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Evolutionary Algorithms for Inversion of Magnetic ResonanceSoundings jointly with DC Resistivity Soundings
Thomas Günther1, Irfan Akca1,2, Mike Müller-Petke1
1Leibniz Institute for Applied Geophysics (LIAG), Hannover; 2Ankara University
Motivation
Evolutionary (better bio-inspired) algorithms (EA)I seek a global optimum of the objective functionI can tell about the variety of model typesI inform about uncertainty of model parametersUnknowns: layer thickness d, θ&T∗2 (MRS), ρ (VES)Application to three joint soundings from Borkum(Günther&Müller-Petke, 2012)
Questions
I Which algorithms are suited and fast?I How to select proper parameters?I Are are the results stable?I How to trade-off convergence and diversity?I What can EA tell us what LS cannot?I How to join different methods?I Can EA and LS methods be combined?
Bio-inspired algorithms
I Genetic Algorithm (GA)I Evolution Strategy (ES)I Differential Evolution Algorithm (DEA)I Estimation of Distribution Algorithm (EDA)I Simulated Annealing (SA)I Particle Swarm Optimization (PSO)I Ant Colony System (ACS)
The python module inspyred
I free and open-source library (inspyred.github.io)I object-oriented implementation for clear scriptsI use of multiple processors for speed-upI flexible design combining classical or creating new
functions
Elements and scheme:Create initial population using GENERATOREvaluate initial population using EVALUATORwhile TERMINATOR is not true:
Choose parents via SELECTORGenerate offspring using VARIATOREvaluate offspring using EVALUATORReplace individuals using REPLACERMigrate individuals using MIGRATORArchive individuals using ARCHIVERCall OBSERVER for export/statistics
e.g. GA withVARIATOR=blended crossover + gaussian mutation,SELECTOR=tournament, REPLACER=generational
MRS-Inversion Example Borkum
Least-squares result of sounding CL2
0.0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4θ
0
10
20
30
40
50
60
70
Depth
[m
]
20 50 100 200 500T ∗
2 [ms]
0
10
20
30
40
50
60
70
Depth
[m
]
43.0 113.0 293.0 738.0t [ms]
0.1
0.1
0.2
0.5
0.9
1.8
3.5
6.9
q [
As]
measured data [nV]
43.0 113.0 293.0 738.0t [ms]
0.1
0.1
0.2
0.5
0.9
1.8
3.5
6.9
q [
As]
simulated data [nV]
0 150 300 450 600 750 900 1050 0 150 300 450 600 750 900 1050
0
10
20
30
40
50
60
depth
[m
]
finesand
silt
clay
finesand
clay
sand
measured (left) and simulated (right) datauncertainties by bootstrapping (χ2 test)
Genetic Algorithm
models with χ2<2
0 50 100 150 200 250 300Generation
100
101
102
103
Fitn
ess
median
best
worst
average
population convergence
Particle Swarm Optimization
models with χ2<2
0 50 100 150 200 250 300Generation
100
101
102
103
Fitn
ess
median
best
worst
average
population convergence
Multi-objective joint inversion
Principle of Non-dominated sorting GA (NSGA-II;Deb, 2002) after Akca et al. (2013):
I Pareto-rank defines fitness of individualsI coupling of MRS and VES by common thickness
Sounding CL2 (as above)
100 101
MRS misfit (χ2 )
100
101
102
103
VES m
isfit
(χ2
)
generations
510204080150300
fast convergence & good match
models with χ2<1.5χ2min (black=corner)
Sounding SKD
100 101 102
MRS misfit (χ2 )
100
101
102
103
VES m
isfit
(χ2
)
generations
510204080150300
slow convergence & medium match
models with χ2<2χ2min (no corner)
Sounding OD33
101 102 103
MRS misfit (χ2 )
100
101
102
103
VES m
isfit
(χ2
)
generations
510204080150300
fast convergence & perfect match
models with χ2<1.5χ2min (black=corner)
ERT with GA (Attwa et al., 2014)
Model: thickness@control points and resistivity
Conclusions & Outlook
I advantages of EA: different model types, numberof layers decision, global uncertainty
I GA and PSO are fastest and robustI PSO: very fast, but injective⇒ local uncertainty
GA: slower, but keeps diversity⇒ local uncertaintyI joint inversion using Pareto rank optimization:
shape front⇒ convergence, model matchI outlook: 2D joint inversion of ERT (Attwa et al.
2014) and magnetic resonance tomography
ReferencesGünther, T. & Müller-Petke, M. (2012): Hydraulic properties at the NorthSea island of Borkum derived from joint inversion of magnetic resonanceand electrical resistivity soundings. - Hydrol. Earth Syst. Sci., 16 (9),3279-3291.Akca, I., Günther, T., Müller-Petke, M., Basokur, A.T. & Yaramanci, U.(2013): Joint parameter estimation from magnetic resonance and verticalelectric soundings using a multi-objective genetic algorithm. Geoph. Prosp.62, 364-376.Attwa, M., Akca, I., Basokur, A. & Günther, T. (2014): Structure-basedgeoelectrical models derived from genetic algorithms: A case study forhydrogeological investigations along Elbe River coastal area, Germany. J.of Appl. Geophys., 103, 57-70.Deb, K. (2002): Multi-Objective Optimization using Evolutionary Algorithms.John Wiley & Sons, Ltd, Chichester, England.
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