MT tensor equation

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SAGE MT 2009
George R. Jiracek San Diego State University
"Understanding is More Important Than Knowledge"
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MAGNETOTELLURICS (MT)

• Recording and study of the natural, time- varying
  electric (E) and magnetic (H) fields at the
  surface of the earth
• Objective is to derive the geoelectric
  structure of the earth and relate it to
  geologic structure, tectonics, and subsurface
  conditions

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Sources of Magnetotelluric Energy
Solar Wind
Lightning
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MT Data Collection
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Off Shore of San Diego, California
AOA GEOMARINE OPERATIONS
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San Andreas Fault, Parkfield, California
Deep Fluids ?
(Becken et al., 2008)
SAF Parkfield
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Cascade Range, Washingtion State
(Hill et al., 2009)
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The Himalaya Range
(Unsworth et al., 2005 and Jiracek et al,. 2007)
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South Island, New Zealand
(Wannamaker et al., 2009)
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Southern Alps, New Zealand
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Southern Alps, New Zealand
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Southern Alps, New Zealand
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Southern Alps, New Zealand
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Southern Alps, New Zealand
The Banana
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Southern Alps, New Zealand
New Zealand Earthquakes vs. Resistivity in
Three-Dimensions
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Southern Alps, New Zealand
(Jiracek et al., 2007)
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Marlborough, New Zealand
(Wannamaker et al., 2009)
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Marlborough, New Zealand
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Marlborough, New Zealand
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Marlborough, New Zealand
(Wannamaker et al., 2009)
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Marlborough, New Zealand
(Wannamaker et al., 2009)
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Hydraulic Potential Versus Depth with
Tectonically Induced Neutral Buoyancy
(Modified after Connolly and Podladchikov, 2004)
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Rio Grande Rift. New Mexico
SAGE Study Area
(Modified from Manley, 1979)
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La Bajada Fault
Inverted MT Profile
Santa Fe River Canyon
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SAGE Northern New Mexico
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SAGE Rio Grande Rift, New Mexico
(Winther, 2009)
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Resistivity Values of Earth Materials
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Geologic Units in New Mexico
Rift fill Sediments
Pre-rift
(Baldridge, 2008)
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SAGE Rio Grande Rift, New Mexico
(Winther, 2009)
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Three-Dimensional MTPacific Northwest, USA
(Patro and Egbert, 2008)
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Three-Dimensional MT Taupo Volcanic Geothermal
Field, New Zealand
(Heise et al. , 2008)
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EQUALS
THE EARTH EQUALS A BLACK BOX
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BLACK BOX EARTH
OUTPUT
INPUT
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THE INPUT
1. LIGHTNING
2. SOLAR WIND
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THE INPUT
THE OUTPUT
MT DATA
LIGHTNING
SOLAR WIND
BLACK BOX EARTH
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Magnetotellurics (MT)

• Low frequency (VLF to subHertz)
• Natural source technique
• Energy diffusion governed by ?(x,y,z)

(Ack. Paul Bedrosian, USGS)
Techniques - MT
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Magnetotelluric Signals
(Ack. Paul Bedrosian, USGS)
Techniques - MT
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Always Must SatisfyMaxwells Equations
(Ack. Paul Bedrosian, USGS)
Magnetotellurics
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Quasistatic Approximation
d is skin depth
(Ack. Paul Bedrosian, USGS)
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Graphical Description of Skin Depth, d
l wavelength
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Frequency-Dependent Penetration
(Ack. Paul Bedrosian, USGS)
Techniques - MT
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Magnetotelluric Impedance
(Ack. Paul Bedrosian, USGS)
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After Fourier transforming the E(t) and H(t) data
into the frequency domain the MT surface
impedance is calculated as
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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)
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Apparent resistivity is
Apparent resistivity is the resistivity of an
equivalent, but fictitious, homogeneous,
isotropic half-space
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The goal of MT is the resistivity distribution,
r(x,y,z), of the subsurface as calculated by
the surface electromagnetic impedance, Zs
r7
r1
r2
Dimensionality
r3

• One-Dimensional
• Two-Dimensional
• Three-Dimensional

r4
r5
r6
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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)
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Layered (1-D) Earth
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Two-Layer Earth
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Two-Layer Earth MT Sounding Curves
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Two-Layer Earth MT Sounding Curves
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Two-Layer Earth MT Sounding Curves
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1-D MT Sounding Curve
ra a Z2
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Layered (1-D) Earth
1000
Longer period ? deeper penetration (
)m Using a range of periods a depth sounding
can be obtained
(Ack., Paul Bedrosian, USGS)
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MT Screening of Deep Conductive Layer by
Shallow Conductive Layer
(Ack., Martyn Unsworth, Univ. Alberta)
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1-D MT Inverse Problem Given MT data, i.e.,
impedance (or ra, f) as a function of period,
find a 1-D conductivity-depth model whose MT
response fits the data. A trade-off exists
between data misfit and model roughness.
(Ack., Paul Bedrosian, USGS)
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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
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3-D MT Tensor Equation
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3- D MT Data
Measure time variations of electric (E) and
magnetic (B) fields at the Earths surface.
Estimate transfer functions of the E and B fields.
Subsurface resistivity distribution recovered
through modeling and inversion.
(Ack. Paul Bedrosian, USGS)
Techniques - MT
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2-D MT (Tensor Impedance reduces to two
off- diagonal elements)
Geoelectric
Strike
ra a Z2
0 Zxy Zyx 0
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Boundary Conditions

