1. SAGE MT "Understanding is More Important Than Knowledge"
George R. Jiracek
San Diego State University
"Understanding
is More Important
Than Knowledge"

2. THE INPUT
THE OUTPUT
MT DATA
LIGHTNING
SOLAR WIND
BLACK BOX EARTH

3. MT Data Collection
Depth of sensing is into upper mantle

4. Marlborough, New Zealand

5. Southern Alps, New Zealand

6. Southern Alps, New Zealand

7. Southern Alps, New Zealand

8. Taupo, New Zealand

9. Southern Alps, New Zealand
The “Banana”

10. Southern Alps, New Zealand
(Jiracek et al., 2007)

11. New Zealand Earthquakes vs. Resistivity in Three-Dimensions
Southern Alps, New Zealand
New Zealand Earthquakes vs.
Resistivity in Three-Dimensions

12. Taupo Volcanic Geothermal Field,
Three-Dimensional MT
Taupo Volcanic Geothermal Field,
New Zealand
(Heise et al. , 2008)

13. MT Phase Tensor Plot at 0.67s Period from the Taupo Volcanic Field

14. Magnetotellurics (MT)
Low frequency (VLF to subHertz)
Natural source technique
Energy diffusion governed by ρ(x,y,z)
(Ack. Paul Bedrosian, USGS)
Techniques - MT

15. Magnetotelluric Signals
(Ack. Paul Bedrosian, USGS)
Techniques - MT

16. Always Must Satisfy Maxwell’s Equations
Quasi-static approx, σ >> εω
rf is free charge density
(Ack. Paul Bedrosian, USGS)
Magnetotellurics

17. Quasistatic Approximation
Displacement currents << Conduction currents
d is skin depth
(Ack. Paul Bedrosian, USGS)

18. Graphical Description of Skin Depth, d

19. Magnetotelluric Impedance
After Fourier transforming the E(t) and H(t) data into the frequency domain the MT surface impedance is calculated from:
Ex(w) = Z(w) Hy(w)

20. Note, that since
Ex(w) = Z(w) Hy(w)
is a multiplication in the frequency domain, it is a convolution in the time domain.
Therefore, this is a filtering operation, i.e.,
Ex(t)
Hy(t)
Z(t)

21. Apparent resistivity, ra and phase, f
Apparent resistivity is the resistivity of an equivalent, but fictitious, homogeneous, isotropic half-space
Phase is phase of the impedance
f = tan-1 (Im Z/Re Z)
Take magnitude of complex number, multiply by frequency, another constant.
App res most commonly used quantity in MT.

22. surface electromagnetic impedance, Zs
The goal of MT is the resistivity distribution, r(x,y,z), of the subsurface as calculated from the
surface electromagnetic
impedance, Zs r7 r1 r2
Dimensionality: r3
One-Dimensional
Two-Dimensional
Three-Dimensional r4 r5 r6

23. Geoelectric Dimensionality

24. ra a |Z2| 1-D MT Sounding Curve ra x y z Log Period (s)
Shallow Resistive Layer
Intermediate Conductive Layer
Deep Resistive Layer ra
Period (s)
Log
ra a |Z2|

25. Layered (1-D) Earth Ex Hy (Ack., Paul Bedrosian, USGS) 104 1000 100
Apparent resistivity
Impedance Phase 20 40 60 80
101
102
103
104
100 30
10-2
Period (s)
Degrees
Ohm-m
500 Ex Hy
1000
Longer period  deeper penetration ( )m
Using a range of periods a depth sounding can be obtained
(Ack., Paul Bedrosian, USGS)

26. MT “Screening” of Deep Conductive Layer by Shallow Conductive Layer
(Ack., Martyn Unsworth, Univ. Alberta)

27. When the Earth is either 2-D or 3-D:
Ex(w) = Z(w) Hy(w)
Now
Ex(w) = Zxx(w) Hx(w) + Zxy(w) Hy(w)
Ey(w) = Zyx(w) Hx(w) + Zyy(w) Hy(w)
This defines the tensor impedance, Z(w)

28. 3-D MT Tensor Equation
Ex and Ey depend on Hx, Hy. When it’s multidimensional, impedance has more than one value.

29. 1-D, 2-D, and 3-D Impedance 1-D 2-D Assumes geoelectric strike 3-D
No geoelectric assumptions
[ ] is Tensor Impedance
(Ack., Paul Bedrosian, USGS)

30. 3- D MT Data
Measure time variations of electric (E) and magnetic (H) fields at the Earth‘s surface.
Estimate transfer functions of the E and H fields.
Subsurface resistivity distribution recovered through modeling and inversion.
Impedance Tensor:
App Resistivity & Phase:
(Ack. Paul Bedrosian, USGS)
Techniques - MT

31. 2-D MT ra a |Z2| ra (Tensor Impedance reduces to two off-
diagonal elements) y x z
Geoelectric
Strike
ra a |Z2| ra
Period (s)
Log

32. Boundary Conditions Map View
E-Fields parallel to the geoelectric strike are continuous (called TE mode)
E-Fields perpendicular to the geoelectric strike are discontinuous (called TM mode) TM TE
Map View
E-Parallel
Log ra
E- Perpendicular
Log Period (s)

