File:Position hypocentre selon delais arrivee onde 2 stations.png

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Summary[edit]

Positions possible de l'hypocentre d'un séisme en fonction du délais d'arrivée de l'onde aux stations sismographiques (unités arbitraires).

Valeurs de

${\displaystyle {\sqrt {(x-x_{A})^{2}+(y-y_{A})^{2}+(z-z_{A})^{2}}}-{\sqrt {(x-x_{B})^{2}+(y-y_{B})^{2}+(z-z_{B})^{2}}}}$

pour y fixé (y=y_A=y_B=0), c'est la coupe d'un hyperboloïde à deux nappes.

La localisation nécessite au moins trois stations (intersection de trois surfaces equi-délais).

Possible positions of an earthquake hypocenter according to the delay of arrival of the waves to two distant seismograph stations (arbitrary units).

Values of

${\displaystyle {\sqrt {(x-x_{A})^{2}+(y-y_{A})^{2}+(z-z_{A})^{2}}}-{\sqrt {(x-x_{B})^{2}+(y-y_{B})^{2}+(z-z_{B})^{2}}}}$

for fixed y-value (y=y_A=y_B=0), it is the cut of a two sheets hyperboloid.

The localisaiton requires at least three stations (intersection of three equi-delay surfaces).

Auteur/author : Christophe Dang Ngoc Chan (cdang)

Réalisé avec/made with Scilab

clear;clf;

// position des stations

xa=-1;za=0;
xb=1;zb=0;

// calcul de la différence de distance entre le point (x,0,z) et A et B

deff('d=f(x,z)','d=sqrt((x-xa)^2+(z-za)^2)-sqrt((x-xb)^2+(z-zb)^2)');

// limites du domaine et pas

xmin=-5;xmax=5;
zmin=-5;zmax=0; // l'hypocentre est sous terre, z<0
pas=0.1;

// calcul

X=[xmin:pas:xmax]';
Z=[zmin:pas:zmax]';

D=feval(X,Z,f);

// tracé

contour2d(X,Z,D,[-1.5,-1,0,1,1.5])

plot2d([xa,xb],[za,zb],style=-1)
xtitle('Position possible de l''épicentre en fonction du délais (unités  arbitraires)','x', 'Profondeur')

xstring(xa-0.05,za-0.3,'A')
xstring(xb-0.05,zb-0.3,'B')

Licensing[edit]

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