Geophysical Applications ofElectrical Impedance Tomography
PhD Defence
Alistair Boyle
Systems and Computer EngineeringCarleton University
April 29 2016
A Boyle 2016 Carleton University
PhD Defence 1 15
Motivation
Derailment of 39 railway cars carrying crude oilGogama ON Canada (2015)
1
Average 600 derailments per year 74 with dangerous goods (Canada 2008-2012)2
Gogama clean-up costs will be ldquoin the millionsrdquo ndash MPP F Gelinas3
1Transportation Safety Board of Canada Railway Investigation Report R15H0021 Mar 20152Transportation Safety Board of Canada Statistical Summary - Railway Occurrences 2013 Feb 20143M Stackelberg CBC News Ontario bills CN $350K for Gogama derailment clean-up Dec 2015
A Boyle 2016 Carleton University
PhD Defence 2 15
Motivation
Mount Polley mine tailings spill Likely BC Canada (2014)4
spilled 45 mil m3 of tailings with clean up costs of $200ndash500 mil
4CBC News ldquoMount Polley mine tailings spillrdquo Aug 2014
A Boyle 2016 Carleton University
PhD Defence 3 15
Motivation
Manage slope stability risks
a tool for real-time monitoring of slope movement
electrode movement amp resistivity
robust reliable informative reconstructions
algorithm implementation data
Our tool of choiceElectrical Impedance TomographyElectrical Resistivity Tomography
A Boyle 2016 Carleton University
PhD Defence 4 15
Motivation
Manage slope stability risks
a tool for real-time monitoring of slope movementelectrode movement amp resistivity
robust reliable informative reconstructionsalgorithm implementation data
Our tool of choiceElectrical Impedance TomographyElectrical Resistivity Tomography
A Boyle 2016 Carleton University
PhD Defence 4 15
Electrical Impedance Tomography
Typical ERT Survey EquipmentABEM TerrameterLS5
5[httpwwwnginoupload48876TerrameterLSjpg]
A Boyle 2016 Carleton University
PhD Defence 5 15
Electrical Impedance Tomography
Typical ERT SurveyPont-Pean France6
6correct electrode wiring
A Boyle 2016 Carleton University
PhD Defence 6 15
Electrical Impedance Tomography
Long-term remote monitoringHollin Hill UK7
7Automated Landslide Electrical Resistivity Tomography (ALERT) system
A Boyle 2016 Carleton University
PhD Defence 7 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||22 (1)
δxn = minus(JTnJn)
minus1(JTnb) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus2
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||2W + ||λR(xminus xlowast)||22 (1)
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast)) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast))
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 9 15
Methods
Resistivity
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 10 15
Methods
Resistivity and movement together
electrode 5 10 15 20 25 30
elec
trod
e m
vmt [
m]
-15
-1
-05
0
05upslope
downslope
02 m
true movement reconstructed
Jij =δbiδxj
δxσ
δb W
δb
δb R
xσ
xσ
δxm
0
0xm
xm
xσ
xm
A Boyle 2016 Carleton University
PhD Defence 11 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
Background material
impedance imaging fwd problem hardware (Ch2)
rocks and conductivity a review (Ch3)
inverse problems composing algorithms (Ch4)
A Boyle 2016 Carleton University
PhD Defence 12 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
Motivation
Derailment of 39 railway cars carrying crude oilGogama ON Canada (2015)
1
Average 600 derailments per year 74 with dangerous goods (Canada 2008-2012)2
Gogama clean-up costs will be ldquoin the millionsrdquo ndash MPP F Gelinas3
1Transportation Safety Board of Canada Railway Investigation Report R15H0021 Mar 20152Transportation Safety Board of Canada Statistical Summary - Railway Occurrences 2013 Feb 20143M Stackelberg CBC News Ontario bills CN $350K for Gogama derailment clean-up Dec 2015
A Boyle 2016 Carleton University
PhD Defence 2 15
Motivation
Mount Polley mine tailings spill Likely BC Canada (2014)4
spilled 45 mil m3 of tailings with clean up costs of $200ndash500 mil
4CBC News ldquoMount Polley mine tailings spillrdquo Aug 2014
A Boyle 2016 Carleton University
PhD Defence 3 15
Motivation
Manage slope stability risks
a tool for real-time monitoring of slope movement
electrode movement amp resistivity
robust reliable informative reconstructions
algorithm implementation data
Our tool of choiceElectrical Impedance TomographyElectrical Resistivity Tomography
A Boyle 2016 Carleton University
PhD Defence 4 15
Motivation
Manage slope stability risks
