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%% Dilatación volumétrica debido a una falla finita homogénea
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Variables de entrada para modelar el terremoto de Valdivia
Mo=9.64*1e22;
slip=112*pi/180;
dip=20*pi/180;
strike=0*pi/180;
l=850*1000;%579.927*1000;
c=64.5*1000;%62.428*1000;
c1=20*1000;
w=(c-c1)/sin(dip);
A=Mo/(3*1e10*l*w);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%
%
mhu=3*1e10;
lambda=3*1e10;
alpha=(lambda+mhu)/(lambda+2*mhu);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%
%
x1=250*1000;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Ymax=300*1000;
Ymin=-150*1000;
deltaY=-40*1000;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Zmax=0*1000;
Zmin=-150*1000;
deltaZ=10*1000;
IK
4'E
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%
%
for tip=1:2
if tip==1
tipo='stk';
elseif tip==2
tipo='dip';
end
k1=0;
for y1=Ymax:deltaY:Ymin
for z=Zmin:deltaZ:Zmax
y=x1*sin(strike)+y1*cos(strike);
x=x1*cos(strike)-y1*sin(strike);
for k=[z -z]
d=c-k;
p=y*cos(dip)+d*sin(dip);
q=y*sin(dip)-d*cos(dip);
shi1=x-l;
shi2=x;
etha1=p-w;
etha2=p;
i1=0;
for i=[shi1 shi2]
for j=[etha1 etha2]
R=sqrt(i^2+j^2+q^2);
Y=j*cos(dip)+q*sin(dip);
D=j*sin(dip)-q*cos(dip);
C=D+k;
S=comp(R,i,j,dip,q,k);
K=sub(R,D,i,q,S(4),dip,Y);
J=jotas(R,i,Y,D,K(1),K(2),K(4),S(4),dip);
L=sud_2(R,Y,D,C,S(1),S(2),S(5),S(7),S(9),dip,q,k,i);
N=sud_3(R,Y,D,C,S(1),S(2),S(5),S(7),S(9),dip,q,k,i);
switch lower (tipo)
IG
4'E
case {'stk'}
U=A*cos(slip);
fa1=-((1-alpha)/2)*q*S(4)-(alpha/2)*i^2*q*S(5);
fb1=i^2*q*S(5)-((1-alpha)/alpha)*J(1)*sin(dip);
fc1=(1-alpha)*S(8)*cos(dip)-alpha*q*S(9);
ka2=(alpha/2)*L(1);
kb2=-L(1)+((1-alpha)/alpha)*((1/R)+J(5))*sin(dip);
kc2=2*(1-alpha)*((D/R^3)-S(8)*sin(dip))*sin(dip)(Y/R^3)*cos(dip)-alpha*(((C+D)/R^3)*sin(dip)-(j/R^3)-((3*C*Y*q)/R^5));
ka3=((1-alpha)/2)*((cos(dip)/R)+q*S(4)*sin(dip))(alpha/2)*q*L(2);
kb3=q*L(2)-((1-alpha)/alpha)*(q*S(4)-J(6))*sin(dip);
kc3=-(1-alpha)*(q/R^3)+((Y/R^3)-S(8)*cos(dip))*sin(dip)
+alpha*(((C+D)/R^3)*cos(dip)+((3*C*D*q)/R^5)-(S(8)*cos(dip)
+q*S(9))*sin(dip));
la2=(alpha/2)*N(1);
lb2=-N(1)+((1-alpha)/alpha)*Y*K(1)*sin(dip);
lc2=2*(1-alpha)*((Y/R^3)-S(8)*cos(dip))*sin(dip)+
(D/R^3)*cos(dip)-alpha*(((C+D)/R^3)*cos(dip)+((3*C*D*q)/R^5));
la3=-((1-alpha)/2)*((sin(dip)/R)-q*S(4)*cos(dip))(alpha/2)*q*N(2);
lb3=q*N(2)+((1-alpha)/alpha)*K(3)*sin(dip);
lc3=((Y/R^3)-S(8)*cos(dip))*cos(dip)alpha*(((C+D)/R^3)*sin(dip)-((3*C*Y*q)/R^5)S(8)*(sin(dip))^2+q*S(9)*cos(dip));
