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 m eters (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 1000m 1000 100 103 Ohm-m Ex 104 500 102 30 101 Apparent resistivity 2 30m 3 500m 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 ΦX 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( ) p2D( ) 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.