法的检测阈值，而未被大地测量方法识别到.
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图 4 （a）互相关波形随时间变化图. 颜色深浅表示相对于长时平均测量的走时dt；（b）研究时段内的dt测量值及小波相干性. 黑色虚线表示线性回归（引自Sheng et al., 2022）Figure 4. (a) Cross-correlation waveform versus time. Color shades represent travel time dt measurements relative to long-term average. (b) The dt measurements and the coherence of wavelet during the study period. The black dashed lines represent linear regression (from Sheng et al., 2022)2.6 可能的内核差速旋转相关的介质时变研究
来自核爆或者地震对的重复地震波形的变化已经证实了地球内核随时间变化的存在（Song and Richards, 1996; Vidale et al., 2000; Yang and Song, 2020a; Zhang et al., 2005）. 这种时间变化存在两种解释：内核的差速旋转、内核边界的局部生长或熔融. 内核差速旋转认为这种时间变化源自内核的内部（Wang and Vidale, 2022; Yang and Song, 2020b），并进一步估计了内核差速旋转速率（Yang and Song, 2022）. 最近，Yang和Song（2023）分析了20世纪90年代初的重复地震波形，发现所有之前显示出显著时间变化的路径在过去十年中几乎没有变化，并表明内核的旋转在这段时间内暂停了. Wang等（2024）表明内核从2003年到2008年逐渐超速旋转，然后从2008年到2023年以同样的路径缓慢两到三倍地旋转（图5）. 内核的生长或熔融则认为内核因生长或者熔融导致了其表面的非均匀性变化，进而导致介质时变的存在（Wen, 2006）. 在同一研究下获得的相矛盾的旋转速率在一定程度上反对了差速旋转的解释（Mäkinen and Deuss, 2011）. Yao等（2019）通过分析南 Sandwich群岛和中美洲俯冲带重复地震时间变化的能量、旋转速率的差异及数值否定了差速旋转的解释，认为观测到的内核相位的时间变化是由内核表面局部区域的时间变化引起的. 两种解释均有着相应的研究分析来论证，但确切的解释机制依旧存在争论.
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图 5 两组重复地震波形的比较. （a）表示在2003年、2009年以及2020年的一组重复地震波形；（b）表示在2002年、2009年以及2022年的一组重复地震波形（引自Wang et al., 2024）Figure 5. Comparison of two sets of repetitive seismic waveforms. (a) Represents a set of repeated seismic waveforms in 2003, 2009 and 2020; (b) Represents a set of repeated seismic waveforms in 2002, 2009 and 2022 (from Wang et al., 2024)2.7 与降雨和地下水相关的地下介质时变研究
与地下水和降雨相关的地下介质波速变化研究是近年来研究的热点. 许多研究观察到与其相关的变化，表明了水文效应对地震波速的重要性（Clements and Denolle, 2023; Hillers et al., 2014; Lecocq et al., 2017; Meier et al., 2010; Poli et al., 2020; Sens-Schönfelder and Wegler, 2006; Tsai, 2011; Wang et al., 2017），当降雨增加时，雨水的渗透在地壳顶部数公里处产生延迟的孔隙压力增强，导致有效应力减小，从而导致地震波速度的降低. 同时，与日降水峰值相比，水力扩散相关的速度变化略有延迟，如Luan等（2023）利用气枪震源研究中国西南宾川介质变化，发现长期的延迟变化与水库水位相关. 最近，Mao等（2022）利用地震干涉测量技术计算美国加州地区地震波速变化的时空特征，地震速度变化与井的地下水位和卫星遥感测量的地表变形相匹配（图6），长期地震波速变化的时空特征揭示了盆地中地下水储存的独特模式（下降或恢复）. 此研究弥补了地震学和水文学之间的差距，并展示了利用全球地震仪提供地下水和其他近地表参数的四维特征的前景. Fokker等（2021）提供了一种利用面波相速度变化监测孔隙压力的物理模型，分析表明孔隙压力的变化可以解释测量到的相速度相位和幅度变化. 之后，他们推导出孔隙压力敏感核，将面波速度随频率的变化与孔隙压力变化随深度的变化联系起来（Fokker et al., 2023）.
