Electromagnetic Methods in Geophysics. Fabio Giannino
the simple relation b = μ0 h we can now solve for bz by 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 bz = μ0I/2°. The time derivative, or the impulse response, dbz/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 ρa is derived from:
(2.4.17)
(2.4.18)
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