Transcript ESS135_2013_Lecture18+

Lecture 19
VLF GPR
Phase
let
t
BP  B0 cos(t)  B0 cos(2ft)  B0 cos(2 )
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 (current) 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
of phase with inducing field. But if the body has
since emf   A
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.
-
Vlf meter measures tilt
Of field. If secondary
Field is zero tilt is zero
Field for line current
Bs 
0 I
2 r
I  emf / Z
Z  R 2  2 L2
 B / t
1
Bs   0
2 r
R 2  2 L2
  RA / L
Current=> BS
Inducing field
Bocos(wt)

emf from Faraday’s law
B  B0 cos(t )

emf  
 AB0 sin(t )
t
emfT
I L

IR
emf 0
emf

sin(t   )
2
2 2
Z
R  L
Secondary field is less than 90+ degrees out of phase
  atan( L / R )
With the primary inducing field.
0
Good conductor   90
0
Poor conductor   0
I
VLF over a dike
L0 / length 
0 h  t / 2
ln(
)

t/2
h  distance apart
t  thickness
t
h
Mt Etna 2001 Lava Flow
Tilt and Ellipticity in % across 2001 Etna Flow
Showing molten magma persists at depth in 2004
Uses of Electromagnetic methods
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Magma bodies
Buried chambers
Polluted water table
Buried tanks, pipes
Mineral exploration (e.g sulphides)
Archaeology
Oil reservoirs from boreholes
Magnetotellurics
Recall skin depth
z s  500
1

 500
f
f
From: Stacey, Physics of the Earth