﻿ 用<i>P</i>波初动资料确定地震震源机制教程（一）
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 地震地磁观测与研究  2021, Vol. 42 Issue (3): 1-14  DOI: 10.3969/j.issn.1003-3246.2021.03.001 0

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CHEN Yun-tai, LIU Ruifeng. The use of the first P motion data for earthquake focal mechanism determination: A tutorial (1)[J]. Seismological and Geomagnetic Observation and Research, 2021, 42(3): 1-14. DOI: 10.3969/j.issn.1003-3246.2021.03.001.

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P波初动资料确定地震震源机制教程（一）

1. 中国北京 100049 中国科学院大学地球与行星科学学院;
2. 中国北京 100081 中国地震局地球物理研究所

The use of the first P motion data for earthquake focal mechanism determination: A tutorial (1)
CHEN Yun-tai 1,2, LIU Ruifeng 2
1. College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
2. Institute of Geophysics, China Earthquake Administration, Beijing 100081, China
Abstract: The fundermental principal and technique for earthquake focal mechanism (fault-plane solution) from compression and dilatation distribution of the first P motion data are presented brieftly. Take graphic technique as an example, the related physical idea and technique, are illustated step by step, to meet various needs (such as general understanding, study, applications, etc.) of various readers (such as students, teachers, disaster-managers, etc.) of various professional background (such as seimology, geophysics, geology, geodesy, engineering seismology, disaster-science, management science, etc.)
Key words: focal mechanism solution    fault-plane solution    first motion of P wave    Wulff net    Schmidt net
0 引言

1 断层面解 1.1 P波初动的压缩与膨胀的分布

 图 1 由一个垂直于地面的断层FF′的纯水平运动产生的地震P波初动的压缩（实心圆）与膨胀（空心圆）的分布 Fig.1 Distribution of compression (solid circle) and dilatation (open circle) of initial motion of seismic P waves resulting from pure horizontal motion FF′ a fault perpendicular to the ground
 图 2 压缩初动（a）与膨胀初动（b） Fig.2 First motions of compression(a) dilatation(b)
1.2 震源球和离源角

 图 3 台站的延伸位置 (a) 表面震源；(b) 有一定深度的震源 Fig.3 The extended position of a station (a) For a surface source; (b) For any focal depth

 图 4 离源角 Fig.4 Take-off angle
 图 5 震源球 Fig.5 Focal sphere

 $\frac{{{r_h}\sin {i_h}}}{{{v_h}}} = \frac{{{r_0}\sin {i_0}}}{{{v_0}}},$ (1)

 $\sin {i_0} = {v_0}\frac{{{\rm{d}}t}}{{{\rm{d}}\Delta }},$ (2)

 $\sin {i_h} = \frac{{{r_0}}}{{{r_0} - h}}{v_h}\frac{{{\rm{d}}t}}{{{\rm{d}}\Delta }}.$ (3)

1.3 投影方法的应用 1.3.1 极射赤面投影.

 图 6 极射赤面投影 (a) 震源球下半球投影；(b) 震源球上半球投影 Fig.6 Stereographic progection (a) Lower hemispheric projection of focal sphere; (b) Upper hemispheric projection of focal sphere

 $r = R\tan (\frac{{{i_h}}}{2}).$ (4)

 图 7 震源球下半球等面积投影 Fig.7 Lower hemispheric equal-area projection of focal sphere
 图 8 乌尔夫网(a)和斯密特网(b) Fig.8 Wulff net (a) and Schmidt net(b)

1.3.2 等面积投影.

 $r = 2R\sin (\frac{{{i_h}}}{2}).$ (5)

P点的面积元R2sinihdihdφ经过投影，变成在P′点的面积元，且投影前后面积元的面积相等，即

 $2R\sin (\frac{{{i_h}}}{2}){\rm{d}}\varphi \frac{{\rm{d}}}{{{\rm{d}}{i_h}}}[2R\sin (\frac{{{i_h}}}{2})]{\rm{d}}{i_h} = {R^2}\sin {i_h}{\rm{d}}{i_h}{\rm{d}}\varphi,$ (6)

 图 9 正交条件 Fig.9 Orthogonal condition

1.3.3 其他投影方法.

 图 10 确定震中方向的伽里津Galitgin’s（Гaлицын）方法 Fig.10 Galitgin's method for determining the direction of an earthquake epicenter

 图 11 各种投影方法之比较 (a) 拜尔利（Byerly）所提出并采用的台站延伸位置概念与极射赤面投影方法；(b) 诺波夫（Knopoff）所采用的台站延伸位置概念与中心投影方法；(c) 斯陶德尔（Stauder）所采用的震源球概念与中心投影方法；(d) 震源球概念与极射赤面投影；(e) 震源球概念与等面积投影；(f) 本多弘吉(Honda) 所采用的机制图 Fig.11 Comparison of different projection methods (a) The concept of station extended position and stereographic projection method proposed and used by Byerly; (b) The concept of station extended position and central projection method used by Knopoff; (c) The concept of focal sphere and central projection method use by Stauder; (d) The concept of focal sphere and stereographic projection; (e) The concept of focal sphere and equal area projection; (f) The mechanism diagram used by Honda

1.3.4 各种方法的等效性.

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