Fabio Giannino - Electromagnetic Methods in Geophysics

Using the simple relation b = μ 0h we can now solve for b zby evaluating the integral and applying an inverse Laplace transform:

(2.4.13)

(2.4.14)

where,

σ=1/ρ is the conductivity of the half‐space,

t is the time window

erf is the error function

For t that tend to 0 b z= μ 0I/2°. The time derivative, or the impulse response, db z/dt is found through differentiation to be:

(2.4.15)

When θ tends to 0 , (at late times) the time‐derivative of the magnetic field can be approximated by:

(2.4.16)

The apparent resistivity ρ ais derived from:

(2.4.17)

(2.4.18)

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