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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Inversion of 3D Electromagnetics:
A maturing technique in applied geophysics
Eldad Haber
Collaborators: Doug Oldenburg, Roman Shekhtman,Scott Napier, and Rob Eso
http://www.dma.state.mn.us/
http://www.centennialofflight.gov
Environmental: UXOEnergy 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
(half sine, step…)
I
Time
Source
(Loop or grounded electrode)
Measurements
(E, H, dB/dt)
Borehole
(E, H, dB/dt)
Depth
3D TEM SetupBoundary conditions
Initial conditions
Mathematical Setuptime [0, tf]
This must be solved in both space and time.
where
Need initial conditions to start time stepping.
Case 1:
t
0
Case 2:
E0, H0 fields are from DC currents
t
0
Solve
DC Resistivity
MMR
Initial ConditionsTime stepping starts with fields at time t = 0
 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:
Maxwell’s Equations:
Source term:
Maxwell’s equations:
Write:
Solve: Aj (m)uj = qj using BICGStab with ILU preconditioner.
Solve An, Φ system using BICGstab with block ILU preconditioner (same as EH3D)
Solving the systemSolve
Let nc = number of cells
number of unknowns ~ 7(nc)3
if nc = 64 matrix size = (2x106)2
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 Ohmm
The Cominco exampleThe “Cominco” model: loop source, conductive target in a host
Velocity of smoke ring
Nabighian (1979)
Currents decay
Induction finished t~0.01 sec
Sampling time for movies: 62 frames [10^6 – 10^2]
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
Airborne, surface or borehole measurements
Inversion
processing
?
Inversion
What is Inversion?Goal: Estimate the Earth model
Inversion
Measurements
Preprocessing
Physical property
distributions = Inversion
3D, and ~ 105 cells
Inversion procedure:A priori information: reference model, structural detail...
Model objective function:
Misfit:
Inversion as optimization:
= d + m.0 < < is a constant
Choose such that d < Tolerance
Inversion as optimization: 3 partsMinimize = d + m
where
: Regularization parameter
Q: Projection matrix
u: Potentials
: Observations
: Model and Reference model
Wd,W : Measurement error, model weighting
Differentiating the objective function with model m
where sensitivity matrix
and
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!
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:
Choose0, mref
Evaluate (mref), g(mref), matrices Wd, W...
For cooling loop
For k = 1 max iterations
End
Reduce
End
Flow chartMafic 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 DepositGeologic cross section
Location
Physical properties
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 NicolasLoop 1
Loop 9
San Nicolas UTEM Geophysics SurveyUTEM channel 4 (1.513ms)
1075
dBz/dt
northing
nT/s
1300
220
3000
easting
background model
discretize
validate
forward model
error assignment
a priori
information
inversions
evaluate results
A simplified procedure for inverting timedomain electromagnetic (TEM) surveysObserved 15 m isosurface
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 ObservationsResistivity 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
1000
Recovered cross section at 450 S
Recovered cross section at 1380 W
m
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?
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 DepositGeologic cross section
Physical properties
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.
300
ohmm
55
10
3D model from many 1D columnmodels
Isosurface view of the same 3D conductivity model
300
ohmm
55
10
3D inversion results: Frequencies ..
Isosurface view of the same 3D conductivity model
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
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 DepositGeologic cross section
Physical properties
magnetic susceptibility
densitycontrast
conductivity
chargeability