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

c

1chargeability= (area under curve)

V

Shallow , massive pyrrhotiteBody (FeS) ore in steeply dipping sheets

Chapter 14 Electromagnetic methods

T

frequencyf=1/T=1/period

BASIC PHYSICS

Thumb in direction of I Fingers curl in direction of B

B

FARADAYS LAW

( )emf=

B is magnetic field

A is area

is flux.

BA

t t

(2)

Flux=Magnetic field Area

=BA

(1)

Magnetic field threading an conductor

Bp=Bprimary

Bs=Bsecondary Emf=>IS

Bp=Bprimary

Bs

Bp

Currents (eddy) are setup in the conductor thatTry to cancel B. But if there is resistance they are out of phaseand do not perfectly cancel.

Ohm’s Law for AC field

2 2 2 2emf=I R (2 ) I R ( )

Inductance (Henries)

Note at f=0

emf=IR

(same as Ohm's law).

2phase =atan( ) between current and

voltage.

fL L

L

fLR

Phase

P 0 0 0

S 0

let

B cos( ) cos(2 ) cos(2 / )

B cos( )

Phase difference is

2Note =2 f=

is angular frequency (radians/sec)

is frequency (Hz)

is period (sec)

B t B ft B t T

B t

T

f

T

Phasor

In phasecos(wt)

Advanced in phasecos(wt+Ф)

Ф

VR

V

VL

V

VR

VL

Voltage in inductorLeads voltage in Resistor by 90 degrees

Total voltage leadsCurrent by Ф

Inductor

resistance

Ф

tanL

R

o

o

PHASE

since

from induced currents is 90 out

of phase with inducing field. But if the body has

inductance the phase may be different > 90

However if the body is magnetic and the secondary

Bemf A

t

emf

Pr

field is mainly

due to magnetism rather than eddy currents

i.e., in phase. So phase can be used to distinguish

between gold (non-magnetic)

and steel (magnetic).

Secondary imaryB B

Magnetic versus non magnetic

Decay of electromagnetic radiation with depth in earth due to eddy currents

/0

s

= wavelength

v=velocity

f=frequency

=1/ =conductivity

=resistivity

1z 500 500

Sz z

Velocity f

Amplitude A e

f f

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.