teori electromagnetic (pengantar em2-theory)
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CSAMTTRANSCRIPT
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Electromagnetic Methods
By Doddy Sutarno
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Electromagnetic Theory and Classification
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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.
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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….
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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)
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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
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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
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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
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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
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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
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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
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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.
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Skin depths for Different Resistivities
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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.
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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
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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.
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EM SpectrumG
ener
al S
pect
rum
Geo
phys
ical
Spe
ctru
m
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Classification of EM Methods
Magnetotellurics Methods
Continuous Wave Methods
Transient Methods