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Eldad Haber

Inversion of 3D Electromagnetics: A maturing technique in applied geophysics. Eldad Haber. Collaborators: Doug Oldenburg, Roman Shekhtman,Scott Napier, and Rob Eso. Outline:. Introduction: Example problems Environmental, geotechnical, resource exploration Geophysical surveys Inversion

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Eldad Haber

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  1. Inversion of 3D Electromagnetics: A maturing technique in applied geophysics Eldad Haber Collaborators: Doug Oldenburg, Roman Shekhtman,Scott Napier, and Rob Eso

  2. Outline: • Introduction: Example problems • Environmental, geotechnical, resource exploration • Geophysical surveys • Inversion • Mineral exploration example • Summary/discussion

  3. http://www.nohowinc.com/ http://www.dma.state.mn.us/ http://www.centennialofflight.gov Environmental: UXO • Military proving grounds • Regions of conflict • Avalanche control

  4. Environmental: How do we find UXO? ?

  5. Geotechnical: A Canadian potash mining

  6. Geotechnical problem • Water gushing into the mine

  7. Mineral exploration What do we have? Map of surface geology

  8. Solutions … Geophysics Energy from source physical properties - Density - Magnetic susceptibility - Electrical resistivity - Chargeability - others … Physical properties and contrasts - Gravity - Magnetic field anomalies - DC or electromagnetics - Induced polarization - etc. … Measurements

  9. Physical properties • UXO: • Electrical conductivity and magnetic susceptibility • Water (at potash mine): • Electrical conductivity: high if it has dissolved salt • Minerals: • magnetic susceptibility • electrical conductivity • chargeability • density

  10. Waveform (half sine, step…) I Time Source (Loop or grounded electrode) Measurements (E, H, dB/dt) Borehole (E, H, dB/dt) Depth 3D TEM Setup

  11. Outline: • Introduction: Example problems • Environmental, geotechnical, resource exploration • TEM forward modelling • Inversion • Mineral exploration example • Summary/discussion

  12. Maxwell’s Equations Boundary conditions Initial conditions Mathematical Setup time [0, tf] This must be solved in both space and time.

  13. Implicit Method • Backward Differentiation Formula (BDF) • E n depends upon E n-1, H n-1(BDF1) where Need initial conditions to start time stepping.

  14. I(t) Case 1: t 0 Case 2: E0, H0 fields are from DC currents t 0 Solve DC Resistivity MMR Initial Conditions Time stepping starts with fields at time t = 0

  15. Formulation as potentials (1) (2) where and Helmholtz decomposition Coulomb Gauge Yields

  16. Discretization with FV on staggered grid -- A, J are defined on the faces --  is in the centers -- H is on the edges Finite Volume discretization: Each equation is integrated over a volume. Yields:

  17. Formulating the forward problem Maxwell’s Equations: Source term: Maxwell’s equations: Write: Solve: Aj (m)uj = qj using BICGStab with ILU preconditioner.

  18. Solve An, Φ system using BICGstab with block ILU preconditioner (same as EH3D) Solving the system Solve Let nc = number of cells number of unknowns ~ 7(nc)3 if nc = 64 matrix size = (2x106)2

  19. Y Z Loop source, 1km square 625 m X (0,0,0) target Surface Target (x, y, z) = (250, 500, 100) Conductivity = 1.0 S/m Host resistivity = 200 Ohm-m The Cominco example The “Cominco” model: loop source, conductive target in a host

  20. Forward modelling of fields Velocity of smoke ring Nabighian (1979) Currents decay Induction finished t~0.01 sec Sampling time for movies: 62 frames [10^-6 – 10^-2]

  21. Examples: H field

  22. Examples: J field

  23. Examples: Js field

  24. Examples: Surface (Ex,Hx, dB/dt)

  25. Examples: Profiles of (E,H)

  26. Waveform Source (half sine, step…) I (Loop or grounded electrode) Time Surface Measurement (E, H, dB/dt) Borehole Measurement (E, H, dB/dt) Depth Next Step: Inversion Conclusion

  27. Airborne, surface or borehole measurements Inversion processing ? Inversion What is Inversion? Goal: Estimate the Earth model

  28. Prior information Inversion Measurements Pre-processing Physical property distributions = Inversion 3D, and ~ 105 cells Inversion procedure: • Divide earth into cells (each with fixed size and unknown value). • Inversion: find values for cells • Use mathematical optimization theory. • Difficulties: • Solution is non-unique. • Computationally demanding.