a tool for real-time monitoring of slope movementelectrode movement amp resistivity
robust reliable informative reconstructionsalgorithm implementation data
Our tool of choiceElectrical Impedance TomographyElectrical Resistivity Tomography
A Boyle 2016 Carleton University
PhD Defence 4 15
Electrical Impedance Tomography
Typical ERT Survey EquipmentABEM TerrameterLS5
5[httpwwwnginoupload48876TerrameterLSjpg]
A Boyle 2016 Carleton University
PhD Defence 5 15
Electrical Impedance Tomography
Typical ERT SurveyPont-Pean France6
6correct electrode wiring
A Boyle 2016 Carleton University
PhD Defence 6 15
Electrical Impedance Tomography
Long-term remote monitoringHollin Hill UK7
7Automated Landslide Electrical Resistivity Tomography (ALERT) system
A Boyle 2016 Carleton University
PhD Defence 7 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||22 (1)
δxn = minus(JTnJn)
minus1(JTnb) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus2
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||2W + ||λR(xminus xlowast)||22 (1)
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast)) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast))
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 9 15
Methods
Resistivity
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 10 15
Methods
Resistivity and movement together
electrode 5 10 15 20 25 30
elec
trod
e m
vmt [
m]
-15
-1
-05
0
05upslope
downslope
02 m
true movement reconstructed
Jij =δbiδxj
δxσ
δb W
δb
δb R
xσ
xσ
δxm
0
0xm
xm
xσ
xm
A Boyle 2016 Carleton University
PhD Defence 11 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
Background material
impedance imaging fwd problem hardware (Ch2)
rocks and conductivity a review (Ch3)
inverse problems composing algorithms (Ch4)
A Boyle 2016 Carleton University
PhD Defence 12 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
Motivation
Mount Polley mine tailings spill Likely BC Canada (2014)4
spilled 45 mil m3 of tailings with clean up costs of $200ndash500 mil
4CBC News ldquoMount Polley mine tailings spillrdquo Aug 2014
A Boyle 2016 Carleton University
PhD Defence 3 15
Motivation
Manage slope stability risks
a tool for real-time monitoring of slope movement
electrode movement amp resistivity
robust reliable informative reconstructions
algorithm implementation data
Our tool of choiceElectrical Impedance TomographyElectrical Resistivity Tomography
A Boyle 2016 Carleton University
PhD Defence 4 15
Motivation
Manage slope stability risks
a tool for real-time monitoring of slope movementelectrode movement amp resistivity
robust reliable informative reconstructionsalgorithm implementation data
Our tool of choiceElectrical Impedance TomographyElectrical Resistivity Tomography
A Boyle 2016 Carleton University
PhD Defence 4 15
Electrical Impedance Tomography
Typical ERT Survey EquipmentABEM TerrameterLS5
5[httpwwwnginoupload48876TerrameterLSjpg]
A Boyle 2016 Carleton University
PhD Defence 5 15
Electrical Impedance Tomography
Typical ERT SurveyPont-Pean France6
6correct electrode wiring
A Boyle 2016 Carleton University
PhD Defence 6 15
Electrical Impedance Tomography
Long-term remote monitoringHollin Hill UK7
7Automated Landslide Electrical Resistivity Tomography (ALERT) system
A Boyle 2016 Carleton University
PhD Defence 7 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||22 (1)
δxn = minus(JTnJn)
minus1(JTnb) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus2
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||2W + ||λR(xminus xlowast)||22 (1)
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast)) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast))
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 9 15
Methods
Resistivity
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 10 15
Methods
Resistivity and movement together
electrode 5 10 15 20 25 30
elec
trod
e m
vmt [
m]
-15
-1
-05
0
05upslope
downslope
02 m
true movement reconstructed
Jij =δbiδxj
δxσ
δb W
δb
δb R
xσ
xσ
δxm
0
0xm
xm
xσ
xm
A Boyle 2016 Carleton University
PhD Defence 11 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
Background material
impedance imaging fwd problem hardware (Ch2)
rocks and conductivity a review (Ch3)
inverse problems composing algorithms (Ch4)
A Boyle 2016 Carleton University
PhD Defence 12 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
Motivation
Manage slope stability risks
