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Lecture 8

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# Lecture 8 - PowerPoint PPT Presentation

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

Surface Field from a dipole

-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=x-x0;

xd2=x-x0-w;

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)^2-sin(I)^2)*(phi1-phi3);

F=A*(term1+term2);

% plot(x,F,'r')

% figure(1)

%%%%%% 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=y-mean(y);

[X,Y]=deg2utm(lat,lon);

x=X-420000;

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=F1-mean(F1);

f=f';

plot(x,y,'*',x,f,'linewidth',2)