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图 6 相对波速变化、降雨量、水头时间序列. （a）波速变化与累积年降雨量对比；（b）波速变化与水力水头对比（引自Mao et al., 2022）Figure 6. Time series of relative seismic velocity changes, precipitation, and hydraulic head. (a) Comparison of seismic velocity changes with cumulative annual precipitation; (b) Comparison of seismic velocity changes with hydraulic head (from Mao et al., 2022)2.8 与其它环境因素相关的地下介质时变研究
除了与构造和火山有关的地震速度变化外，环境扰动对地下介质也起着重要作用. 研究与这些环境扰动相关的瞬态变化，有助于区分与构造相关的变形，并促进理解地壳在不同外力驱动机制下的行为. 大量研究监测到浅层结构的环境变化（Clements and Denolle, 2018; Illien et al., 2022; Lecocq et al., 2017; Mao et al., 2022; Richter et al., 2014; Sens-Schönfelder and Wegler, 2006; Wang et al., 2017）.
在浅层，热弹性应力以年为周期改变地震波的速度（Lecocq et al., 2017; Meier et al., 2010; Richter et al., 2014），大气压强（Silver et al., 2007）也是如此. 潮汐效应（Hillers et al., 2015b; Mao et al., 2019; Sens-Schönfelder and Eulenfeld, 2019; Takano et al., 2014, 2023; Wang et al., 2020; Yamamura et al., 2003）以及永久冻土冻结和融化（James et al., 2017）也可以对地震波速度变化产生相当大的影响. 此外，降雪、降雨和海面高度变化均可引起直接的弹性加载效应（Donaldson et al., 2019; Wang et al., 2017）. 部分地区则能观测到浅层地壳日变特征（Li and Ben-Zion, 2023）.
2.9 信号源性质对地下介质时变监测的影响
随着研究的日渐深入，研究发现监测到的变化并不一定完全归因于地下介质的真实变化，它也可以由其它因素产生，比如信号源的变化. 信号源的变化会从根本上引入监测到的变化，因而在分析研究中讨论信号源的变化与否是必要的. 针对信号源的变化的研究此前较少（谢晓峰等, 2014; Zeng and Ni, 2010），但有研究人员在探讨地下介质变化的机制时讨论了源的变化（如, Hillers et al., 2015b; Withers et al., 1996）. 近年气枪震源的发展提供了很好的研究机会. Liu等（2021）在云南宾川地区水库区域的研究发现基于气枪震源的走时变化模式与来自背景噪声数据的不同，深入分析表明水库水位的变化导致了气枪震源的主频发生变化进而引起走时的变化，即这部分差异源自震源信号的变化而并非地下介质的变化，Luan等（2023）的研究再次印证了这一结论. 因此在分析时有必要对信号源的特性进行一定的分析来避免出现地下介质“伪”变化.
3. 基于地震波的地下介质时变研究展望
基于地震波方法的地下介质时变研究方法多样，但依旧存在许多不足之处. 近些年利用重复信号的监测方法发展迅速（如DAS、气枪、瓦斯震源等），新的震源信号提供了更稳定、更便捷的重复信号；同时，现阶段的研究方法在时间分辨率上提高显著，但在空间分辨率上发展缓慢；人工智能的发展使大数据处理成为可能，如何有效地利用人工智能推进介质时变监测自动化、智能化意义显著；再者，目前对地下介质时变实时监测方面略有不足，在滑坡监测上取得了一定的成效（如，谢凡等，2020），在更多的场景下的应用则有待开发. 地下介质时变机理复杂多样，如何更有效地区分和甄别依旧存在挑战性；多种研究结果表明了单一的物理属性很难对地下的复杂系统进行准确的研究分析，因此多领域方法的结合潜力巨大；现阶段跨行星的研究也逐步开展，如何将地球上的研究方法应用于其它行星天体也是丞待解决的问题. 基于上述分析，对地震波的地下介质时变研究做出以下展望.
3.1 发展新的观测技术
近年来，分布式声学传感（DAS）技术已经出现，可以将通信光纤电缆转换为具有成本效益的密集地震阵列，并已成功应用于近地表地震监测（Dou et al., 2017），其对断裂带区域速度时变监测方面展现了良好的潜力. 气枪震源的高度可控、可重复性在水库区的研究中取得了良好的应用，观测到显著的环境因素相关的变化（Liu et al., 2021）. 气爆震源相比炸药震源更环保、更安全，在城市区域更为适用（徐善辉等，2021）. Sheng等（2022）则利用列车产生的信号监测地震波速变化，提取了稳定、高频的体波，识别到与以前未记录到的慢滑移事件相关的速度变化. 随着科技的发展，人为干扰影响程度愈发深入，尤其在城市地区，传统的信号源难以恢复良好的格林函数，DAS、气枪震源、列车信号等新的观测技术将大为丰富地下介质时变监测手段，多信号源的联合使用，可以有效地相互补充，并扩大可监测区域的范围和连续性.