  29. A priori information: reference model, structural detail... Model objective function: • s, x … constants • m0 : reference model Misfit: •  i: standard deviation Inversion as optimization:  = d +  m.0 <  <  is a constant Choose  such that d < Tolerance Inversion as optimization: 3 parts

  30. Inverse problem Minimize  = d +  m where  : Regularization parameter Q: Projection matrix u: Potentials : Observations : Model and Reference model Wd,W : Measurement error, model weighting

  31. Solving the inverse problem Differentiating the objective function with model m where sensitivity matrix and

  32. Gauss-Newton method Solve g(m) = 0, and let F[m+m] = F[m] + J m The sensitivity matrix J has been normalized by and the gradient is Matrices Wd, W, S, Q, , G(m,u) are SPARSE!

  33. IPCG solver with preconditioner (1) J v = -Wd S QG v Forward modelling: Solve (2) JT v = - GT QT ST WdT v Adjoint modelling: Solve Update the model Solution of the matrix system Computations: So each CG iteration has two forward modellings:

  34. Recall we are solving … Choose0, mref Evaluate (mref), g(mref), matrices Wd, W... For  cooling loop For k = 1  max iterations • IPCG to solve • Line search for step length  • Update model • Exit if End Reduce  End Flow chart

  35. Two-prism example • Loop size 130 x 130 m • Step off current • Receivers: Hx, Hy, Hz, Ex, Ey inside the loop • Times: 32 logarithmically spaced (10-6 – 10-3) • Gaussian noise (1%) added (N=16,000) • Inversion model: 423 • Starting and reference model equals true halfspace

  36. -1.75 -2.02 -2.30 Two-prism inversion

  37. Misfit for Two-Prism Example

  38. Tertiary Breccia Mafic Volcanics 2000 Quartz Rhyolite Massive Sulphide Elevation (m) Mafic Volcanics “Keel” Unit Unit Density Susceptibility Resistivity Density Susceptibility Resistivity Chargeability Chargeability (g/cc) (S.I. x10 (g/cc) (S.I. x103 ) (ohm ) (ohm - m) (msec) m) (msec) 1600 - 10 (20) - 5 - 5 - 10 - 5 - 30 - 40 - 50 - 50 - 20 - 70 Qal Qal 2 0 2 0 50 5 50 5 -2000 Easting (m) -1100 Tv Tv 2.3 0 2.3 0 20 20 - - 30 30 10 10 Mst./Lst Mst./Lst . . 2.4 0 2.4 0 150 20 150 20 Mafic Vol. Mafic Vol. 2.7 0 2.7 0 80 30 80 30 Mafic/Int Mafic/Int Vol. Vol. 2.7 0 2.7 0 80 30 80 30 3.5 10 3.5 10 20 200 20 200 Sulphide Sulphide Qtz Qtz . Rhyolite . Rhyolite 2.4 0 2.4 0 100 10 100 10 Graphitic Graphitic Mst Mst . . 2.4 0 2.4 0 100+ 30 100+ 30 Field Example: San Nicolas Deposit Geologic cross section Location Physical properties

  39. 3 large loop transmitters 2 km by 1.5 km dB/dt receivers mainly z component I(t) 15 ms dI dt dB dt Introduction to UTEM Geophysics Survey at San Nicolas • transmitter waveform • 30 Hz sawtooth wave • dI/dt constant over half cycle

  40. Loop 2 Loop 1 Loop 9 San Nicolas UTEM Geophysics Survey UTEM channel 4 (1.513ms) 1075 dBz/dt northing nT/s -1300 -220 -3000 easting

