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