障碍体和凹凸体对地震矩的影响
EFFECTS OF BARRIERS AND ASPERITIES ON SEISMIC MOMENT
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摘要: 本文利用具有非均匀剪切应力分布的圆盘状裂缝问题的解,定量计算了障碍体和凹凸体对地震矩的影响.我们发现,除非障碍体的尺寸很小或很接近于整个断层的尺寸,含有障碍体的断层的地震矩,大致为具有均匀应力降的等面积断层的地震矩的40%.由此可以推知,在障碍体的这种尺寸范围内,视应力降大致也是△Af=SA-f的40%.这里SA是远场应力,f是残余摩擦应力.另外,已存在滑动带对于凹凸体破坏的地震矩有明显的放大作用,这种作用在凹凸体尺寸较小时特别显著.例如,当凹凸体半径是整个断层半径的2/10时,凹凸体上的矩被放大7倍多;当其半径为整个断层半径的1/10时,凹凸体的矩将被放大约30倍. 文中还比较了三维效应和二维效应的差异.我们发现,Mx0/M0c在三维情形对障碍体尺寸的变化并不敏感,这是与二维情形很不相同的.这里,Mx0是具有障碍体的断层破裂所产生的地震矩,M0c是相应的均匀断层破裂的矩.所以,二维分析不适用于具有障碍体的三维断层.然而,在分析已存在滑动带对凹凸体破裂的矩的影响时,平面应变结果与三维结果差异并不很大.Abstract: In this paper,the effects of barriers and asperities on the determination of seismic moment have been quantitatively examined by using the solution for a penny-shaped crack with non-uniform traction. It has been found that the moment of a fault with a barrier is about 40 percent of the moment on the fault with uniform stress drop and the same area,if the radius of the barrier is not very small,nor approximates to that of the fault. Therefore,it follows that,in this case,the apparent stress drop is about 40 percent of △Af=SA-f where SA is the far-field stress and f is the uniform residual frictional stress. Furthermore,a pre-existing slip zone can substantially amplify the seismic moment due to the failure of an asperity. Especially,the amplification is very large when the radius of the asperity is small. For example,the moment on the asperity is over 7 times and 30 times of the moment at the failure of a uniform shear fault with radius C,respectively,when the radius of the asperity is 20 percent and 10 percent of the radius C of the fault.The difference between three-dimensional and two-dimensional effects is compared in this paper. It is founl that Mx0/M0c is not sensitive to the change of asperity radius for three-di-mensionad faults,this differs very mith from the result with two-dimensional fault,where Mx0 is the moment due to the failure of the fault with an asperity and M0c is the moment of a uniform fault. Therefore,two-dimensional analsis is not suitable to a three-dimensional fault with asperity. However,when examining the effect of pre-existing slip zones on the moment due to failure of asperity,the difference between the results of plane strain and three-dimensional case is not apparent.
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本目录中的地震参数来自“中国地震台站观测报告”(简称“月报”)． 其中， 国内及邻区给出M≥4.7的事件， 全球给出M≥6.0的事件． “月报”由中国地震台网中心按月做出．
本目录中的发震时刻采用协调世界时(UTC)； 为了方便中国读者， 也给出北京时(BTC)． 震中位置除给出经纬度外， 还给出参考地区名， 它仅用作查阅参考， 不包含任何政治意义； 还给出测定震源位置的台数(n)和标准偏差(SD)．
面波震级MS是用中周期宽频带SK地震仪记录， 采用北京台1965年面波震级公式MS=lg(AH/T)+1.66 lg(Δ)+3.5 (1°＜Δ＜130°)求得． AH是两水平分向最大面波位移的矢量合成位移． MS7是对763长周期地震仪记录， 采用国际上推荐的面波震级公式MS7=lg(AV/T)+1.66 lg(Δ)+3.3 (20°＜Δ＜160°)求得． AV是垂直向面波最大地动位移． mb是短周期体波震级， ML是近震震级， 为避免混乱, 震级之间一律不换算．
