$30 off During Our Annual Pro Sale. View Details »

3D magnetic inversion by planting anomalous densities

3D magnetic inversion by planting anomalous densities

Leonardo Uieda

May 15, 2013
Tweet

More Decks by Leonardo Uieda

Other Decks in Science

Transcript

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

    View Slide

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

    View Slide

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

    View Slide

  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

    View Slide

  5. In a nutshell
    the data

    View Slide

  6. In a nutshell
    the data

    View Slide

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

    View Slide

  8. In a nutshell
    inversion

    View Slide

  9. In a nutshell
    Estimate geometry!

    View Slide

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

    View Slide

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

    View Slide

  12. Behind the scenes
    (aka, Methodology)

    View Slide

  13. the data
    the “truth”

    View Slide

  14. the seed

    View Slide

  15. the predicted data

    View Slide

  16. the neighbors

    View Slide

  17. add the best

    View Slide

  18. the new predicted
    add the best

    View Slide

  19. the new predicted
    the new
    neighbors add the best

    View Slide

  20. View Slide

  21. View Slide

  22. View Slide

  23. View Slide

  24. View Slide

  25. View Slide

  26. View Slide

  27. View Slide

  28. View Slide

  29. View Slide

  30. View Slide

  31. View Slide

  32. View Slide

  33. View Slide

  34. View Slide

  35. the same shape

    View Slide

  36. the fattening

    View Slide

  37. the fattening

    View Slide

  38. the fattening

    View Slide

  39. View Slide

  40. View Slide

  41. View Slide

  42. View Slide

  43. the final solution

    View Slide

  44. the final solution
    fits!

    View Slide

  45. 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

    View Slide

  46. Γ=ψ+μθ
    θ=∑
    k
    l
    k
    regularizing function compactness
    distance of added cells to seed
    = scalar
    μ

    View Slide

  47. 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

    View Slide

  48. Real data
    (Morro do Engenho, Brazil)

    View Slide

  49. Previous interpretation
    ME for short

    View Slide

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

    View Slide

  51. The data

    View Slide

  52. The data
    ME

    View Slide

  53. The data
    ME
    A2

    View Slide

  54. The data
    ME
    A2
    ?

    View Slide

  55. The data
    ME
    A2
    ?
    same as ME?

    View Slide

  56. Test this hypothesis

    View Slide

  57. The seeds

    View Slide

  58. N

    View Slide

  59. N

    View Slide

  60. N
    Outcropping

    View Slide

  61. View Slide

  62. View Slide

  63. View Slide

  64. Poor fit!

    View Slide

  65. Get rid of “tentacles”

    View Slide

  66. Use data weights

    View Slide

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

    View Slide

  68. 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
    )

    View Slide

  69. 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

    View Slide

  70. 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

    View Slide

  71. with weights
    N

    View Slide

  72. N

    View Slide

  73. with weights
    without weights

    View Slide

  74. N
    still outcropping

    View Slide

  75. N
    still outcropping
    still poor fit

    View Slide

  76. hypothesis

    View Slide

  77. Conclusion

    Fast geometry estimation

    Known magnetization

    Seed position

    Data weights = more robust

    Magnetization of A2 ≠ ME
    – Probably higher

    View Slide

  78. Developed open-source
    fatiando.org

    View Slide

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

    View Slide

  80. the model
    the data

    View Slide

  81. Single seed at the top

    View Slide

  82. the not very good estimate

    View Slide

  83. the not very good estimate

    View Slide

  84. Extract new seeds from estimate

    View Slide

  85. the much better estimate

    View Slide

  86. the much better estimate

    View Slide