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In the 19th century, Clerk Maxwell (1831-1879), Scottish physicist, gathered Electric and Magnetic Theory to create EM (with the help of Faraday). He developed the notion of EM planar wave with an electric field orthogonal to the magnetic field.
Step 1: Homogeneous Maxwell Equations
Maxwell’s theory is based on 4 formulae and 1st of all, no sources in our volume of interest (they are sufficiently faraway). Two of them link time and space. EM state could be described everywhere at all times.
Step 2: The Inductive Effect
When a target is more conductive than the surrounding formations, inductive currents lines (induced by the EM wave) draw circles restrained to the conductive target. That leads to the creation of a magnetic dipole of which the orientation depends on the target geometry, the resistivity contrasts and the primary field.
That phenomenon is fairly described by Maxwell’s equations.
Step 3: The constitutive relationships
Step 4: From Maxwell to wave equations
Step 5: Diffusion versus Propagation
Hypothesis on frequencies at stake enables to neglect some terms in favor of others in the Helmholtz’s equation. Observed phenomena are subsequently different, between Propagation and Diffusion.
Step 6: Boundary conditions
Step 7: The Galvanic Effect
When a target is more conductive than the surrounding formations, currents (induced by the EM wave) are focused within the target. That channeling effect is the consequence of a charge accumulation at the surface of the target which creates an electric depolarization field in opposition of the primary electric field.
That phenomenon is fairly described by the Ohm’s law.
Step 8: Snell-Descartes - TE/TM modes
Snell-Descartes is a very high frequency (propagation) vision. In a low frequency approximation, it can be explained by current density boundary conditions: electric field getting orthogonal to boundary (hence wave number parallel to the boundary).
In MT prospection used to image sub-vertical structures, TM and TE modes are defined as follows:
TE: electric field along strike maximizes inductive coupling
TM: electric field across strike maximizes galvanic coupling
In mCSEM prospection used to image sub horizontal structure, TM and TE modes are defined as follows:
TE: horizontal current loops maximizes inductive coupling
TM: electric field across strike maximizes galvanic coupling
Step 9: Local EM Source - Heterogeneous Maxwell’s Equations
Step 10: Physical Phenomena Wrap-up (Electric dipole source example)
Difficulty in understanding EM methods is that several mechanisms are at work to produce changes in amplitude and phase. The first is geometric spreading from the transmitter. The second is the galvanic effect associated with current passing across a conductivity boundary. Like the geometric effects, it has no effect on signal phase. Finally, the process of inductive attenuation and phase shift occurs when the skin depths are comparable to the distance over which the EM energy has traveled. (Constable, 2010).
Chargeability has been deliberately put aside without any details. However, that phenomenon could be investigate when dealing with minerals exploration and induced polarization technique.
