A geophysical technique that uses naturally-occurring (or man-made) electromagnetic fields to probe the electrical conductivity structure of the Earth.
Electromagnetic fields arise from time-varying currents in the ionosphere and tropical storms (lightning strikes).
Fields propagate as plane-waves vertically into the Earth, inducing secondary currents.
Earth's behavior is Ohmic (follows microscopic Ohm's law):
We exploit the skin depth relationship:
(km)
Typical numbers
f:{10-3 -> 104 Hz}
r:{100 -> 105 Ohm-m}
d:{10-2 -> 103 km}
Here is an image showing a typical MT data acquisition system.
But what do they really look like?
MT Response Functions
Time series for the horizontal components of the electric and magnetic fields and the vertical component magnetic field are Fourier transformed into the frequency domain and ("robustly") band-averaged into em field estimates vs. frequency/period.
Impedance:
Induction Arrow:
Apparent Resistivity:
(Ohm-m)
Phase:
(degrees)
MT Response Functions
Multi-dimensional Earth (electrical) conductivity models are sought. The simulated responses of these models should match observations made at the Earth's surface. For 1-D and 2-D models, inversions of observed data are possible.
Here is a graphic that summarizes MT modeling.
An Example
An example of the utility of magnetotellurics-- project EMSLAB which intended to map the lithosphere of the Pacific Northwest. We didn't quite accomplish that, but here is an interesting result from EMSLAB.
Inversion of MT Response Functions
In modern times, multi-dimensional Earth (electrical) 2-D conductivity models are sought via an inversion process.
Observations, their errors, and an a priori model are used to begin a linearized inversion process to yield a conductivity model that is consistent with the observations.
Tikhonov's method defines a regularized solution to be the model, m, that minimizes the objsective function:
Notes:
Each datum, di, is log amplitude or phase of TE or TM impedance at a particular station and frequency.
The model vector is log resistivity as a function of position.
d2_inv (Mackie, Rieven and Rodi, inversion used here) uses:
Solution of minimization problem:
Solving the minimization of S (above) involves taking the derivative w.r.t. the model vector, m, and setting it equal to zero, yielding:
d2_inv uses a non-linear conjugate gradient (NLCG) method to solve for m in an iterative fashion.
