3D magnetic inversion by planting anomalous densities

3D magnetic inversion by planting anomalous densities

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Leonardo Uieda

May 15, 2013
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  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

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  35. the same shape

  36. the fattening

  37. the fattening

  38. the fattening

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  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 (d i o−d i )2 ]1 2 Γ=ψ+μθ
  46. Γ=ψ+μθ θ=∑ k l k regularizing function compactness distance of

    added cells to seed = scalar μ
  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
  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

  61. None
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  64. Poor fit!

  65. Get rid of “tentacles”

  66. Use data weights

  67. Use data weights φ=[∑ i w i (d i o−d

    i )2]1 2
  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 )
  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
  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
  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