pyGIMLi
On inversion of frequency domain electromagnetic data in salt water problems Thomas Günther Leibniz Institute for Applied Geophysics (LIAG), Hannover
Questions
Imaging of 2-layer case (100 − 3 Ωm) Resolution measures
66 82 100
IP d=100m h=1m
IP d=200m h=1m
IP d=10m h=40m
16 z in m
32 50 66
56k 28k 14k 7k 3.5k 1.7k 880 440 220 110
56k 28k 14k 7k 3.5k 1.7k 880 440 220 110
56k 28k 14k 7k 3.5k 1.7k 880 440 220 110
100
56k 28k 14k 7k 3.5k 1.7k 880 440 220 110
82
IP d=200m h=1m
32 50 66 82 100 0
OP d=50m h=1m
OP d=100m h=1m
OP d=200m h=1m
66 100
20
20 z in m
δ=4.3m
30 δ=52.3%
30
Rx-Tx=100m
10
δ=4.7%
δ=25.7%
40
50 δ=30.8%
50 δ=14.2%
3
10
30
100 300 601
30
40
δ=8.1m
50
0
Rx-Tx=150m
10
δ=3.8%
10
30
δ=1.0m δ=10.3% δ=4.2m
100 300 601
3
10
30
δ=1.2%
30 δ=0.9m δ=17.0%
40 δ=4.4m
40
50 δ=21.4% 601
3
30
50
0
DC
10
δ=0.6%
10
30
δ=4.0m δ=89.1% δ=25.2m
100 300 601
3
δ=0.5%
δ=1.3m δ=16.0%
f [Hz]
1760 440 110
200
250
300 x [m]percent outphase
350
400
f [Hz]
7040 1760 440 110
200
250
300 x [m]
350
300
d1 d2 d3 ρ 1 ρ 2 ρ 3
δ=5.1m
0
err=1.0%
20
20 δ=5.8m
δ=2.0m
30 δ=16.9%
10
30
100 300 601δ=19.2%3
30 δ=50.8%
40 δ=37.6m
50 δ=13.7m
3
err=2.0%
50 δ=25.3% 10
30
100 300 601
3
10
30
100 300
δ=8.8%
30
0 δ=1.5%
10 δ=18.0%
10 δ=27.8%
20 δ=5.6m
20 δ=6.8m
20
30
30
30
δ=0.3m
δ=193.8%
δ=128.9%
40
δ=0.1m 10 δ=6.3% δ=0.8m
40
40 δ=1.5m
50 δ=19.9m
50 δ=40.6m
50
δ=1.1%
60 δ=36.2%
60
60
100 300 601
3
10
30
δ=8.7% δ=2.2m δ=6.2%
δ=8.6% DC EM 701 3 10 30 100 300 701 3 10 30 100 300 701 Results of individual and joint inversion with lithology
100 300
3
10
30
DCEM 100 300
Conclusions & Outlook Tx-Rx geometry highly influences FDEM sensitivity I resolution properties depend on noise level I combination of Tx-Rx can improve result slightly I DC resolves resistors, EM resolves conductors ⇒ combined inversion highly recommended 2 I χ test underestimates, MCM overestimates uncertainty I
20 40 60 80 100
10 0 10 20 30 40 50 60 70
28160
100
10 δ=12.2%
40
0
7040
30
10 δ=5.2%
δ=2.5%
Shallow salt water over Eem clay layer and deep saltwater intrusion (Attwa et al., 2011) 30 15 0 15 30 45 60 75 90
10
RD
I14k I7k I3k I2k I880 I440 I220 I110 O14k O7k O3k O2k O880 O440 O220 O110 ρ4 I14k I2k I220 O7k O880O110
Inversion and resolution analysis of synthetic model: χ2 test (bars), model variance (numbers), model covariance matrix (MCM), model (RM) & data (RD) resolution matrix
-50
0
Laterally Constrained Inversion: Cuxhaven profile
28160
3
0 δ=1.7%
40
Combined inversion DC+FDEM is superior to single and decreases uncertainty
inphase percent
δ=53.9m
1
δ=1.3m
30 δ=0.4m
50 10
d1 d2 d3 ρ1 ρ2 ρ3 ρ4
0 δ=59.8%
DCEM
20
δ=1.3%
δ=62.4m
d1 d2 d3 ρ 1 ρ 2 ρ 3 ρ 4
