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Leonardo Uieda
Valéria C. F. Barbosa
Observatório Nacional - Brazil
3D magnetic inversion by planting
anomalous densities
2013 AGU Meeting of the Americas
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Leonardo Uieda
Valéria C. F. Barbosa
Observatório Nacional - Brazil
3D magnetic inversion by planting
anomalous densities
2013 AGU Meeting of the Americas
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Leonardo Uieda
Valéria C. F. Barbosa
Observatório Nacional - Brazil
3D magnetic inversion by planting
anomalous magnetization
2013 AGU Meeting of the Americas
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(Short) History of planting inversion
● Uieda and Barbosa (early 2012) based on René (1986)
● For gravity and gradients
● Deal with computational difficulties
– A lot of data
– Large meshes
● A way to input geologic/geophysical information
● Improvements at SEG 2012
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In a nutshell
the data
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In a nutshell
the data
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In a nutshell
the data
the seeds(known physical properties)
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In a nutshell
inversion
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In a nutshell
Estimate geometry!
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In a nutshell
(~ 1 min)Estimate geometry!
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In a nutshell fits!
(~ 1 min)Estimate geometry!
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Behind the scenes(aka, Methodology)
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the data
the “truth”
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the seed
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the predicted data
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the neighbors
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add the best
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the new predicted
add the best
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the new predicted
the new neighbors add the best
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the same shape
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the fattening
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the fattening
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the fattening
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the final solution
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the final solution
fits!
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Why it grows that way
● Choice of the best:
1. Not random
2.
3. Smallest goal function
φ=[∑i(d i
o−d i)2 ]
12
Γ=ψ+μθ
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Γ=ψ+μθ
θ=∑kl k
regularizing function compactness
distance of added cells to seed
= scalarμ
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Γ=ψ+μθ
θ=∑kl k
regularizing function compactness
distance of added cells to seed
ψ=[∑i(α d i
o−d i)
2 ]12
shape-of-anomaly function (René, 1986)
scale factor between observed and predicted
= scalarμ
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Real data(Morro do Engenho, Brazil)
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Previous interpretation
ME for short
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Geologic profile
Forward modeling
After Dutra and Marangoni (2009)
Layered complex
Magnetization
Dunite center
Know the magnetization
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The data
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The data
ME
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The data
ME
A2
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The data
ME
A2
?
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The data
ME
A2
?same as ME?
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Test this hypothesis
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The seeds
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N
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N
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N
Outcropping
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Poor fit!
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Get rid of “tentacles”
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Use data weights
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Use data weights
φ=[∑iwi (d i
o−d i)2 ]
12
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Use data weights
φ=[∑iwi (d i
o−d i)2 ]
12
w i=exp(−[(xi−x s)2+( yi− y s)
2]2
σ4 )
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Use data weights
φ=[∑iwi (d i
o−d i)2 ]
12
w i=exp(−[(xi−x s)2+( yi− y s)
2]2
σ4 )s = closest seed
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Use data weights
φ=[∑iwi (d i
o−d i)2 ]
12
w i=exp(−[(xi−x s)2+( yi− y s)
2]2
σ4 )s = closest seed
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with weights
N
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N
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with weights
without weights
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N
still outcropping
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N
still outcropping
still poor fit
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hypothesis
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Conclusion
● Fast geometry estimation
● Known magnetization
● Seed position
● Data weights = more robust
● Magnetization of A2 ≠ ME
– Probably higher
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Developed open-source
fatiando.org
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What we're working on(seed positioning)
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the model
the data
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Single seed at the top
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the not very good estimate
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the not very good estimate
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Extract new seeds from estimate
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the much better estimate
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the much better estimate