fc2=(1-alpha)*((cos(dip)/R)+2*q*S(4)*sin(dip))alpha*((C*q)/R^3);
fc3=(1-alpha)*q*S(4)*cos(dip)-alpha*(((C*j)/R^3)k*S(4)+i^2*S(7));
case {'dip'}
U=A*sin(slip);
fa1=-(alpha/2)*((i*q)/R^3);
fb1=((i*q)/R^3)+((1-alpha)/alpha)*J(4)*sin(dip)*cos(dip);
fc1=-(1-alpha)*(i/R^3)*cos(dip)+i*q*S(5)*sin(dip)
+alpha*((3*C*i*q)/R^5);
ka2=((1-alpha)/2)*D*S(1)+(i/2)*S(4)*sin(dip)+
I=
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(alpha/2)*j*L(3);
kb2=-j*L(3)-i*S(4)*sin(dip)+((1alpha)/alpha)*J(2)*sin(dip)*cos(dip);
kc2=(1-alpha)*(S(1)-Y^2*S(2))alpha*C*((D+2*q*cos(dip))*S(2)-Y*j*q*S(3));
ka3=((1-alpha)/2)*Y*S(1)-(alpha/2)*q*L(3);
kb3=q*L(3)+((1-alpha)/alpha)*J(3)*sin(dip)*cos(dip);
kc3=i*L(5)*sin(dip)
+Y*D*S(2)+alpha*C*((Y+2*q*sin(dip))*S(2)-Y*q^2*S(3));
la2=((1-alpha)/2)*Y*S(1)+(i/2)*S(4)*cos(dip)+
(alpha/2)*j*N(3);
lb2=-j*N(3)-i*S(4)*cos(dip)-((1alpha)/alpha)*i*K(1)*sin(dip)*cos(dip);
lc2=(1-alpha)*Y*D*S(2)-alpha*C*((Y2*q*sin(dip))*S(2)+D*j*q*S(3));
la3=-((1-alpha)/2)*D*S(1)-(alpha/2)*q*N(3);
lb3=q*N(3)-((1-alpha)/alpha)*K(5)*sin(dip)*cos(dip);
lc3=-i*N(5)*sin(dip)+S(1)-D^2*S(2)-alpha*C*((D2*q*cos(dip))*S(2)-D*q^2*S(3));
fc2=(1-alpha)*Y*S(1)-alpha*C*j*q*S(2);
fc3=-D*S(1)-i*S(4)*sin(dip)-alpha*C*(S(1)-q^2*S(2));
end
if k==z
i1=i1+1;
j1(i1,:)=[fa1 fb1 fc1];
k2(i1,:)=[ka2 kb2 kc2];
k3(i1,:)=[ka3 kb3 kc3];
l2(i1,:)=[la2 lb2 lc2];
l3(i1,:)=[la3 lb3 lc3];
uz(i1,:)=[fc2 fc3];
elseif k==-z
i1=i1+1;
J1(i1,:)=fa1;
K2(i1,:)=[ka2 ka3];
L2(i1,:)=[la2 la3];
end
J/
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end
end
end
j1a=j1(4,1)-j1(3,1)-j1(2,1)+j1(1,1);
j1b=j1(4,2)-j1(3,2)-j1(2,2)+j1(1,2);
k2a=k2(4,1)-k2(3,1)-k2(2,1)+k2(1,1);
k2b=k2(4,2)-k2(3,2)-k2(2,2)+k2(1,2);
k3a=k3(4,1)-k3(3,1)-k3(2,1)+k3(1,1);
k3b=k3(4,2)-k3(3,2)-k3(2,2)+k3(1,2);
l2a=l2(4,1)-l2(3,1)-l2(2,1)+l2(1,1);
l2b=l2(4,2)-l2(3,2)-l2(2,2)+l2(1,2);
l3a=l3(4,1)-l3(3,1)-l3(2,1)+l3(1,1);
l3b=l3(4,2)-l3(3,2)-l3(2,2)+l3(1,2);
u2c=uz(4,1)-uz(3,1)-uz(2,1)+uz(1,1);
j1A=J1(4)-J1(3)-J1(2)+J1(1);
j1c=j1(4,3)-j1(3,3)-j1(2,3)+j1(1,3);
k2A=K2(4,1)-K2(3,1)-K2(2,1)+K2(1,1);
k2c=k2(4,3)-k2(3,3)-k2(2,3)+k2(1,3);
k3A=K2(4,2)-K2(3,2)-K2(2,2)+K2(1,2);
k3c=k3(4,3)-k3(3,3)-k3(2,3)+k3(1,3);
l2A=L2(4,1)-L2(3,1)-L2(2,1)+L2(1,1);
l2c=l2(4,3)-l2(3,3)-l2(2,3)+l2(1,3);
l3A=L2(4,2)-L2(3,2)-L2(2,2)+L2(1,2);
l3c=l3(4,3)-l3(3,3)-l3(2,3)+l3(1,3);
u3c=uz(4,2)-uz(3,2)-uz(2,2)+uz(1,2);
dUx=(U/(2*pi))*(j1a-j1A+j1b+z*j1c);
dUy=(U/(2*pi))*((k2a-k2A+k2b+z*k2c)*cos(dip)-(k3ak3A+k3b+z*k3c)*sin(dip));