表 1 中国及邻区地震目录(2015年9—10月， M≥4.7)Table 1. Catalog of earthquakes within and near China (September--October， 2015, M≥4.7)编号 发 震 时 刻 地 理 坐 标 深度/km 震级 标准偏差(SD) 使用台数 (n) 地 区 UTC BTC 日-时 纬度/°N 经度/°E M S M S7 ML mb 月-日 时:分:秒 1 09-01 13:24:44.8 01-21 23.93 121.54 10 5.2 5.1 5.2 4.7 2.3 96 台湾岛 2 01 17:34:06.8 02-01 24.06 122.41 21 4.7 4.6 4.4 4.4 2.0 76 台湾岛 3 13 07:51:10.8 13-15 45.08 91.52 7 4.7 4.3 5.0 4.6 2.2 69 新疆自治区北部 4 15 19:37:33.2 16-03 24.35 121.90 10 5.6 5.5 5.7 5.0 1.6 98 台湾岛 5 16 11:10:07.7 16-19 35.46 78.47 8 4.5 4.2 4.9 4.6 2.2 66 克什米尔东部 6 16 13:08:57.1 16-21 24.25 121.90 10 5.3 5.2 5.4 4.9 1.6 101 台湾岛 7 10-12 10:04:14.7 12-18 34.36 98.20 10 5.3 5.1 5.1 4.9 2.6 92 青海省 8 12 11:14:46.8 12-19 22.47 121.48 12 4.7 4.4 4.9 4.5 1.7 84 台湾地区 9 19 02:17:36.1 19-10 24.93 122.00 10 5.5 5.3 5.6 4.9 1.9 97 台湾岛 10 19 05:42:13.1 19-13 24.97 121.79 10 4.7 4.5 4.5 4.4 2.2 71 台湾岛 11 19 07:20:16.7 19-15 24.98 121.99 10 4.7 4.5 4.6 4.4 1.9 73 台湾岛 12 21 05:58:21.0 21-13 44.68 124.16 10 4.5 4.3 5.1 4.3 2.0 50 中国东北部 13 26 18:11:23.8 27-02 30.17 98.01 6 4.6 4.4 4.4 4.7 2.3 58 西藏自治区 14 28 20:12:08.5 29-04 27.55 100.30 10 4.8 4.6 4.5 4.5 2.5 78 云南省 15 30 11:26:39.4 30-19 25.04 99.44 10 5.0 4.7 5.1 4.7 2.5 84 缅甸—中国边境地区 表 2 全球地震目录(2015年9—10月， M≥6.0)Table 2. Catalog of earthquakes all over the world (September--October， 2015， M≥6.0)编号 发 震 时 刻 地 理 坐 标 深度/km 震级 标准偏差(SD) 使用台数 (n) 地 区 UTC BTC 日-时 纬度/° 经度/° MS MS7 mb 月-日 时:分:秒 1 09-01 15:25:06.6 01-23 31.19N 141.88E 20 6.1 5.9 5.3 1.6 67 本州以南地区 2 07 09:13:56.6 07-17 33.07S 177.99W 29 6.2 5.9 5.4 1.7 74 克马德克群岛以南地区 3 07 14:06:24.7 07-22 32.98S 177.83W 12 6.0 5.7 5.3 1.9 84 克马德克群岛以南地区 4 08 08:03:55.0 08-16 14.70N 93.90W 10 6.0 5.7 1.4 56 墨西哥恰帕斯海岸近海 5 10 10:26:42.3 10-18 52.46N 169.64W 18 6.0 5.9 5.6 1.1 98 福克斯群岛 6 13 08:14:10.0 13-16 25.14N 109.38W 10 6.8 6.7 5.5 2.6 64 加利福尼亚湾 7 16 07:40:57.5 16-15 1.89N 126.42E 50 6.1 6.0 5.7 1.3 101 马鲁古海峡 8 16 14:03:21.7 16-22 6.03S 151.48E 20 6.0 5.8 5.3 1.6 102 新不列颠地区 9 16 22:54:31.5 17-06 31.59S 71.62W 20 8.3 8.3 1.3 80 中智利海岸近海 10 16 23:18:40.3 17-07 31.45S 71.20W 30 6.8 6.8 2.3 91 中智利海岸近海 11 17 01:41:10.2 17-09 31.10S 71.45W 40 6.4 6.4 1.4 88 中智利海岸近海 12 17 03:55:17.5 17-11 31.10S 71.35W 40 6.5 6.5 1.9 67 中智利海岸近海 13 17 04:10:27.7 17-12 31.55S 71.70W 30 6.9 6.9 2.8 94 中智利海岸近海 14 18 09:10:50.0 18-17 32.25S 72.10W 25 6.3 6.3 2.3 93 中智利海岸近海 15 18 15:59:42.5 18-23 15.30N 46.00W 10 6.2 6.0 2.5 53 北大西洋海岭 16 19 12:52:19.7 19-20 32.25S 71.80W 10 6.4 6.4 1.4 99 中智利海岸近海 17 19 13:08:56.5 19-21 30.89S 72.68W 10 6.3 6.0 3.1 37 中智利海岸近海 18 21 05:39:32.6 21-13 31.55S 71.70W 20 6.2 6.1 1.2 92 中智利海岸近海 19 21 17:39:57.4 22-01 31.65S 71.60W 20 6.8 6.8 1.3 95 中智利海岸近海 20 24 15:53:28.8 24-23 0.55S 131.25E 30 6.5 6.2 5.9 1.3 97 西伊里安地区 21 24 15:56:53.8 24-23 9.81S 160.70E 18 6.4 6.2 5.9 0.7 71 所罗门群岛 22 26 02:51:15.7 26-10 30.80S 71.30W 30 6.3 6.3 1.2 102 中智利海岸近海 23 10-11 00:58:29.0 11-08 54.60S 135.80W 10 6.0 5.8 3.0 40 南太平洋山系 24 14 05:43:04.0 14-13 48.88N 156.25E 10 6.3 6.3 5.6 1.3 99 千岛群岛 25 17 11:33:08.0 17-19 24.89S 64.31W 10 6.0 5.9 2.2 74 阿根廷萨尔塔省 26 20 21:52:0.0 21-05 14.82S 167.32E 130 6.2 1.3 82 瓦努阿图(新赫布里底) 27 26 09:09:31.2 26-17 36.59N 70.79E 207 6.1 0.9 94 兴都库什地区 -
[1] Aki, K,1966. Generation and propagation of G}waves from the Niigata earthquake of June 16, 1964,2, Estimation of earthquake moment, released energy, and stress——strain drop from G——waves spectrum.Bulh Earthg, Rcs. Irur, Tokyo Uniu., 44, 7 3——88.