a tool for real-time monitoring of slope movement
electrode movement amp resistivity
robust reliable informative reconstructions
algorithm implementation data
Our tool of choiceElectrical Impedance TomographyElectrical Resistivity Tomography
A Boyle 2016 Carleton University
PhD Defence 4 15
Motivation
Manage slope stability risks
a tool for real-time monitoring of slope movementelectrode movement amp resistivity
robust reliable informative reconstructionsalgorithm implementation data
Our tool of choiceElectrical Impedance TomographyElectrical Resistivity Tomography
A Boyle 2016 Carleton University
PhD Defence 4 15
Electrical Impedance Tomography
Typical ERT Survey EquipmentABEM TerrameterLS5
5[httpwwwnginoupload48876TerrameterLSjpg]
A Boyle 2016 Carleton University
PhD Defence 5 15
Electrical Impedance Tomography
Typical ERT SurveyPont-Pean France6
6correct electrode wiring
A Boyle 2016 Carleton University
PhD Defence 6 15
Electrical Impedance Tomography
Long-term remote monitoringHollin Hill UK7
7Automated Landslide Electrical Resistivity Tomography (ALERT) system
A Boyle 2016 Carleton University
PhD Defence 7 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||22 (1)
δxn = minus(JTnJn)
minus1(JTnb) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus2
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||2W + ||λR(xminus xlowast)||22 (1)
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast)) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast))
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 9 15
Methods
Resistivity
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 10 15
Methods
Resistivity and movement together
electrode 5 10 15 20 25 30
elec
trod
e m
vmt [
m]
-15
-1
-05
0
05upslope
downslope
02 m
true movement reconstructed
Jij =δbiδxj
δxσ
δb W
δb
δb R
xσ
xσ
δxm
0
0xm
xm
xσ
xm
A Boyle 2016 Carleton University
PhD Defence 11 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
Background material
impedance imaging fwd problem hardware (Ch2)
rocks and conductivity a review (Ch3)
inverse problems composing algorithms (Ch4)
A Boyle 2016 Carleton University
PhD Defence 12 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
Motivation
Manage slope stability risks
a tool for real-time monitoring of slope movementelectrode movement amp resistivity
robust reliable informative reconstructionsalgorithm implementation data
Our tool of choiceElectrical Impedance TomographyElectrical Resistivity Tomography
A Boyle 2016 Carleton University
PhD Defence 4 15
Electrical Impedance Tomography
Typical ERT Survey EquipmentABEM TerrameterLS5
5[httpwwwnginoupload48876TerrameterLSjpg]
A Boyle 2016 Carleton University
PhD Defence 5 15
Electrical Impedance Tomography
Typical ERT SurveyPont-Pean France6
6correct electrode wiring
A Boyle 2016 Carleton University
PhD Defence 6 15
Electrical Impedance Tomography
Long-term remote monitoringHollin Hill UK7
7Automated Landslide Electrical Resistivity Tomography (ALERT) system
A Boyle 2016 Carleton University
PhD Defence 7 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||22 (1)
δxn = minus(JTnJn)
minus1(JTnb) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus2
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||2W + ||λR(xminus xlowast)||22 (1)
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast)) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast))
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 9 15
Methods
Resistivity
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 10 15
Methods
Resistivity and movement together
electrode 5 10 15 20 25 30
elec
trod
e m
vmt [
m]
-15
-1
-05
0
05upslope
downslope
02 m
true movement reconstructed
Jij =δbiδxj
δxσ
δb W
δb
δb R
xσ
xσ
δxm
0
0xm
xm
xσ
xm
A Boyle 2016 Carleton University
PhD Defence 11 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
Background material
impedance imaging fwd problem hardware (Ch2)
rocks and conductivity a review (Ch3)
inverse problems composing algorithms (Ch4)
A Boyle 2016 Carleton University
PhD Defence 12 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
Electrical Impedance Tomography
Typical ERT Survey EquipmentABEM TerrameterLS5
5[httpwwwnginoupload48876TerrameterLSjpg]
A Boyle 2016 Carleton University
PhD Defence 5 15
Electrical Impedance Tomography
Typical ERT SurveyPont-Pean France6
6correct electrode wiring
A Boyle 2016 Carleton University
PhD Defence 6 15
