George R. Jiracek
San Diego State University
THE INPUT
THE
OUTPUT
MT
DATA
LIGHTNING
SOLAR WIND
BLACK BOX EARTH
MT Data Collection
Marlborough, New Zealand
Southern Alps, New Zealand
Southern Alps, New Zealand
Southern Alps, New Zealand
Taupo, New Zealand 2010-12
Southern Alps, New Zealand
South Island , New Zealand Geoelectric Section
NW WestlandndAFFSouthern Alps Canterbury Plain SE
4
W
DEPTH (KM)
3.5
3
The “Banana”
2.5
2
1.5
1
DISTANCE (KM)
LOG
 (-M)
Southern Alps, New Zealand
(Jiracek et al., 2007)
Southern Alps, New Zealand
New Zealand Earthquakes vs.
Resistivity in Three-Dimensions
Three-Dimensional MT
Taupo Volcanic Geothermal Field,
New Zealand
(Heise et al. , 2008)
MT Phase Tensor Plot at 0.67s Period from the
Taupo Volcanic Field
Magnetotellurics (MT)
 Low frequency (VLF to subHertz)
 Natural source technique
 Energy diffusion governed by ρ(x,y,z)
(Ack. Paul Bedrosian, USGS)
Techniques - MT
Magnetotelluric Signals
(Ack. Paul Bedrosian, USGS)
Techniques - MT
Always Must Satisfy
Maxwell’s Equations
Quasi-static approx, σ >> εω
  H  J   E  t
  E    H  t
H  0
E   f 
(Ack. Paul Bedrosian, USGS)
f is free charge density
Magnetotellurics
Quasistatic Approximation
  
 2 E(r, t )   E t
 2 E(r,  )  i E
E x ( z ,  )  E0 e
 kz
where k   (1  i ) 
 is skin depth
  2    500  f meters
(Ack. Paul Bedrosian, USGS)
Graphical Description of Skin Depth, 
Magnetotelluric Impedance
After Fourier transforming the E(t) and H(t) data
into the frequency domain the MT surface
impedance is calculated from:
Ex() = Z() Hy()
Note, that since
Ex() = Z() Hy()
is a multiplication in the frequency
domain, it is a convolution in the time
domain.
Therefore, this is a filtering operation, i.e.,
Hy(t)
Z(t)
Ex(t)
Apparent resistivity, a and phase, f
a 
1
0
Z
2
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)
The goal of MT is the resistivity distribution,
x,y,z, of the subsurface as calculated from the
surface electromagnetic
7
impedance, Zs
1
Dimensionality:
•One-Dimensional
•Two-Dimensional
•Three-Dimensional
2
3
4
5
6
Geoelectric Dimensionality
1-D
2-D
3-D
x
1-D MT Sounding
Curve
y
Shallow
Resistive Intermediate
Layer
Conductive
Layer
z
a
a
2
|Z |
Log a
Z xy
Ex
=
Hy
Log Period (s)
Deep
Resistive
Layer
Layered (1-D) Earth
Hy
1  1000m
1000
100
103
Ohm-m
Ex
104
500
102
30
101
Apparent resistivity
2  30m
3  500m
Longer period  deeper
penetration (  500 T )m
Using a range of periods a
depth sounding can be
obtained
Degrees
80
Impedance Phase
60
40
20
0
10-2
(Ack., Paul Bedrosian, USGS)
100
102
Period (s)
104
MT “Screening” of Deep Conductive Layer
by Shallow Conductive Layer
(Ack., Martyn Unsworth, Univ. Alberta)
When the Earth is either 2-D or 3-D:
Ex() = Z() Hy()
Now
Ex() = Zxx() Hx() + Zxy() Hy()
Ey() = Zyx() Hx() + Zyy() Hy()
This defines the tensor impedance, Z()
3-D MT Tensor Equation
Ex   Z xx
E    Z
 y   yx
Z xy  H x 



