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"

1. Leonardo Uieda
Valéria C. F. Barbosa
Observatório Nacional - Brazil
3D magnetic inversion by planting
anomalous densities
2013 AGU Meeting of the Americas

2. Leonardo Uieda
Valéria C. F. Barbosa
Observatório Nacional - Brazil
3D magnetic inversion by planting
anomalous densities
2013 AGU Meeting of the Americas

3. Leonardo Uieda
Valéria C. F. Barbosa
Observatório Nacional - Brazil
3D magnetic inversion by planting
anomalous magnetization
2013 AGU Meeting of the Americas

4. (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

5. In a nutshell
the data

6. In a nutshell
the data

7. In a nutshell
the data
the seeds
(known physical properties)

8. In a nutshell
inversion

9. In a nutshell
Estimate geometry!

10. In a nutshell
(~ 1 min)Estimate geometry!

11. In a nutshell fits!
(~ 1 min)Estimate geometry!

12. Behind the scenes
(aka, Methodology)

13. the data
the “truth”

14. the seed

15. the predicted data

16. the neighbors

17. add the best

18. the new predicted
add the best

19. the new predicted
the new
neighbors add the best

35. the same shape

36. the fattening

37. the fattening

38. the fattening

43. the final solution

44. the final solution
fits!

45. Why it grows that way
● Choice of the best:
1. Not random
2.
3. Smallest goal function
φ=[∑i
(di
o
−di)2
]
1
2
Γ=ψ+μθ

46. Γ=ψ+μθ
θ=∑k
lk
regularizing function compactness
distance of added cells to seed
= scalarμ

47. Γ=ψ+μθ
θ=∑k
lk
regularizing function compactness
distance of added cells to seed
ψ=[∑i
(α di
o
−di)
2
]
1
2
shape-of-anomaly function (René, 1986)
scale factor between observed and predicted
= scalarμ

48. Real data
(Morro do Engenho, Brazil)

49. Previous interpretation
ME for short

50. Geologic profile
Forward modeling
After Dutra and Marangoni (2009)
Layered complex
Magnetization
Dunite center
Know
the magnetization

51. The data

52. The data
ME

53. The data
ME
A2

54. The data
ME
A2
?

55. The data
ME
A2
?
same as ME?

56. Test this hypothesis

57. The seeds

58. N

59. N

60. N
Outcropping

64. Poor fit!

65. Get rid of “tentacles”

66. Use data weights

67. Use data weights
φ=[∑i
wi (di
o
−di)2
]
1
2

68. Use data weights
φ=[∑i
wi (di
o
−di)2
]
1
2
wi=exp(−[(xi−xs)2
+( yi−ys)2
]2
σ4 )

69. Use data weights
φ=[∑i
wi (di
o
−di)2
]
1
2
wi=exp(−[(xi−xs)2
+( yi−ys)2
]2
σ4 )
s = closest seed

70. Use data weights
φ=[∑i
wi (di
o
−di)2
]
1
2
wi=exp(−[(xi−xs)2
+( yi−ys)2
]2
σ4 )
s = closest seed

71. with weights
N

72. N

73. with weights
without weights

74. N
still outcropping

75. N
still outcropping
still poor fit

76. hypothesis

77. Conclusion
● Fast geometry estimation
● Known magnetization
● Seed position
● Data weights = more robust
● Magnetization of A2 ≠ ME
– Probably higher

78. Developed open-source
fatiando.org

79. What we're working on
(seed positioning)

80. the model
the data

81. Single seed at the top

82. the not very good estimate

83. the not very good estimate

84. Extract new seeds from estimate

85. the much better estimate

86. the much better estimate