3.2 开展高时空分辨率监测
现阶段的地下介质时变监测往往获得的是研究区的一个平均的变化，实现空间上变化位置的定位也是一个丞待解决的问题. 在波速时变方面，目前基于尾波监测的二维或三维成像通常采用线性插值或反演，而尾波灵敏度核通常是在具有均匀能量速度和传输平均自由程的各向同性散射假设下计算的（Margerin et al., 2016; Mayor et al., 2014）. Obermann等（2019）的研究表明，体波和面波的灵敏度核的线性组合可以有效地约束三维多重散射介质中的变化深度.
利用相似的灵敏度核，我们可以在空间中定位测量到的走时扰动，并更准确地解释变形的起源. 然而，由于传播路径的复杂性，我们目前还没有一个精确的灵敏度核可以准确地表征尾波的传播特征，从而精确地定位测量到的变化. 因此，对二维和三维尾波灵敏度核的进一步研究势在必行. 利用直达波监测，空间定位变得相对简单，但其时间分辨率和速度变化的稳定性均低于尾波. 因此，了解如何提高直达波监测的信噪比将变得至关重要.
在时间分辨率方面，根据格林函数在不同频率下的收敛速度，目前噪声监测的最小可检测时间分辨率通常只有一天或一小时. 对于主动源，格林函数的可重复性是可控的，时间分辨率也是可控的. 捕捉瞬时变化的能力有助于更好地理解地震或其它破裂或火山爆发的瞬时应力变化，这将促进对其机制和过程的认识. 因此，提高时间分辨率也将成为一个重要的研究目标.
3.3 人工智能辅助地下介质时变研究
地震台站大量布设及多种观测手段的实现，使得地震资料愈发丰富，更高效、更充分地利用这些海量的数据亦是需要考虑的问题. 近年发展的人工智能方法渐渐进入地震学领域，其在微震监测方面已经取得了丰富的研究成果，倍受地震学者关注，但在地下介质时变监测方面依旧发展缓慢. 现阶段鲜有利用人工智能进行介质时变研究，如在火山区利用机器学习自动识别非火山震颤阶段下的平稳噪声记录波形（Makus et al., 2023）、利用机器学习的方法对互相关函数进行聚类（Yates et al., 2023）. 这些应用均是在介质时变监测的某个环节中的应用，更为广泛深入的利用有待挖掘.
3.4 开发地下介质时变实时监测系统
随着目前计算能力的提高，实时监测变得尤为现实. 地震时间序列的连续变化可以在永久地震台网中记录下来，有必要同时分析局部环境因素，以区分它们，并校正与非构造活动有关的可能的瞬态速度变化. 实时监测的实现有助于发现潜在的速度异常，推进地震预报、预警相关研究的发展.
3.5 地下介质时变机理分析
地下介质随时间变化的机理复杂多样，受多种机制混合约束. 地下介质变化的机制可能是动态应力/应变变化、静态应变变化和流体等. 以往许多研究中，其观测到的时变对应的物理机制分析不够明确，如地下浅层介质真实的构造相关变化易受“长期变化”的掩盖，致使时变机理混淆，因此需要开展更为细致的研究（如对“长期变化”的提取/消除），深化对地下介质变化物理机理的认识.
3.6 跨行星的时变研究
随着从其他行星（如月球和火星）获取新的连续地震数据和信息的增加，研究人员已经成功地将基于噪声的相关技术应用于监测月球（Larose et al., 2005; Sens-Schönfelder and Larose, 2010）、火星（Suemoto et al., 2020）上的地震速度变化. 这些应用是通过在典型的微地震带之外或更高的频率范围内使用扩散波来研究的，结果揭示了与环境相关的动态过程. Tanimoto等（2008）利用高频噪声互相关技术成功提取瑞利波群速度，发现其振幅和统计的热月震数据存在良好的相关性. Suemoto等（2020）通过地震数据的极化分析来估计火星噪声场的时间变化和频率依赖性，发现低频P波受火星大气和气候影响显著，低频瑞利波则与近地表风活动有关，高频部分则是由着陆器本身产生. 这些研究表明了基于地震波的技术在未来行星探测中的应用是可行的.
