3D magnetic inversion by planting anomalous densities

Transcript

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

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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
   

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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
   

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5. In a nutshell
   the data
   

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6. In a nutshell
   the data
   

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

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8. In a nutshell
   inversion
   

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9. In a nutshell
   Estimate geometry!
   

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

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

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12. Behind the scenes
    (aka, Methodology)
    

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13. the data
    the “truth”
    

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14. the seed
    

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15. the predicted data
    

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16. the neighbors
    

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17. add the best
    

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18. the new predicted
    add the best
    

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19. the new predicted
    the new
    neighbors add the best
    

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35. the same shape
    

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36. the fattening
    

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37. the fattening
    

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38. the fattening
    

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43. the final solution
    

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44. the final solution
    fits!
    

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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
    

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

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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
    

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48. Real data
    (Morro do Engenho, Brazil)
    

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49. Previous interpretation
    ME for short
    

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

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51. The data
    

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52. The data
    ME
    

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53. The data
    ME
    A2
    

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54. The data
    ME
    A2
    ?
    

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55. The data
    ME
    A2
    ?
    same as ME?
    

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56. Test this hypothesis
    

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57. The seeds
    

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58. N
    

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59. N
    

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60. N
    Outcropping
    

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64. Poor fit!
    

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65. Get rid of “tentacles”
    

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66. Use data weights
    

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

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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
    )
    

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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
    

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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
    

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71. with weights
    N
    

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72. N
    

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73. with weights
    without weights
    

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74. N
    still outcropping
    

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75. N
    still outcropping
    still poor fit
    

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76. hypothesis
    

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

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78. Developed open-source
    fatiando.org
    

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

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80. the model
    the data
    

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81. Single seed at the top
    

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82. the not very good estimate
    

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83. the not very good estimate
    

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84. Extract new seeds from estimate
    

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85. the much better estimate
    

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86. the much better estimate
    

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