Discussion on the overestimated magnitude of the 1920 Haiyuan earthquake
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摘要: 1920年海原大地震作为史料记载以来中国大陆震级最高、伤亡最多的极具破坏性的地震之一，开启了我国用现代地震学方法研究大地震的新篇章，在我国地震研究史上具有里程碑的意义。最新研究结果表明，1920年海原大地震的矩震级为MW（7.9±0.2），与文献和大众广泛接受的M8${\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 2$}} $的数值相差较大。本文通过对震级标度及其演化历史的总结和梳理，阐述了仪器记录早期阶段基于地震波波形振幅和频率的震级标定存在系统偏差的问题，这与仪器限制、台站稀疏、标定不统一等因素有关，也使得1920年海原大地震和同时期世界上其它一些重要大地震的震级不同程度被高估。在各种震级标度中，矩震级MW与地震破裂面积和位移等物理参数关联，是地震震级的最佳标定方法。震级作为表述地震大小和能量的重要参数，被广泛地用于评估断层未来的地震潜势；震级的偏差对地震活动时空分布样式的研究会产生重要影响，并造成基于历史地震资料的地震危险性评价和灾害评估等产品的可信度降低。因此，本文倡导对历史地震震级进行检验和修订，并建议1920年海原大地震的震级采用矩震级MW（7.9±0.2）表示，修正后的1920年海原大地震的震级与2008年汶川地震（MW7.9，MS8.0）和2001年昆仑山大地震（MW7.8，MS8.1）相当。Abstract: The great 1920 Haiyuan earthquake, resulting in tremendous casualties, ranks as one of the largest and most devastating earthquakes in China. This significant event marks the start of investigating earthquakes through modern scientific approaches in China. Recent studies show that the moment magnitude of the 1920 Haiyuan earthquake is MW（7.9±0.2）, prominently smaller than the widely known and often cited magnitude M8${\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 2$}} $. This paper reviews the re-calibration and conversion of different types of magnitude in the early developing phase of seismometers and analogue seismographs. Similar to the 1920 Haiyuan earthquake, the magnitude of many large shallow earthquakes that occurred in this period are systematically overestimated due to factors such as developing technology, sparse instrumentation and data, and diverse calibration functions. The moment magnitude, linked to physical parameters of earthquake rupture, is the best magnitude scale. For magnitude is the most commonly used parameter in describing an earthquake’s size and energy and is an essential factor in seismic hazard assessment, bias and errors in magnitude conversion have significant consequences in understanding the spatio-temporal pattern of historical seismicity and the reliability of various products of seismic potential and hazard evaluation. We thus advocate citing revised moment magnitude MW（7.9±0.2） for the 1920 Haiyuan earthquake in future studies and re-evaluating the magnitude of historical earthquakes in general. With a revised magnitude, the 1920 Haiyuan earthquake is similar in size to the 2008 Wenchuan earthquake （MW7.9, MS8.0） and the 2001 Kunlun earthquake （MW7.8, MS8.1）.
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图 1 青藏高原东北缘活动断裂和1920年海原大地震等震线（绿色）分布图
Figure 1. Map showing active faults in northeast Tibetan Plateau and the isoseismal contour lines of the 1920 Haiyuan earthquake shown in green
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图 2 1920年海原大地震地表破裂几何形态平面展布（修改自国家地震局地质研究所，宁夏回族自治区地震局，1990）（a）和同震左旋位移沿断裂分布的不同研究结果对比（b），图（b）右侧为位移量直方图
Figure 2. Surface rupture geometry of the 1920 Haiyuan earthquake （revsied from Institute of Geology of State Seismological Bureau，Seimological Bureau of Ningxia Hui Autonomous Region，1990）（a） and comparison of coseismic left-lateral offsets along fault strike in different studies （b）. The right panel of Fig. （b） is the histogram of all measured offsets
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图 3 （a） 高精度LiDAR三维地形再现干盐池唐家坡村1920年地表破裂形成的陡坎和石垒田埂（7.5±1） m的左旋错断；（b） 在该点位附近沿断裂约400 m范围内Zhang等（1987）量测多个左旋同震位移，从4.8 m到7.5 m不等
Figure 3. （a） High-resolution 3D LiDAR topography shows the stone wall being left-lateral offset （7.5±1） m near the village of Tangjiapo，Ganyanchi；（b） Near the site，Zhang et al （1987） measured multiple sinistral coseismic offsets from 4.8 m to 7.5 m over about 400 m distance along the fault
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图 4 1920年海原大地震的烟熏纸质记录扫描并数字化示例
Figure 4. Example of original seismogram on smoked paper of the 1920 Haiyuan earthquake that was scanned and digitized
表 1 1920年海原地震震级的不同估算值及文献来源 （修改自Ou et al，2020）
Table 1 Estimates of the magnitude of the 1920 Haiyuan earthquake （modified from Ou et al，2020）
震级 计算或估算方法 文献来源 M8.5 频率约为20 s的面波振幅 Gutenberg和Richter （1941） m7.9 体波震级公式${{m}_{{\rm{B}}}＝\mathrm{lg}{\left({ {A}_{{\rm{H}}} }/{T}\right)}_{{\rm{max}}}＋Q （ \varDelta ） }$ Gutenberg和Richter （1956） MW8.3 基于瑞雷面波频谱密度与45°断层倾角假设 Chen和Molnar （1977） MW7.8 由Chen和Molnar （1977）给出的地震矩计算而得 Kanamori （1977） MS8.6 根据Gutenberg的笔记重新修订 Abe （1981） mB7.9 根据Gutenberg的笔记重新修订 Abe （1981） M8.5 基于地震烈度M＝0.58I0＋1.5 顾功叙等（1983） MW8 基于90°断层倾角假设对Chen和Molnar （1977）结果进行修正 Deng等（1984） M8.6 根据Gutenberg （1945b）的方法编译 谢毓寿和蔡美彪 （1986） MS8.4 从MS8.6修正 Pacheco和Sykes （1992） MW8.3 引用Chen和Molnar （1977） International Seismological Centre （2013） MS8.7 基于三个地震记录计算得到 International Seismological Centre （2014） MW7.8 基于地表破裂长度约240 km和同震位移最大值和平均值 Liu-Zeng等（2015） MW8.2 基于震源物理动态模拟的理论计算 Xu等（2019） MW（7.9±0.2） 将早期地震波形记录扫描并数字化，计算体波震级和面波
震级并换算，辅以体波波形进行正演拟合Ou等（2020） 
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