Geophysical Applications of Electrical Impedance Tomography Ph.D. - PowerPoint PPT Presentation

Geophysical Applications of Electrical Impedance Tomography Ph.D. Defence Alistair Boyle Systems and Computer Engineering Carleton University April 29, 2016 A. Boyle, 2016 Carleton University Ph.D. Defence 1 / 15

Motivation Derailment of 39 railway cars carrying crude oil 1 Gogama, ON, Canada (2015) Average 600 derailments per year, 74 with dangerous goods (Canada, 2008-2012) 2 Gogama clean-up costs will be “in the millions” – MPP F. Gelinas 3 1 Transportation Safety Board of Canada, Railway Investigation Report R15H0021 , Mar 2015 2 Transportation Safety Board of Canada, Statistical Summary - Railway Occurrences 2013 , Feb 2014 3 M. Stackelberg, CBC News, Ontario bills CN $350K for Gogama derailment clean-up , Dec 2015 A. Boyle, 2016 Carleton University Ph.D. Defence 2 / 15

Motivation 4 Mount Polley mine tailings spill, Likely, BC, Canada (2014) spilled 4.5 mil. m 3 of tailings with clean up costs of $200–500 mil. 4 CBC News, “Mount Polley mine tailings spill” , Aug 2014 A. Boyle, 2016 Carleton University Ph.D. Defence 3 / 15

Motivation Manage slope stability risks a tool for real-time monitoring of slope movement robust, reliable, informative reconstructions Our tool of choice: Electrical Impedance Tomography Electrical Resistivity Tomography A. Boyle, 2016 Carleton University Ph.D. Defence 4 / 15

Motivation Manage slope stability risks a tool for real-time monitoring of slope movement electrode movement & resistivity robust, reliable, informative reconstructions algorithm, implementation, data Our tool of choice: Electrical Impedance Tomography Electrical Resistivity Tomography A. Boyle, 2016 Carleton University Ph.D. Defence 4 / 15

Electrical Impedance Tomography Typical ERT Survey Equipment ABEM TerrameterLS 5 5 [http://www.ngi.no/upload/48876/TerrameterLS.jpg ] A. Boyle, 2016 Carleton University Ph.D. Defence 5 / 15

Electrical Impedance Tomography Typical ERT Survey ean, France 6 Pont-P´ 6 correct electrode wiring A. Boyle, 2016 Carleton University Ph.D. Defence 6 / 15

Electrical Impedance Tomography Long-term remote monitoring Hollin Hill, UK 7 7 Automated Landslide Electrical Resistivity Tomography (ALERT) system A. Boyle, 2016 Carleton University Ph.D. Defence 7 / 15

Methods Absolute imaging problem; large conductivity contrasts ... a Gauss-Newton nonlinear iterative solver x || Ax − b || 2 min (1) 2 δ x n = − ( J T n J n ) − 1 ( J T n b ) (2) x n +1 = x n + α n +1 δ x n +1 (3) 1 2 0.8 0.6 1 0.4 0.2 0 0 − 0.2 − 0.4 − 1 − 0.6 − 0.8 − 1 − 2 − 1 − 0.5 0 0.5 1 A. Boyle, 2016 Carleton University Ph.D. Defence 8 / 15

Methods Absolute imaging problem; large conductivity contrasts ... a Gauss-Newton nonlinear iterative solver x || Ax − b || 2 W + || λ R ( x − x ∗ ) || 2 min (1) 2 δ x n +1 = − ( J T n WJ n + λ 2 R T R ) − 1 ( J T n Wb − λ 2 R T R ( x n − x ∗ )) (2) x n +1 = x n + α n +1 δ x n +1 (3) 1 2 0.8 0.6 1 0.4 0.2 0 0 − 0.2 − 0.4 − 1 − 0.6 − 0.8 − 1 − 1 − 0.5 0 0.5 1 A. Boyle, 2016 Carleton University Ph.D. Defence 8 / 15

Methods n WJ n + λ 2 R T R ) − 1 ( J T n Wb − λ 2 R T R ( x n − x ∗ )) δ x n +1 = − ( J T x δ x δ b J i , j = δ b i x x δ b δ b W R δ x j A. Boyle, 2016 Carleton University Ph.D. Defence 9 / 15

Methods Resistivity x δ x δ b J i , j = δ b i x x δ b δ b W R δ x j A. Boyle, 2016 Carleton University Ph.D. Defence 10 / 15

Methods Resistivity and movement together 0.5 upslope 0.2 m electrode mvmt [m] 0 downslope -0.5 -1 -1.5 true movement reconstructed 5 10 15 20 25 30 electrode # x σ x m δ x σ δ x m δ b J i , j = δ b i x σ x σ δ b δ b W R 0 δ x j x m x m 0 A. Boyle, 2016 Carleton University Ph.D. Defence 11 / 15

This Work Addresses more improved improved inverse adaptable image decision solver models quality outcomes boundary/electrode movement fewer artifacts better detectability Background material impedance imaging: fwd problem, hardware ( Ch2 ) rocks and conductivity: a review ( Ch3 ) inverse problems: composing algorithms ( Ch4 ) A. Boyle, 2016 Carleton University Ph.D. Defence 12 / 15

This Work Addresses more improved improved inverse adaptable image decision solver models quality outcomes boundary/electrode movement fewer artifacts better detectability Contributions; with geophysics applications problems with inverse problems: reliable algorithms ( Ch5 ) data quality and model mismatch: reliable data ( Ch6 ) electrode mvmt and modelling errors: reliable Jacobians ( Ch7 ) reconstructing surface movement: [ x σ x m ] T ( Ch8 ) A. Boyle, 2016 Carleton University Ph.D. Defence 13 / 15

This Work Addresses more improved improved inverse adaptable image decision solver models quality outcomes boundary/electrode movement fewer artifacts better detectability A. Boyle, 2016 Carleton University Ph.D. Defence 14 / 15

Thank You A. Boyle, 2016 Carleton University Ph.D. Defence 15 / 15