Lecture 8. Magnetic Dipoles. Comparing with equation (1). Surface Field from a dipole. m. . +m. +. M is magnetic moment; M=m Δz=JV. Magnetic Susceptibility. H. I. Z. Magnetic north. x. z. R. function F=magdike(x,x0,k,Fe,w,z1,I,beta);
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Lecture 8
Magnetic Dipoles
Comparing with equation (1)
m

+m
+
M is magnetic moment; M=m Δz=JV
H
I
Z
Magnetic north
x
z
R
function F=magdike(x,x0,k,Fe,w,z1,I,beta);
%%%% magnetic field from a vertical dike using Telford Eq.3.44c
%%%% I = inclination (degrees)
%%%% beta= strike (degrees) of dike anticlockwise from North magnetic
%%% x = coordinates
%%% x0 = the dike location
%%% k = susceptibility factor
%%% Fe = Earth's field
%%% w = dike width
%%% z1 = depth to top of dike
%%% I = inclination in degrees
%%% Bring angles to radians
I=I*pi/180;beta=beta*pi/180;
%%% Constant term
A=2*Fe*k;
xd1=xx0;
xd2=xx0w;
phi1=atan2(z1,xd1); r1=sqrt(z1^2+xd1.^2);
phi3=atan2(z1,xd2); r3=sqrt(z1^2+xd2.^2);
term1=sin(2*I)*sin(beta)*log(r3./r1);
term2=(cos(I)^2*sin(beta)^2sin(I)^2)*(phi1phi3);
F=A*(term1+term2);
% plot(x,F,'r')
% figure(1)
MAGNETIC FIELD FROM A DIKE
ϕ2
0
X
X0
Φ1
r1
r2
D
%%%%%% plots mag data for day 2 Trona Field trip.
%%%%%
clf
data=load('magnetic_readings_20120128.dat');
n1=47;n2=145;
y=data(n1:n2,3)';
lat=data(n1:n2,6);
lon=data(n1:n2,7);
y=ymean(y);
[X,Y]=deg2utm(lat,lon);
x=X420000;
plot(x,y,'*')
Fe=50000;
%%% Dike 1
I=60;
beta=10;
x0=a(2);
k=a(1);
z1=a(3);w=20;
F1=magIdike(x,x0,k,Fe,w,z1,I,beta);
f=F1mean(F1);
f=f';
plot(x,y,'*',x,f,'linewidth',2)