# Radio Magneto Tellurics: role of reflection

In the technique of radio magneto tellurics (RMT), plane wave EM radiation incident upon Earth's surface is used to measure subsurface properties. I have read a number of different sources on the technique. Essentially, Maxwell's equations couple the electric field amplitude and magnetic field amplitude of perpendicular components of the impinging wave source (I think the coupling is generally more complicated, but the plane wave assumption limits the wave orientation to a plane and thus the z-field component is zero). Now, the ratio of the magnetic field amplitude to electric field amplitude is given as the ratio of the magnetic permeability of the medium to the electric permittivity. Since most materials have a magnetic permeability almost the same as the vacuum permeability and they are static, this ratio is a proxy measurement of the impedance of the medium. Another way to think about this is that the wave induces secondary currents in the medium, which produce their own waves of the same frequency and superimpose on the original wave to reduce the amplitudes of the electric and magnetic field components respectively.

My question is this: The measurement is made at the surface of the medium of interest (the Earth-sky boundary as far as I'm concerned). In all the resources I have read, they say that because the skin depth is frequency dependent, making this measurement for a range of frequencies allows one to infer the spatial distribution of impedance. What I don't understand is how a measurement at the surface can tell you things about the subsurface, unless there are reflections. However, the resources never mention measuring reflected waves. Do I misunderstand something about light? I'm kind of thinking about causality here, because the light travels in time from the atmosphere, then interacts with the boundary and continues propagating through the medium. Is it possible that the wavelength of light determines what the "boundary" is? For example, we could call the boundary the region that extends below Earth's surface up to a tenth of a wavelength or so. Then for very low frequency, the "boundary" could be on the order of km. But it still seems to violate causality because the light is sensing stuff ahead of it which determines how it acts at the surface. I understand that the skin depth determines to what depth the wave can induce secondary currents. Do these secondary currents create waves that propagate back to the surface?

I know there are a lot of resources on RMT, and I've looked pretty hard but none address these confusions.

PS: I didn't post this on Earth Science stack exchange because I feel like the essence of the problem is physics (even though the method is used in geophysics).

I would not call it reflection although some of the energy which enters the ground does come out again in the opposite direction.

Variations in the Earth's magnetic field principally due to the solar wind interacting with the and lightning result in electromagnetic waves with whole range of frequencies being incident on the Earth's surface.

Because the ground is a conductor these incoming electromagnetic waves produce telluric currents in the ground.

In turn these telluric currents produce electromagnetic waves which can be detected at the surface of the Earth (or just below it) using sensors which can detect electric and magnetic fields.

The incoming electromagnetic waves penetrate the Earth's surface to a degree (skin depth) which depends amongst other things on the frequency of the waves and the resistivity of the ground.

An approximate value for the skin depth when the amplitude of the electromagnetic wave falls to approximately $e^{-1}$ of its original value is approximately $500\sqrt{\dfrac{\rho_{\rm a}}{f}}$ (metre) where $\rho_{\rm a}$ (ohm metre) is the apparent resistivity of the ground and $f$ (hertz) the frequency of the electromagnetic wave.

The penetration of electromagnetic waves into the ground at higher frequencies is lower so the higher frequency signals recorded at the surface by the probes give information about a smaller thickness of the ground than lower frequency signals.

The data which is recorded is then processed so that the signal over a given (small) frequency range is determined.
The signals over a given frequency range give information about the ground up to a depth of order of magnitude the skin depth.

And then the processing and interpretation really starts.

• Can you please elaborate on why you say "you wouldn't call it reflection"? – Hunter Akins Jul 24 '17 at 19:16
• Just to differentiate the mechanism by which a signal returns from something like echo sounding. – Farcher Jul 25 '17 at 18:22
• I don't see how they are different. Acoustic waves that penetrate a medium jiggle the atoms in the solid, which in turn produce waves that return back towards the original source. In this case, the electrons in the conductive earth jiggle and produce the return signal. How is this not reflection? – Hunter Akins Jul 26 '17 at 2:44
• Also what are the units of the resistivity and frequency in your equation? – Hunter Akins Jul 26 '17 at 2:46
• @HunterAkins I have added the units to the skin depth formula and put in the correct value for the constant. – Farcher Jul 26 '17 at 14:31