Z yy  H y 
1-D, 2-D, and 3-D Impedance
• 1-D
Z ij ( )  E i ( ) / H j ( )
Z 1 D ( )  E| | ( ) / H  ( ) 
• 2-D
– Assumes geoelectric strike
 e i
4
Z 2D
 0
 
 Z yx
Z xy 

0 
Z 3D
 Z xx
 
 Z yx
Z xy 

Z yy 
[ ] is Tensor Impedance
• 3-D
– No geoelectric assumptions
(Ack., Paul Bedrosian, USGS)
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:
E    Z    H  
 Ex   Z xx
 
 E y   Z yx
Z xy   H x 
 

Z yy   H y 
(Ack. Paul Bedrosian, USGS)
App Resistivity & Phase:
 a ( ) 
1
Z ( )
2

f ( )  Arg Z ( ) 
Techniques - MT
2-D MT
x
(Tensor Impedance
reduces to two offdiagonal elements)
æ0
ç
Z = çç
çèZ yx
y
a
Log a
z
Log Period (s)
Z xy ö
÷
÷
0 ÷
÷
ø
a
2
|Z |
Boundary
Conditions
1. E-Fields parallel to the
geoelectric strike are
continuous (called TE
mode)
2. E-Fields perpendicular
to the geoelectric strike
are discontinuous
(called TM mode)
EPerpendicular
Map View
TM
Log a
E-Parallel
TE
Log Period (s)
TE (Transverse Electric) and TM (Transverse Magnetic)
Modes
MT1
MT2
-2-D Earth structure
-Different results at MT1 (Ex and Hy)
and MT2 (Ey and Hx)
TRANSVERSE ELECTRIC MODE (TE)
TRANSVERSE MAGNETIC MODE (TM)
Visualizing
Maxwell’s Curl Equations
(Ack., Martyn Unsworth, Univ. Alberta)
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)
MT Phase Tensor
1
ΦX Y
• 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)
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) and
a rotating, family of unit vectors, c(), that describe a unit circle.
2-D Tensor Ellipse p2D() is:
 tan(f yx) cos( ) 
p 2D( )   2D c( )  

tan(
f
xy
)
sin(

)


http://www-rohan.sdsu.edu/~jiracek/DAGSAW/Rotation_Figure/
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
2-D
TP
1-D
TP
2-D
Tc
TP
2-D
TP
Tc
Phase Tensor Determinations of
Dimensionality (1-D. 2-D), Transition
Periods (TP), and Threshold Periods (Tc)
SAGE MT
Caja Del Rio
Geoelectric Section From Stitched 1-D TE Inversions
(MT Sites Indicated by Triangles)
E
Elevation (m)
W
Conductive Basin
Resistive Basement
Distance (m)
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
Geoelectric Section From 2-D MT Inversion
(MT Sites Indicated by Triangles)
Elevation (m)
W
E
Conductive Basin
Resistive Basement
Distance (m)
SAGE – Rio Grande Rift, New Mexico
(Winther, 2009)
Resistivity Values of Earth Materials
MT Interpretation
Geology
Well Logs
SAGE – Rio Grande Rift, New Mexico
(Winther, 2009)
MT-Derived Midcrustal Conductor Physical State
Eastern Great Basin (EGB), Transition Zone (TZ), and Colorado
Plateau (CP) (Wannamaker et al., 2008)
Field Area Now
The Future?
References
Bibby, H. M., T. G. Caldwell, and C. Brown, 2005, Determinable and nondeterminable parameters of galvanic distortion in magnetotellurics,
Geophys. J. Int., 163, 915 -930.
Caldwell, T. G., H. M. Bibby, and C. Brown, 2004, The magnetotelluric phase
tensor, Geophys. J. Int., 158, 457- 469.
Heise, W., T. G. Caldwell, H. W. Bibby, and C. Brown, 2006, Anisotropy and
phase splits in magnetotellurics, Phys. Earth. Planet. Inter., 158, 107-121.
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., 103-129.
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 CaliforniaUSA, in Tectonics of A Continental Transform Plate Boundary: The South
Island, New Zealand, Amer. Geophys. Un. Mono. Ser. 175, 347-369.
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.