関数tws_set_MandFandT_double_couple マニュアル

(The documentation of function tws_set_MandFandT_double_couple)

Last Update: 2021/12/8


◆機能・用途(Purpose)

大きさと向きで与えられた地震波動ソースを 直交座標に沿った行列成分表記に変換する。 ダブルカップル型のメカニズム用。
Convert the mechanism of a seismic wave source, given by the magnitude and orientation, to matrix representations based on a cartesian coordinate, for a double-couple type source mechanism.


◆形式(Format)

#include <tws/source.h>
inline void tws_set_MandFandT_double_couple
(const double intensity,const double strike, const double dip,const double rake,
 struct matrix ∗M,struct columnvector ∗F, struct columnvector ∗T)


◆引数(Arguments)

intensity 地震モーメント。
The seismic moment.
strike 断層の走向(rad)。
Strike (rad) of the source fault.
dip 断層の傾斜角(rad)。
Dip angle (rad) of the source fault.
rake 断層すべりのrake角(rad)。
Rake angle (rad) of the dislocation on the source fault.
M 計算したモーメントテンソル成分から成る行列の代入先。 宣言しただけの構造体を渡す。 関数内で\(3\times 3\)行列として動的メモリの確保と値の設定が行われる。 モーメントテンソル成分\(M_{ij}\)が (∗M).main[i][j]に代入される。 ここで\(i,j=0,1,2\)はそれぞれ\(x\), \(y\), \(z\)成分を表す。
A memory into which a matrix composed of the moment tensor components is inserted. Give a structure which is only declared (without setting the values). In the function, the dynamic memories for a \(3\times 3\) is allocated and the values are set. Each moment tensor component \(M_{ij}\) is inserted into (∗M).main[i][j]. Here, \(i,j=\) 0, 1, and 2 represent \(x\)-, \(y\)-, and \(z\)-components, respectively.
F 計算したシングルフォース成分から成る行列の代入先。 宣言しただけの構造体を渡す。 関数内で3成分の列ベクトルとして動的メモリの確保と値の設定が行われる。 シングルフォース成分\(F_i\)が (∗F).main[i]に代入される。 ここで\(i=0,1,2\)はそれぞれ\(x\), \(y\), \(z\)成分を表す。
A memory into which a matrix composed of the single force components is inserted. Give a structure which is only declared (without setting the values). In the function, the dynamic memories for a 3-component column vector is allocated and the values are set. Each single force component \(F_i\) is inserted into (∗F).main[i]. Here, \(i=\) 0, 1, and 2 represent \(x\)-, \(y\)-, and \(z\)-components, respectively.
T 傾斜変動を相反定理を用いて計算するために観測点の位置に置く 仮想的なソース成分 ( 利用できるメカニズム一覧のtilt, tilt2の説明参照) から成る行列の代入先。 宣言しただけの構造体を渡す。 関数内で6成分の列ベクトルとして動的メモリの確保と値の設定が行われる。 水管傾斜計用の仮想ソースの3成分\(T_i\)が(∗T).main[i]に、 ボアホール型傾斜計用の仮想ソースの3成分\(T_{2i}\)が (∗T).main[i+3]に代入される。 ここで\(i=0,1,2\)はそれぞれ\(x\), \(y\), \(z\)成分を表す。
A memory into which a matrix composed of virtual source components, exerted at the station location to compute tilt based on the reciprocity theorem (see the descriptions for tilt and tilt2 in List of mechanisms available), is inserted. Give a structure which is only declared (without setting the values). In the function, the dynamic memories for a 6-component column vector is allocated and the values are set. The three components of the virtual source for a water tube tiltmeter (\(T_i\)) are inserted into (∗T).main[i], and that for a borehole tiltmeter (\(T_{2i}\)) are inserted into (∗T).main[i+3]. Here, \(i=\) 0, 1, and 2 represent \(x\)-, \(y\)-, and \(z\)-components, respectively.


