Seismic dislocation theory of spherical Earth model and its application
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摘要: 地震位错理论是研究地震断层滑动与地球物理场变化之间关系的理论，是震源机制、地球内部构造、地震预测等基本地球物理问题与大地测量、地球物理观测数据之间的联系纽带。被广泛使用的半无限空间介质模型的位错理论，由于其几何模型的限制，在地震变形和地球动力学等应用研究中会导致一定程度的误差。此外，现代大地测量技术可以在全球和区域尺度上精确地观测地震变形，亟需一个适用于全球地震变形研究的地震位错理论。为此，本团队基于球形地球模型，经过多年系统性研究，建立了地震位错理论新体系。所构建的球形地球模型的地震位错理论，促进了全球地震变形和地球动力学变化的研究，是近年来地球物理学领域取得的重要理论进展之一。本文简要地介绍了国内球形地球模型地震位错理论的发展及其应用研究。首先，介绍了弹性球形地球模型、三维不均匀地球模型和黏弹地球模型的位错理论；其次，介绍球形地球模型的位错理论在地球动力学变化研究、断层与地下介质结构反演和地震大地测量学研究方面的相关应用；最后，对球形地球模型的位错理论的发展方向作出展望。Abstract: Seismic dislocation theory is the theory of studying the relationship between seismic fault slip and geophysical field change, and also it is the link between the source mechanism, the internal structure of the Earth, earthquake forecasting and other basic geophysical problems and geodetic-geophysical observation. The widely used dislocation theory of the semi-infinite medium model, due to the limitation of its geometric attribute, will riskily result in a certain degree of oversight and even fault in the application of seismic deformation and geodynamics analysis. In addition, modern geodesy technology can accurately observe seismic deformation on global and regional scales, and a suitable seismic dislocation theory born for global seismic deformation study is urgently required. For this purpose, our team has developed a new system of seismic dislocation theory based on the spherical Earth model through many years of systematic research. The establishment of such theory has promoted the study of global seismic deformation and geodynamic process, and expanded the study of earthquake-induced global geodynamic changes. This informative article briefly introduces the domestic development and application of seismic dislocation theory of spherical Earth model. The first section introduces the dislocation theory of elastic spherical Earth model, three-dimensional inhomogeneous Earth model and viscoelastic Earth model. The second section introduces the relevant applications of the dislocation theory of spherical Earth model in geodynamic change, fault and underground structure inversion and others in seismological geodesy. The seismic dislocation theory of the spherical Earth model has promoted the study of global seismic deformation and geodynamic changes. It is one of the important theoretical advances in the field of geophysics in recent years.
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2021年5月21日21时48分（北京时间）云南省大理白族自治州漾濞县（99.87°E，25.67°N）发生MS6.4地震。该地震发生后，我们对震中附近的地下流体观测资料进行了系统的总结，结果显示云南省地震台在2021年2月24日提出洱源井水温异常，该井水温在漾濞MS6.4地震前呈现明显的异常现象。