dUz=(U/(2*pi))*((l2a+l2A+l2b-u2c-z*l2c)*sin(dip)+(l3a+l3A+l3b-u3cz*l3c)*cos(dip));
if tipo=='stk'
k1=k1+1;
dUs(k1,:)=dUx+dUy+dUz;
elseif tipo=='dip'
k1=k1+1;
dUd(k1,:)=dUx+dUy+dUz;
end
end
end
end
dUt=dUs+dUd;
X=[]; Z=[]; Y=[];
for y1=Ymax:deltaY:Ymin
for z=Zmin:deltaZ:Zmax
Z=[Z z/1000];
J0
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%Y=[Y -1*(((y/1000)-177.2)/86)-74.83];
Y=[Y -1*(y1/1000)];
X=[X 40];
end
end
X=X'; Y=Y'; Z=Z';
M=[X Y Z dUt];
fid1=fopen('deform_YZ_s0.txt','w');
fprintf(fid1,'%3.3f %3.3f %3.3f %16.15f\n',M');
fclose(fid1);
121
$%)
-"/ ##Gráfica el campo de deformación y fuerza
reg=-76/-71.4816/-60/5
reg2=-76.5979/-71.4816/-200/0
ps=grad_YZmorenoN_10.ps
more deform_cosisYZ_moreno680_10.txt
fza_yz_cosis.xyz
|
awk
'{print
$2,
$3,
$4}'
>
more deform_cosisYZ_moreno680_10.txt | awk '{print (($2+177.2)/86)-75.10,
$3, $4}' > deform_yz_cosis.xyz
surface deform_yz_cosis.xyz -Gdeform_yz_cosis.grd -R$reg2 -I0.058139/1.0
grd2cpt deform_yz_cosis.grd -Cred2green -R$reg2 > grad.cpt
## Pone color a los contornos
grdimage deform_yz_cosis.grd -Cgrad.cpt
> $ps
-B1/20WsNe -JX15.0 -R$reg -P -V -K
## Grafica los contornos de dilatación o compresión
grdcontour deform_yz_cosis.grd -B1/20WsNe -JX15
-W0.5p/0/0/0 -Gd10c -O -K >> $ps
-C0.5
-A2.0
-R$reg
## Calcula las derivadas de los achivos en kilometros
surface fza_yz_cosis.xyz -Gfza_yz_cosis.grd -R-300/140/-200/0 -I5.0/1.0
grdmath fza_yz_cosis.grd DDX = dPdy_cosis.grd
J.
4'E
grdmath fza_yz_cosis.grd DDY = dPdz_cosis.grd
## combierte las derivadas grd en xyz ya en grados
grd2xyz dPdy_cosis.grd > dPdy_cosis.xyz
grd2xyz dPdz_cosis.grd > dPdz_cosis.xyz
more dPdy_cosis.xyz | awk '{print ((($1+177.2)/86)-75.10), $2, $3}' >
dPdy_cosisGR.xyz
more dPdz_cosis.xyz | awk '{print ((($1+177.2)/86)-75.10), $2, $3*1}' >
dPdz_cosisGR.xyz
#Cambia las derivadas de archivo xyz a grd
surface dPdy_cosisGR.xyz -GdPdy_cosisGR.grd -R$reg2 -I0.058139/1.0
surface dPdz_cosisGR.xyz -GdPdz_cosisGR.grd -R$reg2 -I0.058139/1.0
# Grafica los vectores de fuerza
grdvector dPdy_cosisGR.grd dPdz_cosisGR.grd -I0.09/7.5
-Q0.03i/0.12i/0.09in0.55i -G0 -S0.5i -O -K >> $ps
-JX15.0
-R$reg
# grafica el plano de falla
psxy -R$reg -JX15.0 -W20/0/0/255 -O -K <<END>> $ps
-75.15 -4.148
-73.06 -55
END
## pone la topografia
project -C-76.678/-40.58 -E-70.562/-40.58 -G0.001 > track2.xy
grdtrack track2.xy -Gw100s10.Bathymetry.srtm.grd > topotrack2.xydz
more topotrack2.xydz | awk '{print $1, ($4+650)/1000}' |psxy -R$reg -JX15.0
-B -W8/0/0/255 -O -K >> $ps
JI