Electromagnetic Methods

By Doddy Sutarno

Electromagnetic Theory and Classification

IntroductionElectromagnetic methods provide another way of estimating the resistivity properties of the earth with two benefits compared to DC methods:– Depth sounding by

making measurements at multiple frequencies, or different times after some excitation.

– Contact for electrodesis not necessarily required.

The TransformerWithout making contact to the main power source, a transformer will provide electricity to light bulb (or house).The same physics will allow us to determine resistivity of the earth.To understand we need Maxwell’s Equations. But first some background….

Electromagnetic Field Quantities

Vector Fields– E,e = electric field (volts/m)– H,h = magnetizing force

intensity (A/m)– B,b = magnetic induction

or flux density (Tesla)– D,d = dielectric

displacement (Coulomb/m2)– I,i = current density (A/m2)– V= Voltage (Volts)

Relationships between fieldsD= E where is the dielectric permittivityUnits = Farads/ m (capacitance)= r 00 Dielectric permitivity of free space (8.85x10-12 f/m)r = relative dielectric permitivity or dielectric constantr =1 in airr =80 in water

B=H =magnetic permeabilityUnits = Henrys/m (Inductance) = r 0

0 magnetic permeability of free space (4px10-7H/m)r=relative mag permJ =σ Eσ =electrical conductivity of earthVoltage: V = Edl or E =-V

E

Maxwell’s EquationsFaraday’s Law :

Ampere’s Law :

Gauss’s Law :

Unnamed equation:– (Note, qc is charge

density in Coulombs/m3).

GAUSS LAW

EEDJH σε

tt)(

ttB

)( HE μ

cq )( ED ε

0 B

Wave EquationsAmpere’s and Faraday’s laws can be combined to yield

and/or

Propagation or Radar regime If f >107 Hz or 1/ =σ =0, then >> σ

Induction or Diffusion regime If f < 105, then << σ

2

22

tt

EEE εμμσ

2

22

tt

HHH εμμσ

2

22

t

EE εμ

t

EE μσ2

Solution to Wave Equations indiffusive regime

If the wave is a plane wave traveling in the z direction, solution to wave equation given as

Note that E and H are orthogonal.

2

)cos(

)cos(

0

0

ωμσ

ω

ω

aWhere

azteHH

azteEEaz

y

azx

EM Wave Propagation and Attenuationcos(t-az) indicates wave is propagating as a sinusoid in the z direction.e-az indicates wave is also decaying, or attenuating in the z direction.Skin Depth () defined as the depth at which wave amplitude has decayed to 1/e its original value.– =1/a.– 503(ρ/f)1/2 in meters

Skin Depth yields estimate of maximum depth sensitivity for EM methods.Resistivity/frequency dependence indicates that– Greater sensing

depth in higher resistivity materials.

– Increasing depth sensitivity with decreasing frequency.

Skin depths for Different Resistivities

Back to the TransformerCurrent (I) flowing in conductive wire produces H field via Ampere’s Law (assuming << σ): x H = JHigh m value of core material enhances B field: B=HAn E field is produced which curls around the magnetic field via Faraday’s law: x E= -iBThis results in a voltage in the coil: ( x E )nds=E dl =V Since V=IR, current results in second loop to light bulb.

The Earth ‘Triple’ Transformer….The interaction between an EM geophysical measurement system and the earth can be thought of as an interaction between three different transformer systems:– A transmitter coil and a receiver coil (measured primary field).– A transmitter coil and an ‘Earth’ coil (producing scattering or eddy

currents in earth).– An ‘Earth’ coil and a receiver coil (measured scattered or secondary

field).

This is signal we are interested in

The Earth CircuitThe simplified single eddy current is best represented by a LR circuit.Real earth is best thought of as a series of LR circuits.Note- eddy currents that are produced generate secondary magnetic fields that oppose the timevariations in primary magnetic field.

EM SpectrumG

ener

al S

pect

rum

Geo

phys

ical

Spe

ctru

m

Classification of EM Methods

Magnetotellurics Methods

Continuous Wave Methods

Transient Methods