  41. understanding the data background model discretize validate forward model error assignment a priori information inversions evaluate results A simplified procedure for inverting time-domain electromagnetic (TEM) surveys

  42. UTEM geophysics survey at San Nicolas • 10 time channels (0.024 – 12.1 ms ) • Number of data inverted: 3523 • Error assignment: percentage + floor • Reduced volume: 3.3 × 2.3 × 2.3 km • Number of cells: 241,920 • Reference model: 90 m layer (10 ohm-m) • 100 ohm-m halfspace • Sensitivity weighting for the source loop • Model objective function: (10^-4, 1,1,1)

  43. Observed 15 m iso-surface 1000.0 31.0 1.0 View from SW One decay curve: Observed and predicted Observed Predicted observed dBz/dt nT/s predicted log10(t) Fitting the Observations

  44. 1000 Resistivity from drilling at 450 S Resistivity from drilling at 1380 W m -500 -1000 -500 -2500 5 northing easting San Nicolas inversion results: 1000 Recovered cross section at 450 S Recovered cross section at 1380 W m -500 -1000 -500 -2500 5 northing easting

  45. Stopping Point: 1000 Recovered cross section at 450 S Recovered cross section at 1380 W m • 3 transmitter loops • 3000 (?) • 240,000 cells • First 3D inversion of TD electromagnetics for mineral exploration -500 -1000 -500 -2500 5 northing easting Question: In this case we have extensive drilling and a rock model to compare. How about the other surveys?

  46. Tertiary Breccia Mafic Volcanics 2000 Quartz Rhyolite Massive Sulphide Elevation (m) Other conductivity surveys DC resistivity CSAMT Mafic Volcanics Other Surveys “Keel” Unit Unit Density Susceptibility Resistivity Density Susceptibility Resistivity Chargeability Chargeability (g/cc) (S.I. x103 (g/cc) (S.I. x10 ) (ohm ) (ohm - m) (msec) m) (msec) 1600 Gravity Magnetics Induced Polarization - 10 (20) - 5 - 5 - 10 - 5 - 30 - 40 - 50 - 50 - 20 - 70 Qal Qal 2 0 2 0 50 5 50 5 -2000 Easting (m) -1100 Tv Tv 2.3 0 2.3 0 20 20 - - 30 30 10 10 Mst./Lst Mst./Lst . . 2.4 0 2.4 0 150 20 150 20 Mafic Vol. Mafic Vol. 2.7 0 2.7 0 80 30 80 30 Mafic/Int Mafic/Int Vol. Vol. 2.7 0 2.7 0 80 30 80 30 3.5 10 3.5 10 20 200 20 200 Sulphide Sulphide Qtz Qtz . Rhyolite . Rhyolite 2.4 0 2.4 0 100 10 100 10 Graphitic Graphitic Mst Mst . . 2.4 0 2.4 0 100+ 30 100+ 30 Field Example: San Nicolas Deposit Geologic cross section Physical properties

  47. San Nicolás: CSAMT survey layout Outcrop geology Grid North Transmitter: 15 frequencies (0.5 - 8192 Hz) 1.7km 3.7km Surface projection of the San Nicolas ore body. - 3 receiver lines spaced 200m apart; - 60 stations per line @ 25m spacing.

  48. San Nicolás: CSAMT 1D inversion results 300 ohm-m 55 10 3D model from many 1D column-models Isosurface view of the same 3D conductivity model

  49. San Nicolás: CSAMT 3D inversion results 300 ohm-m 55 10 3D inversion results: Frequencies .. Isosurface view of the same 3D conductivity model

  50. DC Resistivity 3D CSAMT 0 0 200 200 400 400 600 600 800 800 -950 -950 -2150 -1550 -2150 -1550 3D UTEM 1D CSAMT 0 0 200 200 400 400 600 600 800 800 -950 -2150 -1550 -950 -2150 -1550

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