Post on 18-Jan-2016
transcript
Lecture 19
VLF GPR
Phase
let
BPB
0cos(t) B
0cos(2ft) B
0cos(2
tT
)
BSB
0cos(t )
Phase difference is
Note =2f=2T
is angular frequency (radians/sec)
f is frequency (Hz)
T is period (sec)
Phasor
In phasecos(wt)
Advanced in phasecos(wt+Ф)
Ф
VR
V
VL
V
VR
VL
Voltage in inductorLeads voltage in Resistor (current) by 90 degrees
Total voltage leadsCurrent by Ф
Inductor
resistance
Ф
tanL
R
PHASE
since emf ABt
emf from induced currents is 90o out
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).
Magnetic versus non magnetic
Decay of electromagnetic radiation with depth in earth due to eddy currents
Velocity f
Amplitude A0e z / zS
= wavelength
v=velocity
f=frequency
=1/=conductivity
=resistivity
zs500
1f
500f
Low frequency
High frequency
GPR at Parkfield 2006
•Velocity in air>velocity in ground•Gives rise to a critically refractedray at the surface
•Critical angle obeys Snell’s lawSin(ic)=v1/v2
•Direct air wave alwaysarrives 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?
h
x
2 22T x h
V
% these are in nanosecsgpr5=[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))])
func.m for GPR Hyperbola
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 tiltOf field. If secondaryField is zero tilt is zero
0
2 2 2
0
2 2 2
Field for line current
2
/
/ 1
2
/
s
s
IB
r
I emf Z
Z R L
B tB
r R LRA L
Secondary field is less than 90+ degrees out of phaseWith the primary inducing field. Good conductor Poor conductor
0
0
cos( )
sin( )
B B t
emf AB tt
IR
I LemfT
Inducing fieldBocos(wt)
emf from Faraday’s law
Current=> BS
0
2 2 2sin( )
atan( / )
emfemfI t
Z R LL R
090 00
00
/ 2L / length ln( )
/ 2distance apart
thickness
h t
th
t
t
h
VLF over a dike
Mt Etna 2001 Lava Flow
Tilt and Ellipticity in % across 2001 Etna FlowShowing molten magma persists at depth in 2004
Uses of Electromagnetic methods
• Magma bodies
• Buried chambers
• Polluted water table
• Buried tanks, pipes
• Mineral exploration (e.g sulphides)
• Archaeology
• Oil reservoirs from boreholes
Magnetotellurics
From: Stacey, Physics of the Earth
s
Recall skin depth
1z 500 500
f f