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**SAGE MT "Understanding is More Important Than Knowledge"**

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

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

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MT Data Collection Depth of sensing is into upper mantle

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**Marlborough, 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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Taupo, New Zealand

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**Southern Alps, New Zealand**

The “Banana”

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**Southern Alps, New Zealand**

(Jiracek et al., 2007)

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**New Zealand Earthquakes vs. Resistivity in Three-Dimensions**

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

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**Taupo Volcanic Geothermal Field,**

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

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

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**Magnetotellurics (MT)**

Low frequency (VLF to subHertz) Natural source technique Energy diffusion governed by ρ(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 Satisfy Maxwell’s Equations**

Quasi-static approx, σ >> εω rf is free charge density (Ack. Paul Bedrosian, USGS) Magnetotellurics

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**Quasistatic Approximation**

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

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**Graphical Description of Skin Depth, d**

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**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)

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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, 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.

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**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

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**Geoelectric Dimensionality**

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**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|

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**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)

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**MT “Screening” of Deep Conductive Layer by Shallow Conductive Layer**

(Ack., Martyn Unsworth, Univ. Alberta)

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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, Z(w)

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

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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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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

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**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

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**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)

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**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)

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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)

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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)

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**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:

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**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

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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)

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SAGE MT Caja Del Rio

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**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

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**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

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**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

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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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MT Interpretation Geology Well Logs

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**SAGE – Rio Grande Rift, New Mexico**

(Winther, 2009)

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**MT-Derived Midcrustal Conductor Physical State**

Eastern Great Basin (EGB), Transition Zone (TZ), and Colorado Plateau (CP) (Wannamaker et al., 2008)

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Field Area Now The Future?

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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,

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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.

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