1 challenge the future gradient based technique for electromagnetic layered earth model data...
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1Challenge the future
Gradient based technique for electromagnetic layered earth model data inversionClaudio Patriarca, Andrea Di Matteo and Evert Slob
2011 IEEE Internation Geoscience and Remote Sensing Symposium, Vancouver BC, July 2011
2Challenge the future
Local or Global inversionInversion Schemes
Gradient descent Global Multilevel Coordinate search
3Challenge the future
Full-waveform inversion
• Size of parameter space – nr. layers• Number of local minima - nonlinearity• Parameter correlations – limit sensitivity• UWB – many frequency points
EM Inversion Schemes – non linear
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Towards local inversion
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Jacobian
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5Challenge the future
• Numerically evaluated
• Explicitly given
Jacobian calculationNumerical vs Explicit gradient
6Challenge the future
Local Full-waveform inversionNumerical test case #1: smooth model
7Challenge the future
Local Full-waveform inversionNumerical test case #1 result
h2 (m) εq · 10-3 m εm ϕ
Model Parameters 0,10 35 4,5 -
GMCS 0,10 24 3.0 0,135
Gradient 0,10 17 3,7 0,135
8Challenge the future
Full-waveform inversionReal data test case
Marble floor element in the Ancient theatre of Megalopolis, Greece
• Large datasets
• UWB data (SFCW)
9Challenge the future
Local Full-waveform inversionReal data test case
10Challenge the future
Local Full-waveform inversionReal data test case results
h1 (m) h2 (m) ε2 logσ2 (Sm-1) ϕ
GMCS 0,19 0,15 6,08 -1,06 0,24
Gradient 0,19 0,14 5,51 -1,01 0,25
11Challenge the future
Local Full-waveform inversionNumerical test case #2: piecewise layered half-space
12Challenge the future
Objective Function topographyNumerical test case #2: piecewise layered half-space
Global Minimum
ε1
ε2
h2
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Conclusion
• Local inversion advantages in moving downhill; problems with local minima
• Comparison Global and Local search numerical and real data: success of local methods in specialized applications
• Use explicit gradient
• Deep interfaces?
• Convenient implementing Hessian?