The advantage of the nonlinear mixed model and its application in typical seismically active areas in China
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摘要:
b值作为地震预报与危险性评价研究中的重要参数，受到广泛关注与讨论。通过非线性混合模型对中国地震目录数据库开展地震震级-频数分布拟合，并利用该方法计算得到的b值对地震活动进行分析评价。文章首先以中国26个地震带为研究区，收集1920—2019年的4.7级以上地震数据为完整地震目录，分别通过非线性混合模型与传统G-R模型进行拟合，并对比其效果；进一步以西藏地区为具体试验区，选择1920—2019年的地震目录数据，以10年为间隔，将非线性混合模型应用于西藏地区地震震级-频数模型的拟合。其次，利用矩震级与地震矩转换公式计算出非线性混合模型中的相关变量。最后，利用非线性混合模型对地震数据进行非线性回归分析。结果显示：当b值出现低值时，对应时间段前后有地震发生，b值较低时，发生的地震震级大、频次底；b值相对较高时，地震震级小、频次高。将非线性混合模型应用到中国及邻区完整地震数据中，能够对数据进行更加全面的分析，克服了传统模型方法对高震级和地震数据分析中的局限性，合理分析计算b值，进而增强对地震目录数据的分析和评价。
Abstract:As an essential parameter in earthquake prediction and risk assessment research, the b-value has received extensive attention and discussion. In this study, we chose a nonlinear mixed model to fit the earthquake magnitude-frequency distribution to the China Earthquake Catalog database. The b-values calculated by this method were used to analyze and evaluate the seismic activity. This paper takes 27 seismic belts in China as the research area, collects earthquake data of magnitude 4.7 and above from 1920 to 2019 as a complete earthquake catalog, performs mixed model fitting and G-R model fitting for these 27 seismic belts, and compares the fitting effects. Taking Tibet as the test area, the earthquake catalog data from 1920 to 2019 were selected, and the nonlinear mixed model was applied to fitting the earthquake magnitude-frequency model in Tibet at 10-year intervals. Firstly, the earthquake data screened in the study area was classified and counted by magnitude and time; Secondly, the relevant variables in the nonlinear mixed model were calculated using the moment magnitude and seismic moment conversion formula. Finally, a nonlinear hybrid model was used to perform nonlinear regression analysis on the seismic data. The results show that: When low values of b occur, earthquakes occur around the corresponding periods. When b-values are low, earthquakes of large magnitude and low frequency occur. When b-values are relatively high, earthquakes of small magnitude and high frequency occur. Applying the nonlinear mixed model to the complete seismic data in China and neighboring regions enables a more comprehensive analysis of the data and overcomes the limitations of the traditional modeling method in analyzing earthquakes of high magnitude. The b-value will be calculated by rational analysis, which enhances the analysis and evaluation of seismic catalog data.
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图 2 中国1920—2019年4.7级以上地震时间分布(地震数据源自于国家地震科学数据中心;
https://data.earthquake.cn/ )Figure 2.