• E-Fields parallel to the geoelectric strike are
  continuous (called TE mode)
• E-Fields perpendicular to the geoelectric strike
  are discontinuous (called TM mode)

Map View
E-Parallel
Log ra
E- Perpendicular
Log Period (s)
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TM/TE Modes Sense Different Structure
Techniques - MT
(Ack. Paul Bedrosian, USGS)
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TE (Transverse Electric) and TM (Transverse
Magnetic) Modes
MT2

• 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)
(Ack., Martyn Unsworth, Univ. Alberta)
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2-D TE-TM Example from Rift-Like Resistivity
Model(Ack.Alan Jones, DIAS)
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2-D MT Forward Problem
(Ack. Paul Bedrosian, USGS)
Techniques - MT
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2-D Pseudosection Plots (Apparent Resistivity and
Impedance Phase Versus Period (or Frequency)
Plots)
(Ack., Martyn Unsworth, Univ. Alberta)
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2-D MT Forward Problem (Resistivity Model Yields
Predicted MT Data)
0 km
TWO PRISMS
X
5 km
TE Rho data
(Ack., Martyn Unsworth, Univ. Alberta)
TE Phase data
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2-D MT Inversion/Finite-Difference Grid

• M model parameters, N surface measurements, MgtgtN
• A regularized solution narrows the model subspace
• Introduce constraints on the smoothness of the
  model

(Ack. Paul Bedrosian, USGS)
Techniques - MT
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2-D MT Inversion Model
Resolution Synthetic inversion of SAFOD MT
profile, Parkfield, CA
0 km
6 km
0 km
1
6 km
Synthetic inversions study to test if depth
extent of fault zone conductor is well-resolved
with MT data
Vertical exaggeration 11 5 Gaussian noise
added f 1000 0.001 Hz
(Ack., Martyn Unsworth, Univ. Alberta)
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Well Log Correlation with SAGE 2007 2-D MT
Inversion
Res. (O-m)
225
0
Water Table
5
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SAGE MT Sensitivity Testing (Winther, 2009)
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SAGE MT Sensitivity Testing (Winther, 2009)
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SAGE MT Sensitivity Testing (Winther, 2009)
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References

• Becken, M., O. Ritter, S. K. Park, P. A.
  Bedrosian, U. Weckmann, and M. Weber, 2008, A
  deep crustal fluid channel into the San Andreas
  fault system near Parkfield, California, Geophys.
  J. Int., 173(2), 718-732 doi 10.1111/j1365-246X
  2008.03754.x.
• Connolly, J. A. D., and Y. Y. Podladchikov, 2004,
  Fluid flow in compressive tectonic settings
  implications for midcrustal seismic reflectors
  and downward fluid migration, J. Geophys. Res.,
  109 doi10.1029/2003JB002822.
• Heise, W., T. G. Caldwell, H. M. Bibby, S. C.
  Bannister, 2008, Three-dimensional modelling of
  magnetotelluric data from the Rotokawa geothermal
  field, Taupo Volcanic Zone, New Zealand, Geophys.
  J. Int., 173(2), 740-750 doi10.1111/j.1365246X.2
  008.03737.x.

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• Hill, G., T. G. Caldwell, W. Heise, H. Bibby, D.
  Chertkoff, M. Burgess, J. Cull, and R. Cas, 2009,
  Imaging magmatic systems using magnetotelluric
  data Mount St. Helens and Mount Adams, Nature
  Geoscience, submitted.
• 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 California-USA, in Tectonics of A
  Continental Transform Plate Boundary The South
  Island, New Zealand, Amer. Geophys. Un. Mono.
  Ser. 175, 347-369.

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• Manley, K., 1979, Stratigraphy and structure of
  the Espanola Basin, Rio Grande rift, New Mexico,
  in Rio Grande rift tectonics and magmatism, R.E.
  Riecker, ed., Amer. Geophys. Un. Spec. Pub.,
  71-86.
• 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., 53129.
• Patro, P. K., and G. D. Egbert, 2008, Regional
  conductivity structure of Cascadia Preliminary
  results from 3D inversion of USArray
  transportable array magnetotelluric data,
  Geophys. Res. Let., 35 L20311, doi
  10.1029/2008GL035326.
• Wannamaker, P. E., T. G. Caldwell, G. R. Jiracek,
  V. Maris, G. J. Hill, Y. Ogawa, H. M. Bibby, S.
  L. Bennie, and W. Heise, 2009, Fluid and
  deformation regime of an advancing subduction
  system at Marlborough, New Zealand, Nature, in
  press.

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• 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.
• Unsworth. M. J., A. G. Jones, W. Wei, G.
  Marquis, S. Gokarn, J. E. Spratt and the
  INDEPTH-MT team, 2005, Crustal rheology of the
  Himalaya and southern Tibet inferred from
  magnetotelluric data, Nature, 438
  doi10.1038/nature04154.