Zonge GDP-32 - Useful CSAMT Equations

MATHEMATICAL ALGORITHMS
Section 15, Page 11 October 2002
15.5 USEFUL CSAMT EQUATIONS
Cagniard Resistivity, ρ
a
:
a
f
E
H
ρ
=
⊥
1
5
2
(ohm-meters)
Phase difference,Φ :
φ
φ
φ
=−EH
(milliradians)
Skin depth δ is defined by:
δ
µσω
ρ
==
2
503
a
f
(meters)
Equivalent depth of investigation, D:
D
f
a
= 356
ρ
(D in meters)
Wavelength, λ:
λ
π
δ
= 2
where:
E = electric field in mV/km
H = magnetic field in gamma (γ)
or nanoteslas (nT)
Φ = phase in milliradians
µ = magnetic permeability of air
= 4 π x 10
-7
σ = conductivity in
siemen/meter
= 1/ρ
ω = 2 π f,
f=frequency in Hz
ρ = resistivity in ohm-meters
= 1/ σ
1
10
100
1000
0.1 1 10 100 1000 10,000
Frequency (hertz
)
Far Field CSAMT Depth of Investigation
G
r
ound Resistivity (ohm-m)