Joint inversion field case Cuxhaven
20 z in m
z in m
20
MCM-scaled
60 δ=16.6%
err=0.5%
601
100 300
z in m
10
d1 d2 d3 ρ 1 ρ 2 ρ 3 ρ 4
δ=200.5%
50
d1 d2 d3 ρ1 ρ2 ρ3 ρ4
Result for combined Tx-Rx data and different noise
z in m
10
EM
40
50 δ=11.0%
Joint inversion FDEM+DC 0
30
40
Synthetic model inversion for three Tx-Rx separations
0
30 δ=101.5%
20
δ=7.5%
3
0
RM
d1 d2 d3 ρ1 ρ2 ρ3 ρ4
Synthetic experiment combined geometry
20
40 δ=56.4m
601
0
δ=2.4m
20 δ=12.3m
Anomaly of a saltwater interface as a function of depth
z in m
10
z in m
10 δ=8.2%
10
-40
82
z in m
Rx-Tx=50m
10 δ=32.2%
-30
50
synthetic estimated
20
-20
32
MCM
0
30
-10
OP d=10m h=40m
16
Synthetic experiment for different geometry 0
%
16
Layer sensitivity for different Tx-Rx (d) and height (h)
0
IP d=10m h=40m
z in m
IP d=50m h=1m
0
IP d=100m h=1m
z in m
50
IP d=50m h=1m
z in m
z in m
32
0
4 3 3 2 2 1 1 0 0 0 -1 -1 -2 -2 -3 -3 -4
112k 56k 28k 14k 7k 3.5k 1.7k 880 440 220 110
16
%
112k 56k 28k 14k 7k 3.5k 1.7k 880 440 220 110
IP d=10m h=40m
112k 56k 28k 14k 7k 3.5k 1.7k 880 440 220 110
IP d=200m h=1m
z in m
IP d=100m h=1m
z in m
IP d=50m h=1m
z in m
Depth sensitivity: geometries 0
Geophysical Inversion & Modelling Library in Python I error-weighted Gauss-Newton minimization 2 I block (λ → 0) or smooth discretization (λ: χ =1) I very simple joint inversion for same or other parameters 2 I uncertainty analysis by parameter variation (χ test), model covariance/resolution and data importance matrices
How do the different frequencies contribute? I Influence of loop separation and system height? I How is the resolution compared to VES (or TEM)? I What can we improve by prior knowledge? I Improvement by combination of different techniques? I How to combine line data with coupled soundings? I
112k 56k 28k 14k 7k 3.5k 1.7k 880 440 220 110
saltwater is an important issue on coasts and inland (N. Germany) I FDEM represents fast large-scale conductivity imaging I applied airborne (HEM) and on ground (MaxMin/Promys)
I
Framework – pyGIMLi
z in m
Motivation
400
120 200
1.0
250
4.2
300
350
17
72
Data (left) and 2d model (top) from LCI type inversion
Attwa, M., Günther, T., Grinat, M. & Binot, F. (2011): Evaluation of DC, FDEM and IP resistivity methods for imaging perched saltwater and a shallow channel within coastal tidal flat sediments, J. Appl. Geoph. 75, 656-670.
http://www.liag-hannover.de
Outlook
400
300
more rigorous treatment of HEM data I Strategy: first combined inversions (with VES, TEM, MRS, etc.), then 2d/3d LCI/SCI inversion using results of combined inversion as reference I
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