E-poster presentation given at the 2012 SEG Annual Meeting in Las Vegas. Abstract: We present an improvement to the method of 3D gravity gradient inversion by planting anomalous densities. This method estimates a density-contrast distribution defined on a grid of right-rectangular prisms. Instead of solving large equation systems, the method uses a systematic search algorithm to grow the solution, one prism at a time, around user-specified prisms called “seeds”. These seeds have known density contrasts and the solution is constrained to be concentrated around the seeds as well as have their density contrasts. Thus, prior geologic and geophysical information are incorporated into the inverse problem through the seeds. However, this leads to a strong dependence of the solution on the correct location, density contrast, and number of seeds used. Our improvement to this method consists of using the “shape-of-anomaly” data-misfit function in conjunction with the l2-norm data-misfit function. The shape-of-anomaly function measures the different in shape between the observed and predicted data and is insen- sitive to differences in amplitude. Tests on synthetic and real data show that the improved method not only has an increased robustness with respect to the number of seeds and their locations, but also provides a better fit of the observed data.

1. Use of the “shape-of-anomaly” data misfit in
3D inversion by planting anomalous densities
Leonardo Uieda
Valéria C. F. Barbosa

2. Difference in shape

4. Scale factor: d i =α g i

5. Scale factor: d i =α g i
√
N
SOA= ∑ (α g i −d i )
2
i=1

6. Scale factor: d i =α g i
√
N
SOA= ∑ (α g i −d i ) 2
i=1
N
∑ gi di
i=1
min SOA α= N
∑ gi 2
i=1

7. Predicted (model)
d, g α SOA
Observed

10. Planting anomalous densities

11. g i (observed)

12. mesh

13. d i (predicted)
seed

14. Choose the best:
√
N
φ= ∑ ( g i −d i )
2
i=1
&
min of Γ=φ+μ θ
compactness

15. Choose the best:
√
N
φ= ∑ ( g i −d i )
2
i=1
&
min of Γ=SOA+μ θ
Exchange for shape-of-anomaly

16. SOA Γ=φ+μ θ Γ=SOA+μ θ SOA

17. SOA Γ=φ+μ θ Γ=SOA+μ θ SOA

18. SOA Γ=φ+μ θ Γ=SOA+μ θ SOA

19. SOA Γ=φ+μ θ Γ=SOA+μ θ SOA

20. SOA Γ=φ+μ θ Γ=SOA+μ θ SOA

21. SOA Γ=φ+μ θ Γ=SOA+μ θ SOA

22. SOA Γ=φ+μ θ Γ=SOA+μ θ SOA

23. SOA Γ=φ+μ θ Γ=SOA+μ θ SOA

24. SOA Γ=φ+μ θ Γ=SOA+μ θ SOA

25. SOA Γ=φ+μ θ Γ=SOA+μ θ SOA

26. SOA Γ=φ+μ θ Γ=SOA+μ θ SOA

27. SOA Γ=φ+μ θ Γ=SOA+μ θ SOA

28. Synthetic tests

32. SOA

33. SOA

34. SOA SOA

35. SOA SOA

37. SOA

38. SOA

39. SOA SOA

41. SOA

42. SOA

43. SOA SOA

44. Redenção granite

45. Bouguer anomaly
Outcrop

46. Bouguer anomaly
Oliveira et al.(2008)
~ 6 km

47. Bouguer anomaly
Oliveira et al.(2008)
Seed at 3km ~ 6 km

48. Known
SOA outcrop

49. Known
SOA outcrop
Outcrop at
wrong place

50. Known
SOA outcrop
Outcrop at
wrong place
~ 9 km

51. SOA

52. SOA
Outcrop at
right place

53. SOA
Outcrop at
right place
~ 6 km

54. SOA SOA
5

55. SOA SOA
5
6 km

56. In conclusion

57. SOA SOA

58. SOA SOA

59. SOA SOA

60. SOA SOA