Electrical Impedance Tomography
Long-term remote monitoringHollin Hill UK7
7Automated Landslide Electrical Resistivity Tomography (ALERT) system
A Boyle 2016 Carleton University
PhD Defence 7 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||22 (1)
δxn = minus(JTnJn)
minus1(JTnb) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus2
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||2W + ||λR(xminus xlowast)||22 (1)
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast)) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast))
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 9 15
Methods
Resistivity
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 10 15
Methods
Resistivity and movement together
electrode 5 10 15 20 25 30
elec
trod
e m
vmt [
m]
-15
-1
-05
0
05upslope
downslope
02 m
true movement reconstructed
Jij =δbiδxj
δxσ
δb W
δb
δb R
xσ
xσ
δxm
0
0xm
xm
xσ
xm
A Boyle 2016 Carleton University
PhD Defence 11 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
Background material
impedance imaging fwd problem hardware (Ch2)
rocks and conductivity a review (Ch3)
inverse problems composing algorithms (Ch4)
A Boyle 2016 Carleton University
PhD Defence 12 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
Electrical Impedance Tomography
Typical ERT SurveyPont-Pean France6
6correct electrode wiring
A Boyle 2016 Carleton University
PhD Defence 6 15
Electrical Impedance Tomography
Long-term remote monitoringHollin Hill UK7
7Automated Landslide Electrical Resistivity Tomography (ALERT) system
A Boyle 2016 Carleton University
PhD Defence 7 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||22 (1)
δxn = minus(JTnJn)
minus1(JTnb) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus2
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||2W + ||λR(xminus xlowast)||22 (1)
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast)) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast))
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 9 15
Methods
Resistivity
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 10 15
Methods
Resistivity and movement together
electrode 5 10 15 20 25 30
elec
trod
e m
vmt [
m]
-15
-1
-05
0
05upslope
downslope
02 m
true movement reconstructed
Jij =δbiδxj
δxσ
δb W
δb
δb R
xσ
xσ
δxm
0
0xm
xm
xσ
xm
A Boyle 2016 Carleton University
PhD Defence 11 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
Background material
impedance imaging fwd problem hardware (Ch2)
rocks and conductivity a review (Ch3)
inverse problems composing algorithms (Ch4)
A Boyle 2016 Carleton University
PhD Defence 12 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
Electrical Impedance Tomography
Long-term remote monitoringHollin Hill UK7
7Automated Landslide Electrical Resistivity Tomography (ALERT) system
A Boyle 2016 Carleton University
PhD Defence 7 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||22 (1)
δxn = minus(JTnJn)
minus1(JTnb) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus2
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||2W + ||λR(xminus xlowast)||22 (1)
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast)) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast))
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 9 15
Methods
Resistivity
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 10 15
Methods
Resistivity and movement together
electrode 5 10 15 20 25 30
elec
trod
e m
vmt [
m]
-15
-1
-05
0
05upslope
downslope
02 m
true movement reconstructed
Jij =δbiδxj
δxσ
δb W
δb
δb R
xσ
xσ
δxm
0
0xm
xm
xσ
xm
A Boyle 2016 Carleton University
PhD Defence 11 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
Background material
impedance imaging fwd problem hardware (Ch2)
rocks and conductivity a review (Ch3)
inverse problems composing algorithms (Ch4)
A Boyle 2016 Carleton University
PhD Defence 12 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||22 (1)
δxn = minus(JTnJn)
minus1(JTnb) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus2
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||2W + ||λR(xminus xlowast)||22 (1)
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast)) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast))
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 9 15
Methods
Resistivity
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 10 15
Methods
Resistivity and movement together
electrode 5 10 15 20 25 30
elec
trod