[2] Kanamori, H, and Stcwart, G. S,1978. Seismological aspects of the Guatemala earthquake of February, 4, 1976. J. Ccophys.Res., 83, 3427——3434.
[3] Das, S. and Aki, K., 1977. Fault plane with barriers:A versatile earthquake model. J. GcopJzys, Res.,82, 5658——5670.
[4] Madariaga, R,1979. On the relation between moment and stress drop in the presence of stress and strength heterogeneity. J. Geophys. Res., 84, 2243——2250.
[5] Rice, J., 1980. The mechanics of earthquake rupture. Proc. Int. Sch. Phys. Enrico Fermi. 78, 555——649.
[6] Aki, K., 1981. Characterization of barriers on an earthquake fault. J. Geophys. Res., 86, 1785——1793.
[7] Rudnicki, J. W, and Kanamori, H., 1981. Effects of fault inter: coon on moment, stress drop, and strain energy release. J. Geoplzys. Rcs., 86, 1785——1793.
[8] Rudnicki, J. W., Hiroshima, K. and Achenbach, J. D,1984. Amplification of moment and strain energy release due to interation between different size fault slip zone. J. Geophys. Res., 89, 5828——5834.
[9] Niu Zhireu, 1988. Stress and displacement field due to a penny——shaped shear crack with non——uniform traction. Geophys.J. R, Astr. Soc,94, 219——235.
[10] Keilis——Borok, V. I,1959. On the estimation of the displacement in an earthquake source and of source dimensions. Ann. Geofis., 12, 205——214.
[11] Rundle, J. B., Kanamori, H, and McNally, K. C., 1984.An inhomogeneous fault model for gaps, aspcrities, barriers, and seismicity migration. J, Geophys. Res,89, 10019——10231.
[12] Dmowska, R. and Rice, J., 1986. Fracture thory and its seismological applications, In "Corrtitrunz Theory in Solzd Earth Physics", ed. Teisseyre, R., Elsevier Publ. Co., Amsterdam, Polish Scient. Publ.,Warsaw.
[13] Niu Zhiren, 1984/85. Estimates of fracture parameters of earthquakes. Purc Appl. Geophys., 122, 645——661.[1] Aki, K,1966. Generation and propagation of G}waves from the Niigata earthquake of June 16, 1964,2, Estimation of earthquake moment, released energy, and stress——strain drop from G——waves spectrum.Bulh Earthg, Rcs. Irur, Tokyo Uniu., 44, 7 3——88.
[2] Kanamori, H, and Stcwart, G. S,1978. Seismological aspects of the Guatemala earthquake of February, 4, 1976. J. Ccophys.Res., 83, 3427——3434.
[3] Das, S. and Aki, K., 1977. Fault plane with barriers:A versatile earthquake model. J. GcopJzys, Res.,82, 5658——5670.
[4] Madariaga, R,1979. On the relation between moment and stress drop in the presence of stress and strength heterogeneity. J. Geophys. Res., 84, 2243——2250.
[5] Rice, J., 1980. The mechanics of earthquake rupture. Proc. Int. Sch. Phys. Enrico Fermi. 78, 555——649.
[6] Aki, K., 1981. Characterization of barriers on an earthquake fault. J. Geophys. Res., 86, 1785——1793.
[7] Rudnicki, J. W, and Kanamori, H., 1981. Effects of fault inter: coon on moment, stress drop, and strain energy release. J. Geoplzys. Rcs., 86, 1785——1793.
[8] Rudnicki, J. W., Hiroshima, K. and Achenbach, J. D,1984. Amplification of moment and strain energy release due to interation between different size fault slip zone. J. Geophys. Res., 89, 5828——5834.
[9] Niu Zhireu, 1988. Stress and displacement field due to a penny——shaped shear crack with non——uniform traction. Geophys.J. R, Astr. Soc,94, 219——235.
[10] Keilis——Borok, V. I,1959. On the estimation of the displacement in an earthquake source and of source dimensions. Ann. Geofis., 12, 205——214.
[11] Rundle, J. B., Kanamori, H, and McNally, K. C., 1984.An inhomogeneous fault model for gaps, aspcrities, barriers, and seismicity migration. J, Geophys. Res,89, 10019——10231.
[12] Dmowska, R. and Rice, J., 1986. Fracture thory and its seismological applications, In "Corrtitrunz Theory in Solzd Earth Physics", ed. Teisseyre, R., Elsevier Publ. Co., Amsterdam, Polish Scient. Publ.,Warsaw.
[13] Niu Zhiren, 1984/85. Estimates of fracture parameters of earthquakes. Purc Appl. Geophys., 122, 645——661.
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