Electromagnetic Methods in Geophysics. Fabio Giannino

Electromagnetic Methods in Geophysics - Fabio Giannino


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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)equation

      (2.4.14)equation

      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)equation

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

      (2.4.16)equation

      The apparent resistivity ρa is derived from:

      (2.4.17)equation

      (2.4.18)equation

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