e m
vmt [
m]
-15
-1
-05
0
05upslope
downslope
02 m
true movement reconstructed
Jij =δbiδxj
δxσ
δb W
δb
δb R
xσ
xσ
δxm
0
0xm
xm
xσ
xm
A Boyle 2016 Carleton University
PhD Defence 11 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
Background material
impedance imaging fwd problem hardware (Ch2)
rocks and conductivity a review (Ch3)
inverse problems composing algorithms (Ch4)
A Boyle 2016 Carleton University
PhD Defence 12 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
Methods
Absolute imaging problem large conductivity contrasts a Gauss-Newton nonlinear iterative solver
minx||Axminus b||2W + ||λR(xminus xlowast)||22 (1)
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast)) (2)
xn+1 = xn + αn+1 δxn+1 (3)
minus1 minus05 0 05 1minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
minus1
0
1
2
A Boyle 2016 Carleton University
PhD Defence 8 15
Methods
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast))
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 9 15
Methods
Resistivity
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 10 15
Methods
Resistivity and movement together
electrode 5 10 15 20 25 30
elec
trod
e m
vmt [
m]
-15
-1
-05
0
05upslope
downslope
02 m
true movement reconstructed
Jij =δbiδxj
δxσ
δb W
δb
δb R
xσ
xσ
δxm
0
0xm
xm
xσ
xm
A Boyle 2016 Carleton University
PhD Defence 11 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
Background material
impedance imaging fwd problem hardware (Ch2)
rocks and conductivity a review (Ch3)
inverse problems composing algorithms (Ch4)
A Boyle 2016 Carleton University
PhD Defence 12 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
Methods
δxn+1 = minus(JTnWJn + λ2RTR)minus1(JT
nWbminus λ2RTR(xn minus xlowast))
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 9 15
Methods
Resistivity
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 10 15
Methods
Resistivity and movement together
electrode 5 10 15 20 25 30
elec
trod
e m
vmt [
m]
-15
-1
-05
0
05upslope
downslope
02 m
true movement reconstructed
Jij =δbiδxj
δxσ
δb W
δb
δb R
xσ
xσ
δxm
0
0xm
xm
xσ
xm
A Boyle 2016 Carleton University
PhD Defence 11 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
Background material
impedance imaging fwd problem hardware (Ch2)
rocks and conductivity a review (Ch3)
inverse problems composing algorithms (Ch4)
A Boyle 2016 Carleton University
PhD Defence 12 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
Methods
Resistivity
Jij =δbiδxj
δx
δb W
δb
δb R
x
x x
A Boyle 2016 Carleton University
PhD Defence 10 15
Methods
Resistivity and movement together
electrode 5 10 15 20 25 30
elec
trod
e m
vmt [
m]
-15
-1
-05
0
05upslope
downslope
02 m
true movement reconstructed
Jij =δbiδxj
δxσ
δb W
δb
δb R
xσ
xσ
δxm
0
0xm
xm
xσ
xm
A Boyle 2016 Carleton University
PhD Defence 11 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
Background material
impedance imaging fwd problem hardware (Ch2)
rocks and conductivity a review (Ch3)
inverse problems composing algorithms (Ch4)
A Boyle 2016 Carleton University
PhD Defence 12 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
Methods
Resistivity and movement together
electrode 5 10 15 20 25 30
elec
trod
e m
vmt [
m]
-15
-1
-05
0
05upslope
downslope
02 m
true movement reconstructed
Jij =δbiδxj
δxσ
δb W
δb
δb R
xσ
xσ
δxm
0
0xm
xm
xσ
xm
A Boyle 2016 Carleton University
PhD Defence 11 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
Background material
impedance imaging fwd problem hardware (Ch2)
rocks and conductivity a review (Ch3)
inverse problems composing algorithms (Ch4)
A Boyle 2016 Carleton University
PhD Defence 12 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
Background material
impedance imaging fwd problem hardware (Ch2)
rocks and conductivity a review (Ch3)
inverse problems composing algorithms (Ch4)
A Boyle 2016 Carleton University
PhD Defence 12 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
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 [xσ xm]T (Ch8)
A Boyle 2016 Carleton University
PhD Defence 13 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
This Work Addresses
inversesolver
improveddecisionoutcomes
boundaryelectrode movement
moreadaptablemodels
fewer artifactsbetter detectability
improvedimagequality
A Boyle 2016 Carleton University
PhD Defence 14 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
Thank You
A Boyle 2016 Carleton University
PhD Defence 15 15
