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3D magnetic inversion by planting anomalous densities
Leonardo Uieda
May 15, 2013
Science
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3D magnetic inversion by planting anomalous densities
Leonardo Uieda
May 15, 2013
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Transcript
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
None
None
None
None
None
None
None
None
None
None
None
None
None
None
None
the same shape
the fattening
the fattening
the fattening
None
None
None
None
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 ]1 2 Γ=ψ+μθ
Γ=ψ+μθ θ=∑ k l k regularizing function compactness distance of
added cells to seed = scalar μ
Γ=ψ+μθ θ=∑ k l k regularizing function compactness distance of
added cells to seed ψ=[∑ i (α d i o−d i )2]1 2 shape-of-anomaly function (René, 1986) scale factor between observed and predicted = scalar μ
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
None
None
None
Poor fit!
Get rid of “tentacles”
Use data weights
Use data weights φ=[∑ i w i (d i o−d
i )2]1 2
Use data weights φ=[∑ i w i (d i o−d
i )2]1 2 w i =exp (−[(x i −x s )2+( y i −y s )2]2 σ4 )
Use data weights φ=[∑ i w i (d i o−d
i )2]1 2 w i =exp (−[(x i −x s )2+( y i −y s )2]2 σ4 ) s = closest seed
Use data weights φ=[∑ i w i (d i o−d
i )2]1 2 w i =exp (−[(x i −x s )2+( y i −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