3.7 多领域联合监测的时变研究
地下介质的变化往往是复杂的、多种地球物理过程的响应，如何区分和认识这些变化的影响机制也将是个复杂的课题. 单独研究某个物理参数（如地震衰减、各向异性、波速等）往往只能解释局部的变化特征，因而实现多参数分析同时结合其它学科观测资料（如地表形变、流变学、实验室模拟等）进行联合分析将有助于解释地下介质变化的本质，理解地球内部多尺度的动态演化.
致谢
感谢审稿专家与期刊编辑的建设性指导与宝贵修改意见.
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图 1 （a）Piton de la Fournaise火山喷发前地震波速的降低及地震能量的时间变化，地震能量是通过记录到的连续地震信号的日平均均方根（RMS）值计算得到，阴影区域表示喷发期（引自Brenguier et al., 2008b）；（b）新西兰Ruapehu火山在1995—1996年的一次喷发前后地震各向异性快波方向变化，白色箭头表示区域应力场方向，黑色箭头表示局部应力场方向（引自Gerst and Savage, 2004）
Figure 1. (a) Reduction of seismic velocity and temporal change of seismic energy before the eruption of Piton de la Fournaise volcano. Seismic energy is calculated from the daily average root-mean-square (RMS) value of the recorded continuous seismic signals, and shadow areas represent the eruption period (from Brenguier et al., 2008b). (b) The fast anisotropic direction changed before and after an eruption in 1995-1996 at Ruapehu volcano, New Zealand. The white arrows indicate the direction of the regional stress field, and the black arrows indicate the direction of the local stress field (from Gerst and Savage, 2004)
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图 2 加利福尼亚州帕克菲尔德地区地震波速变化、地表位移及地震活动性. 曲线表示由GPS站测量的沿圣安德烈斯断层的地震后断层平行位移（引自Brenguier et al., 2008a）
Figure 2. Seismic velocity variations, surface displacements, and tremor activity near Parkfield, California. The curve represents post-seismic fault-parallel displacements along the San Andres Fault measured by GPS stations (from Brenguier et al., 2008a)
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图 3 HAR0-HAR1台站对每天互相关分析. （a）在1～12 Hz的瑞利波速度变化；（b）互相关系数（CC）变化；（c）累计降雨量（蓝色）和空气温度变化（红色）（引自Fiolleau et al., 2020）
Figure 3. Daily cross-correlation analysis for HAR0-HAR1 stations. (a) Rayleigh wave velocity changes between 1 and 12 Hz; (b) Cross-correlation (CC) coefficient changes; (c) Cumulative rainfall (blue) and air temperature changes (red) (from Fiolleau et al., 2020)
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图 4 （a）互相关波形随时间变化图. 颜色深浅表示相对于长时平均测量的走时dt；（b）研究时段内的dt测量值及小波相干性. 黑色虚线表示线性回归（引自Sheng et al., 2022）
Figure 4. (a) Cross-correlation waveform versus time. Color shades represent travel time dt measurements relative to long-term average. (b) The dt measurements and the coherence of wavelet during the study period. The black dashed lines represent linear regression (from Sheng et al., 2022)
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图 5 两组重复地震波形的比较. （a）表示在2003年、2009年以及2020年的一组重复地震波形；（b）表示在2002年、2009年以及2022年的一组重复地震波形（引自Wang et al., 2024）
Figure 5. Comparison of two sets of repetitive seismic waveforms. (a) Represents a set of repeated seismic waveforms in 2003, 2009 and 2020; (b) Represents a set of repeated seismic waveforms in 2002, 2009 and 2022 (from Wang et al., 2024)
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图 6 相对波速变化、降雨量、水头时间序列. （a）波速变化与累积年降雨量对比；（b）波速变化与水力水头对比（引自Mao et al., 2022）
Figure 6. Time series of relative seismic velocity changes, precipitation, and hydraulic head. (a) Comparison of seismic velocity changes with cumulative annual precipitation; (b) Comparison of seismic velocity changes with hydraulic head (from Mao et al., 2022)
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