**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} -> 10^{4} Hz}

r:{10^{0} -> 10^{5} Ohm-m}

d:{10^{-2} -> 10^{3} 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.**