◆使用例(Example)

double intensity=1.0e+12;
double strike=30.0∗pi/180.0;
double dip=45.0∗pi/180.0;
double rake=60.0∗pi/180.0;
struct matrix M;
struct columnvector F;
struct columnvector T;
tws_set_MandFandT_double_couple (intensity,strike,dip,rake,&M,&F,&T);


◆代入される値(Values inserted)

以下で\(m\), \(\phi_s\), \(\delta\), \(\lambda\)はそれぞれ 引数intensity, strike, dip, rakeの値を表す。 また単位ベクトル\(\myvector{v_s}\), \(\myvector{v_d}\), \(\myvector{\nu}\), \(\myvector{v_u}\)を下表のように定義する。
Below, \(m\), \(\phi_s\), \(\delta\), and \(\lambda\) represent the values of arguments intensity, strike, dip, and rake, respectively. Unit vectors \(\myvector{v_s}\), \(\myvector{v_d}\), \(\myvector{\nu}\), and \(\myvector{v_u}\) are defined based on the table below.

単位ベクトルの定義 (Definitions of unit vectors)
ベクトル
Vector
意味
Meaning
x成分
\(x\)-component
y成分
\(y\)-component
z成分
\(z\)-component
\(\myvector{v_s}\) 走向方向の単位ベクトル。
A unit vector in the strike direction.
\(\sin\phi_s\) \(\cos\phi_s\) 0
\(\myvector{v_d}\) 傾斜方向の単位ベクトル。
A unit vector in the dip direction.
\(\cos\phi_s\cos\delta\) \(-\sin\phi_s\cos\delta\) \(-\sin\delta\)
\(\myvector{\nu}\) 断層法線方向の単位ベクトル。
A unit vector in the direction normal to the fault plane.
ベクトル積\(\myvector{v_s}\times\myvector{v_d}\)。 成分を\(\myvector{\nu}=(\nu^x,\nu^y,\nu^z)\)と表す。
A vector product \(\myvector{v_s}\times\myvector{v_d}\). The components are denoted as \(\myvector{\nu}=(\nu^x,\nu^y,\nu^z)\).
\(\myvector{v_u}\) 変位の食い違い方向の単位ベクトル。
A unit vector in the direction of the slip dislocation.
ベクトル\(\myvector{v_s}\cos\lambda-\myvector{v_d}\sin\lambda\)。 成分を\(\myvector{v_u}=(v_u^x,v_u^y,v_u^z)\)と表す。
A vector \(\myvector{v_s}\cos\lambda-\myvector{v_d}\sin\lambda\). The components are denoted as \(\myvector{v_u}=(v_u^x,v_u^y,v_u^z)\).

代入される値 (Values inserted)
代入先
Place to insert
代入先の意味
Meaning of the place to insert
代入される値
The value inserted
(∗)M.main[0][0] \(M_{xx}\) \(2m \nu^x v_u^x\)
(∗)M.main[0][1] \(M_{xy}\) \(m (\nu^x v_u^y + \nu^y v_u^x)\)
(∗)M.main[0][2] \(M_{xz}\) \(m (\nu^x v_u^z + \nu^z v_u^x)\)
(∗)M.main[1][0] \(M_{yx}\) \(m (\nu^y v_u^x + \nu^x v_u^y)\)
(∗)M.main[1][1] \(M_{yy}\) \(2m \nu^y v_u^y\)
(∗)M.main[1][2] \(M_{yz}\) \(m (\nu^y v_u^z + \nu^z v_u^y)\)
(∗)M.main[2][0] \(M_{zx}\) \(m (\nu^z v_u^x + \nu^x v_u^z)\)
(∗)M.main[2][1] \(M_{zy}\) \(m (\nu^z v_u^y + \nu^y v_u^z)\)
(∗)M.main[2][2] \(M_{zz}\) \(2m \nu^z v_u^z\)
(∗)F.main[0] \(F_{x}\) 0.0
(∗)F.main[1] \(F_{y}\) 0.0
(∗)F.main[2] \(F_{z}\) 0.0
(∗)T.main[0] \(T_{x}\) 0.0
(∗)T.main[1] \(T_{y}\) 0.0
(∗)T.main[2] \(T_{z}\) 0.0
(∗)T.main[3] \(T_{2x}\) 0.0
(∗)T.main[4] \(T_{2y}\) 0.0
(∗)T.main[5] \(T_{2z}\) 0.0