洱源水温观测井位于云南省大理白族自治州洱源县玉湖镇，地理坐标为（99.95°E，26.11°N），地处洱源盆地，位于红河断裂带与维西—巍山断裂之间（图1）。该井建成于1984年，井深266.56 m，套管下至165.56 m，其中80.22—144.02 m为滤水管，165.56—266.56 m为裸孔。0—73.16 m的岩性为冲积湖积层，其中上部为黏土及砂土层、下部为石英质、石英颗粒砂土及碎石砾石层；73.16—170.3 m为千枚岩及粉砂质千枚岩，中间夹有变质砾岩、片岩；170.3—175.1 m为千枚岩破碎带；175.1—202.4 m为砂质千枚岩及少量变粒片岩；202.4—266.56 m以变质泥岩为主，中间为片岩及角砾（云南省地震局，2005）。
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图 1 洱源井的构造位置及附近的地震分布断层数据据中国活动构造图（邓起东等，2007）修改补充；地震目录引自中国地震台网中心；震源机制解源于哈佛大学（Dziewonski，Ekström，2021）；地质单元和河流数据源于MapSIS软件（蒋骏等，2000）Figure 1. Tectonic position of the Eryuan well and the distribution of nearby earthquakesThe fault data are revised from China ative tectonic map （Deng et al，2007），earthquake catalogue are from China Earthquake Networks Center，focal mechanisms are from Harvard University （Dziewonski，Ekström，2021），and geological units and rivers refer to MapSIS （Jiang et al，2000）洱源井从1991年开始观测水温，观测仪器为中国地震局地壳应力研究所（现应急管理部国家自然灾害防治研究院）研制的SZW-1A水温仪，温度探头放置在井下190 m。2015年10月SZW-1A水温仪器发生故障，10月13日更换为中科光大公司研制的ZKGD3000-NT水温仪，温度探头置于90 m处，该水温仪的观测精度优于0.05 ℃，1分钟采样1次。
洱源井距离漾濞MS6.4地震仅50 km，洱源井水温在漾濞地震前的变化如图2所示，可见：2020年10月3日水温开始下降，2021年4月中旬下降速率减缓，至2021年5月21日下降幅值约0.15 ℃，下降持续230天；漾濞地震发生时，洱源井水温出现显著的同震上升，上升幅值为0.018 ℃，之后持续上升。
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图 2 漾濞MS6.4地震前洱源井水温的异常变化Figure 2. Water temperature variation in the Eryuan well before the Yangbi MS6.4 earthquake针对洱源井水温的下降异常，云南省地震台于2021年3月1日开展了异常核实。通过观测系统检查、环境因素调查及气象因素分析，认为洱源井水温的下降异常不存在人为、仪器和环境等干扰因素（高文斐，胡小静，2021）。
为分析洱源井水温下降异常与漾濞MS6.4地震的关系，将洱源井水温历史观测资料与周围地震的对应情况进行对比。图3a为洱源观测井自采用中科光大水温仪以来的观测曲线，可见洱源井水温共出现过两次与漾濞MS6.4地震前类似的下降异常。一次为2015年10月至2016年4月出现的持续下降，2016年4月底下降转缓，下降幅值约0.19 ℃，转缓1个月后发生2016年5月18日云龙MS5.0地震，该地震与洱源井相距42 km，地震发生时记录到显著的水温同震响应，响应幅值为0.013 ℃，地震后水温回升。另一次为2016年12月初至2017年3月中旬出现的水温持续下降，降幅为0.11 ℃，下降有所转缓后发生2017年3月27日漾濞MS5.1地震，该地震与洱源井相距29 km，地震发生时同样记录到显著的水温同震响应，响应幅值为0.024 ℃，地震后水温回升。图4为三次MS≥5.0地震前洱源井水温下降变化的对比曲线，可见，2015年观测以来，洱源井水温共出现三次显著下降异常现象，之后周边均发生了MS5.0以上地震，地震发生时均记录到显著的同震响应，震后转折回升，因此三次地震前水温下降异常具有一定的重复性。
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图 3 2015年10月13日至2021年8月21日洱源井水温变化（a）和洱源井100 km范围内的MS5.0以上地震M-t图（b）Figure 3. Variation of water temperature in the Eryuan well （a） and M-t map of MS≥5.0 earthquakes with epicenter distance from the Eryuan well below 100 km （b） during the period from October 13，2015 to August 21，2021![]()
图 4 洱源井水温在三次MS≥5.0地震前的异常变化对比Figure 4. Comparison of the water temperature curves in the Eryuan well before three MS≥5.0 earthquakes将洱源井水温异常与地震的对应情况进行统计检验，图3b为洱源井100 km范围内2015年10月13日至2021年8月21日期间MS5.0以上地震的M-t图，可见该时段内共发生6次MS5.0以上地震，因为2021年5月21日发生在漾濞县的四次地震为前震-主震-余震型地震事件（龙锋等，2021），本文将其视为一个地震序列，即洱源井水温自2015年观测以来在三次地震事件前均出现重复性下降异常。洱源井水温异常与地震一一对应，通过统计检验。
综合洱源井水温历史资料对比分析和统计检验的结果，本文认为洱源井水温2020年10月至2021年5月的异常变化与2021年5月21日漾濞MS6.4地震有关，为水温地震前兆观测积累了一次震例。洱源井水温异常的机理可能与震源断层及外围区域的应力演化有关，尚待进一步研究。
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