33. TE (Transverse Electric) and TM (Transverse Magnetic) Modes
2-D Earth structure
Different results at MT1 (Ex and Hy)
and MT2 (Ey and Hx)
MT1
TRANSVERSE ELECTRIC MODE (TE)
TRANSVERSE MAGNETIC MODE (TM)
Visualizing Maxwell’s Curl Equations
(Ack., Martyn Unsworth, Univ. Alberta)

34. MT Phase Tensor
Described as “elegant” by Berdichevsky and Dmitriev (2008) and a “major breakthrough” by Weidelt and Chave (2012)
“Despite its deceiving simplicity, students attending the SAGE program often have problems grasping the essence of the MT phase tensor” (Jiracek et al., 2014)
The MT Phase Tensor and its Relation to MT Distortion
(Jiracek Draft, June, 2014)

35. MT Phase Tensor
X and Y are the real and imaginary parts of impedance tensor Z, i.e., Z = X + iY
Ideal 2-D, β=0
Recommended β <3° for ~ 2-D
by Caldwell et al., (2004)

36. MT Phase Tensor Ellipse
Ellipses are traced out at every period by the multiplication of
the real 2 x 2 matrix from a MT phase tensor, F(f) and
a rotating, family of unit vectors, c(w), that describe a unit circle.
2-D Tensor Ellipse p2D(w) is:

37. Phase Tensor Example for Single MT Sounding at Taupo Volcanic Field, New Zealand
(Bibby et al., 2005)
1-D TP Tc 2-D TP Tc D TP

38. 1-D TP D TP D TP Tc Tc
Phase Tensor Determinations of Dimensionality (1-D. 2-D), Transition Periods (TP), and Threshold Periods (Tc)

39. SAGE MT
Caja Del Rio

40. Geoelectric Section From Stitched 1-D TE Inversions (MT Sites Indicated by Triangles)W E
Conductive Basin
Elevation (m)
Resistive Basement
Distance (m) W E
Elevation (m)
Basin
Basement

41. 2-D MT Inversion/Finite-Difference Grid
M model parameters, N surface measurements, M>>N
A regularized solution narrows the model subspace
Introduce constraints on the smoothness of the model
(Ack. Paul Bedrosian, USGS)
Techniques - MT

42. Geoelectric Section From 2-D MT Inversion (MT Sites Indicated by Triangles)W E
Conductive Basin
Elevation (m)
Resistive Basement
Distance (m) W E
Elevation (m)
Basin
Basement

44. SAGE – Rio Grande Rift, New Mexico
(Winther, 2009)

45. Resistivity Values of Earth Materials

46. MT Interpretation
Geology
Well Logs

47. SAGE – Rio Grande Rift, New Mexico
(Winther, 2009)

48. MT-Derived Midcrustal Conductor Physical State
Eastern Great Basin (EGB), Transition Zone (TZ), and Colorado Plateau (CP) (Wannamaker et al., 2008)

49. Field Area Now
The Future?

50. References
Bibby, H. M., T. G. Caldwell, and C. Brown, 2005, Determinable and non-determinable parameters of galvanic distortion in magnetotellurics, Geophys. J. Int., 163, Caldwell, T. G., H. M. Bibby, and C. Brown, 2004, The magnetotelluric phase tensor, Geophys. J. Int., 158, Heise, W., T. G. Caldwell, H. W. Bibby, and C. Brown, 2006, Anisotropy and phase splits in magnetotellurics, Phys. Earth. Planet. Inter., 158, Jiracek, G.R., V. Haak, and K.H. Olsen, 1995, Practical magnetotellurics in continental rift environments, in Continental rifts: evolution, structure, and tectonics, K.H. Olsen, ed., Jiracek, G. R., V. M Gonzalez, T. G. Caldwell, P. E. Wannamaker, and D. Kilb, 2007, Seismogenic, Electrically Conductive, and Fluid Zones at Continental Plate Boundaries in New Zealand, Himalaya, and California-USA, in Tectonics of A Continental Transform Plate Boundary: The South Island, New Zealand, Amer. Geophys. Un. Mono. Ser. 175,

51. Palacky, G.J., 1988, Resistivity characteristics of geologic targets, in Investigations in Geophysics Volume 3: Electromagnetic methods in applied geophysics theory vol. 1, M.N. Nabighian ed., Soc. Expl. Geophys., 53–129. Winther, P. K., 2009, Magnetotelluric investigations of the Santo Domingo Basin, Rio Grande rift, New Mexico, M. S thesis, San Diego State University, 134 p. Wannamaker, P. E., D. P. Hasterok, J. M. Johnston, J. A. Stodt, D. B. Hall, T. L. Sodergren, L. Pellerin, V. Maris, W. M. Doerner, and M. J. Unsworth, 2008, Lithospheric Dismemberment and Magmatic Processes of the Great Basin-Colorado Plateau Transition, Utah, Implied from Magnetotellurics: Geochem., Geophys., Geosys., 9, 38 p.