表 1 相关参数MW、MO、MO-1、MO2对应表
Table 1. Correspondence table of MW, MO, MO-1 and MO2
MW MO MO-1 MO2 4.7 1.32396×e12 7.55308×e-13 1.75288×e24 4.9 1.58884×e12 6.29389×e-13 2.52442×e24 5.1 1.90050×e12 5.26178×e-13 3.61189×e24 5.3 2.26613×e12 4.41281×e-13 5.13534×e24 5.5 2.69389×e12 3.71210×e-13 7.25706×e24 5.7 3.19301×e12 3.13184×e-13 1.01953×e25 5.9 3.77386×e12 2.64981×e-13 1.42420×e25 6.1 4.44814×e12 2.24813×e-13 1.97859×e25 6.3 5.22897×e12 1.91242×e-13 2.73421×e25 6.5 6.13107×e12 1.63104×e-13 3.75900×e25 6.7 7.17089×e12 1.39453×e-13 5.14217×e25 6.9 8.36683×e12 1.19520×e-13 7.00038×e25 7.1 8.96245×e12 1.11577×e-13 8.03255×e25 7.3 9.79301×e12 1.02114×e-13 9.59030×e25 
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表 2 各区域参数值表
Table 2. Table of parameter value for each area
区域 a b a1 a2 a3 Ⅰ-1 10.446 1.561 -1.26×e12 1.98×e-26 -3.45×e-13 Ⅰ-2 10.484 1.349 -1.29×e12 1.98×e-27 -8.79×e-14 Ⅱ-1 5.319 0.569 — -4.13×e-26 4.95×e-13 Ⅱ-2 4.874 0.582 — 1.73×e-27 6.03×e-15 Ⅱ-3 10.776 2.002 — — -3.48×e-13 Ⅲ-1 5.473 0.967 5.45×e13 -6.84×e-27 1.82×e-13 Ⅲ-2 8.840 1.300 -1.07×e12 -2.58×e-27 -1.06×e-13 Ⅲ-3 6.856 0.988 -9.46×e10 9.96×e-27 -1.82×e-13 Ⅲ-4 5.423 0.797 3.13×e11 1.87×e-26 -2.77×e-13 Ⅲ-5 5.533 0.666 -8.22×e11 -5.84×e-27 1.22×e-13 Ⅲ-6 3.843 0.341 — — 1.96×e-13 Ⅲ-7 12.194 2.643 — — -1.12×e-12 Ⅳ 11.368 1.839 -1.72×e12 1.58×e-26 -4.18×e-13 Ⅴ-1 11.863 1.769 -1.35×e12 4.21×e-27 -2.07×e-13 Ⅴ2-1 9.317 1.401 -9.47×e11 1.20×e-26 -2.89×e-13 Ⅴ2-2 7.617 1.128 -6.00×e11 5.58×e-27 -1.98×e-13 Ⅴ2-3 12.348 2.125 -9.94×e11 2.67×e-26 -5.89×e-13 Ⅴ3-1 6.950 0.858 -9.84×e11 -1.83×e-26 1.92×e-13 Ⅴ3-2 10.604 1.532 -1.22×e12 9.47×e-27 -2.75×e-13 Ⅴ4-1 7.600 0.876 -5.68×e11 -6.57×e-27 4.51×e-14 Ⅴ4-2 2.570 0.103 7.60×e11 4.95×e-27 6.31×e-14 Ⅴ4-3 5.402 0.714 4.59×e11 2.21×e-26 -2.30×e-13 Ⅵ-1 4.853 0.616 5.98×e11 2.71×e-26 -2.21×e-13 Ⅵ-2 7.534 1.059 -9.93×e11 -1.38×e-27 -8.67×e-14 Ⅵ-3 6.141 0.858 -1.40×e11 -3.72×e-27 -1.60×e-14 Ⅵ-4 6.630 0.859 -6.29×e11 -4.38×e-27 -1.93×e-14 注：Ⅰ-1—台湾西部地震带；Ⅰ-2—台湾东部地震带；Ⅱ-1—长江中游地震带；Ⅱ-2—华南沿海地震带；Ⅱ-3—右江地震带；Ⅲ-1—长江下游-南黄海地震带；Ⅲ-2—郯庐地震带；Ⅲ-3—华北平原地震带；Ⅲ-4—汾渭地震带；Ⅲ-5—银川-河套地震带；Ⅲ-6—朝鲜地震带；Ⅲ-7—鄂尔多斯地震带；Ⅳ—东北地震带；Ⅴ-1—西昆仑-帕米尔地震带；Ⅴ2-1—龙门山地震带；Ⅴ2-2—六盘山-祁连山地震带；Ⅴ2-3—柴达木-阿尔金地震带；Ⅴ3-1—巴颜喀拉山地震带；Ⅴ3-2—鲜水河-滇东地震带；Ⅴ4-1—喜马拉雅地震带；Ⅴ4-2—滇西南地震带；Ⅴ4-3—藏中地震带；Ⅵ-1—南天山地震带；Ⅵ-2—中天山地震带；Ⅵ-3—北天山地震带；Ⅵ-4—阿尔泰山地震带；由于公元1920—2019年Ⅵ-5塔里木-阿拉善地震带仅有1条地震数据，故文中在27个地震带中共建立26个完整地震目录
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表 3 各研究区非线性混合模型拟合度与G-R模型拟合度对比表
Table 3. Comparison table of the fitting degree of the nonlinear mixed model and the G-R model in each study area
区域 非线性拟合度R2 G-R拟合度R2 区域 非线性拟合度R2 G-R拟合度R2 区域 非线性拟合度R2 G-R拟合度R2 Ⅰ-1 0.994 0.955 Ⅲ-5 0.990 0.980 Ⅴ3-2 0.992 0.983 Ⅰ-2 0.995 0.986 Ⅲ-6 0.977 0.957 Ⅴ4-1 0.997 0.995 Ⅱ-1 0.965 0.955 Ⅲ-7 0.965 0.943 Ⅴ4-2 0.993 0.986 Ⅱ-2 0.986 0.984 Ⅳ 0.994 0.963 Ⅴ4-3 0.990 0.963 Ⅱ-3 0.954 0.931 Ⅴ-1 0.996 0.993 Ⅵ-1 0.999 0.957 Ⅲ-1 0.980 0.912 Ⅴ2-1 0.991 0.979 Ⅵ-2 0.997 0.995 Ⅲ-2 0.989 0.986 Ⅴ2-2 0.989 0.987 Ⅵ-3 0.987 0.982 Ⅲ-3 0.993 0.989 Ⅴ2-3 0.992 0.984 Ⅵ-4 0.991 0.987 Ⅲ-4 0.986 0.967 Ⅴ3-1 0.993 0.976 注：Ⅰ-1—台湾西部地震带；Ⅰ-2—台湾东部地震带；Ⅱ-1—长江中游地震带；Ⅱ-2—华南沿海地震带；Ⅱ-3—右江地震带；Ⅲ-1—长江下游-南黄海地震带；Ⅲ-2—郯庐地震带；Ⅲ-3—华北平原地震带；Ⅲ-4—汾渭地震带；Ⅲ-5—银川-河套地震带；Ⅲ-6—朝鲜地震带；Ⅲ-7—鄂尔多斯地震带；Ⅳ—东北地震带；Ⅴ-1—西昆仑-帕米尔地震带；Ⅴ2-1—龙门山地震带；Ⅴ2-2—六盘山-祁连山地震带；Ⅴ2-3—柴达木-阿尔金地震带；Ⅴ3-1—巴颜喀拉山地震带；Ⅴ3-2—鲜水河-滇东地震带；Ⅴ4-1—喜马拉雅地震带；Ⅴ4-2—滇西南地震带；Ⅴ4-3—藏中地震带；Ⅵ-1—南天山地震带；Ⅵ-2—中天山地震带；Ⅵ-3—北天山地震带；Ⅵ-4—阿尔泰山地震带
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表 4 西藏地区1920—2019年10年间隔G-R模型和混合模型b值对比表
Table 4. Comparison table of the b-values of the G-R model and the nonlinear mixed model for 10-year intervals from 1920 to 2019 in Tibet
组别 时间/年 b值
(传统G-R模型)b值
(非线性混合模型)1 1920—1929 0.598 0.228 2 1930—1939 0.576 0.166 3 1940—1949 0.646 0.312 4 1950—1959 0.870 0.565 5 1960—1969 0.951 1.008 6 1970—1979 0.861 0.807 7 1980—1989 0.690 0.312 8 1990—1999 0.691 0.955 9 2000—2009 0.681 0.742 10 2010—2019 0.746 1.201
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