Leonardo Uieda and Valéria C. F. Barbosa Satellite observations of the gravity field have provided geophysicists with exceptionally dense and uniform coverage of data over vast areas. This enables regional or global scale high resolution geophysical investigations. Techniques like forward modeling and inversion of gravity anomalies are routinely used to investigate large geologic structures, such as large igneous provinces, suture zones, intracratonic basins, and the Moho. Accurately modeling such large structures requires taking the sphericity of the Earth into account. A reasonable approximation is to assume a spherical Earth and use spherical coordinates. In recent years, efforts have been made to advance forward modeling in spherical coordinates using tesseroids, particularly with respect to speed and accuracy. Conversely, traditional space domain inverse modeling methods have not yet been adapted to use spherical coordinates and tesseroids. In the literature there are a range of inversion methods that have been developed for Cartesian coordinates and right rectangular prisms. These include methods for estimating the relief of an interface, like the Moho or the basement of a sedimentary basin. Another category includes methods to estimate the density distribution in a medium. The latter apply many algorithms to solve the inverse problem, ranging from analytic solutions to random search methods as well as systematic search methods. We present an adaptation for tesseroids of the systematic search method of "planting anomalous densities". This method can be used to estimate the geometry of geologic structures. As prior information, it requires knowledge of the approximate densities and positions of the structures. The main advantage of this method is its computational efficiency, requiring little computer memory and processing time. We demonstrate the shortcomings and capabilities of this approach using applications to synthetic and field data. Performing the inversion of gravity and gravity gradient data, simultaneously or separately, is straight forward and requires no changes to the existing algorithm. Such feature makes it ideal for inverting the multicomponent gravity gradient data from the GOCE satellite. An implementation of our adaptation is freely available in the open-source modeling and inversion package Fatiando a Terra (http://www.fatiando.org).

1. Gravity inversion
in spherical coordinates
using tesseroids
Leonardo Uieda
Valéria C. F. Barbosa

2. Cartesian Spherical
vs

3. Existing inversion with tesseroids
(Chaves and Ussami, 2013)
● Geoid height anomalies
● Space domain
● Regularization:
– Depth-weighted Minimum Volume
– Similarity to seismic tomography

4. Adapt
Planting anomalous densities
(Uieda and Barbosa, 2012)

5. Planting anomalous densities
● Space domain
● Multicomponent: gravity + gradients
● Non-conventional inversion
– Growth algorithm
– No linear systems
– Efficient sensitivity computations

7. Seed

19. Synthetics
● Possible applications
● Advantages
● Shortcomings

20. Lineament with dense rocks
(magmatic)
Inspired by Chad lineament model
(Braitenberg et al, 2011)

21. After Braitenberg et al (2011)

22. After Braitenberg et al (2011)

23. 10º
N
300 kg.m-3
top=1 km
2º
8km

24. gzz
At 20 km

25. Seeds

26. observed predicted

28. What if height=120 km?

29. at 20 km at 120 km

30. observed predicted

31. at 20 km at 120 km

32. Even higher
height=270 km

33. at 120 km at 270 km

34. observed predicted

35. at 120 km at 270 km

36. Magmatic underplating
Inspired by model of the Paraná basin
by Mariani et al (2013)

37. After Mariani et al (2013)

38. After Mariani et al (2013)

39. 10º
top=30 km
N 200 kg.m-3
5º
15
km

40. gzz at 250 km

41. Seed

43. What if I use wrong density?

44. 250 kg.m-3
150 kg.m-3

45. In conclusion

47. for tesseroids

48. Works well

49. height matters
20km 250km

50. correct
dense
dense

51. Future
● Combinations of tensor components
● Dipping sources (subducting plate)
● Real data (open for collaboration)

52. OPEN SOURCE
fatiando.org
github.com/leouieda/egu2014

53. Extra

54. (Hypothetical) Mantle Plume
Inspired by synthetics in Chaves and Ussami (2013)

55. After Chaves and Ussami (2013)

56. top=100 km
200 km
700 km
2º
-50 kg.m-3

57. gzz at 250 km

58. Seed

60. Joint gz + gzz?

61. Same seed

62. gzz gz

63. gzz Joint

64. gzz Joint

65. single vs joint