Download ESS135_2013_Lecture17+

Lecture 16
Electromagnetic Surveying
Chapter 13 Induced Polarization IP
and Self-Potential SP
• IP charge stored in an ore when a current
flows, it decays when current is turned off
• SP small voltages (potentials) generated
naturally
IP
• Conducting ores in non
conducting matrix
• As current flows electrons
pass through conducting
grain, but delays occur.
• When I=0, acts as a
capacitor that discharges
with time
-
+
Chargeability
chargeability=
1
(area under curve)
Vc
Shallow , massive pyrrhotite
Body (FeS) ore in steeply
dipping sheets
Chapter 14 Electromagnetic
methods
T
frequency
f=1/T=1/period
BASIC PHYSICS
Thumb in direction of I
Fingers curl in direction of B
Flux=Magnetic field  Area
=BA
(1)
FARADAYS LAW
 ( BA)


t
t
B is magnetic field
A is area
 is flux.
emf= 
B
(2)
Magnetic field threading an
conductor
Bp=Bprimary
Bs=Bsecondary
Bp=Bprimary
Emf=>IS
Bs
Bp
Currents (eddy) are setup in the conductor that
Try to cancel B. But if there is resistance they are out of phase
and do not perfectly cancel.
Ohm’s Law for AC field
emf=I R 2  (2 fL) 2  I R 2  ( L) 2
L  Inductance (Henries)
Note at f=0
emf=IR
(same as Ohm's law).
phase =atan(
voltage.
2 fL
) between current and
R
Phase
let
BP  B0 cos( t )  B0 cos(2 ft )  B0 cos(2 t / T )
BS  B0 cos( t  )
Phase difference is 
2
Note =2f=
T
 is angular frequency (radians/sec)
f is frequency (Hz)
T is period (sec)
Phasor
Advanced in phase
cos(wt+Ф)
Ф
In phase
cos(wt)
VR
resistance
V
VL
Voltage in inductor
Leads voltage in
Resistor by 90 degrees
Inductor
V
Total voltage leads
Current by Ф
VL
Ф
tan  
L
R
VR
Magnetic versus non magnetic
PHASE
B
t
emf from induced currents is 90o out
since emf   A
of phase with inducing field. But if the body has
inductance the phase may be different > 90o
However if the body is magnetic and the secondary field is mainly
due to magnetism rather than eddy currents
BSecondary  BPr imary
i.e., in phase. So phase can be used to distinguish
between gold (non-magnetic)
and steel (magnetic).
Decay of electromagnetic radiation with
depth in earth due to eddy currents
Velocity  f  
Amplitude  A0 e  z / zS
 = wavelength
v=velocity
f=frequency
=1/=conductivity
=resistivity
z s  500
1

 500
f
f
High frequency
Low frequency
GPR at Parkfield 2006
•Velocity in air>velocity in ground
•Gives rise to a critically refracted
ray at the surface
•Critical angle obeys Snell’s law
Sin(ic)=v1/v2
•Direct air wave always
arrives first.
Ground Penetrating Radar
f=100 Mhz
V=0.3c=1x108 m/s=0.1 nm/s
lambda=108/108=1m.
zs=500sqrt(20/108)=0.22 meters
EM wave in air
Refracted wave
Reflected wave
Steel at 6.9 meters distance?
T
2 2
x  h2
V
x
h
func.m for GPR Hyperbola
% these are in nanosecs
gpr5=[85 70 62 50 45 50 60 70 80];
%v=0.3 m/ns in air
%a=[75 0.3 2];
y=gpr5;
xx=[62.5:2.5:82.5];
x0=a(1);
v=a(2);
z=a(3);
x=xx-x0;
f=2/v*sqrt(x.^2+z^2);
plot(x,f,x,y,'*')
figure(1);
xlabel ('Distance, (m)')
ylabel('Time (ns)')
title('GPR Line 5 hyperbola')
text(-5,80, ['depth ',num2str(a(3)),' v= ',num2str(a(2))])
Very Low Frequency method (VLF)
• Portable
• f=23 KHz used skin depth several hundred
m compared with GPR
• Used to contact submarines
• Antennas Hawaii, Maine, Portland,
Moscow, France etc.