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Slides for the presentation "3D magnetic inversion by planting anomalous densities" given at the 2013 AGU Meeting of the Americas in Cancun, Mexico. Note: There was an error in the title of the talk. The correct title should be "3D magnetic inversion by planting anomalous magnetization"
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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
Leonardo Uieda
Valéria C. F. Barbosa
Observatório Nacional - Brazil
3D magnetic inversion by planting
anomalous densities
2013 AGU Meeting of the Americas
Leonardo Uieda
Valéria C. F. Barbosa
Observatório Nacional - Brazil
3D magnetic inversion by planting
anomalous magnetization
2013 AGU Meeting of the Americas
(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
In a nutshell
the data
In a nutshell
the data
In a nutshell
the data
the seeds(known physical properties)
In a nutshell
inversion
In a nutshell
Estimate geometry!
In a nutshell
(~ 1 min)Estimate geometry!
In a nutshell fits!
(~ 1 min)Estimate geometry!
Behind the scenes(aka, Methodology)
the data
the “truth”
the seed
the predicted data
the neighbors
add the best
the new predicted
add the best
the new predicted
the new neighbors add the best
the same shape
the fattening
the fattening
the fattening
the final solution
the final solution
fits!
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
Γ=ψ+μθ
θ=∑kl k
regularizing function compactness
distance of added cells to seed
= scalarμ
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
Real data(Morro do Engenho, Brazil)
Previous interpretation
ME for short
Geologic profile
Forward modeling
After Dutra and Marangoni (2009)
Layered complex
Magnetization
Dunite center
Know the magnetization
The data
The data
ME
The data
ME
A2
The data
ME
A2
?
The data
ME
A2
?same as ME?
Test this hypothesis
The seeds
N
N
N
Outcropping
Poor fit!
Get rid of “tentacles”
Use data weights
Use data weights
φ=[∑iwi (d i
o−d i)2 ]
12
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 )
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
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
with weights
N
N
with weights
without weights
N
still outcropping
N
still outcropping
still poor fit
hypothesis
Conclusion
● Fast geometry estimation
● Known magnetization
● Seed position
● Data weights = more robust
● Magnetization of A2 ≠ ME
– Probably higher
Developed open-source
fatiando.org
What we're working on(seed positioning)
the model
the data
Single seed at the top
the not very good estimate
the not very good estimate
Extract new seeds from estimate
the much better estimate
the much better estimate
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