Valéria C. F. Barbosa National Observatory João B. C. Silva Federal University of Pará

1. RECONSTRUCTION OF GEOLOGIC BODIES IN DEPTH ASSOCIATED WITH A SEDIMENTARY BASIN USING GRAVITY AND MAGNETIC DATA Valéria C. F. Barbosa National Observatory João B. C. Silva Federal University of Pará

2. Acknowledgments I thank EGM 2010 organizing committee for the invitation.

3. Objective To present a comprehensive review of the gravity and magnetic interpretation methods for retrieving the geometry of two types of geologic bodiesassociated with a sedimentary basin: 1) sedimentary basement relief; and 2) salt bodies.

4. Reconstruction of basement relief Three groups of methods can be used to map the basement relief: 1) The automatic depth-estimation methods; 2) The spectral methods; and 3) The nonspectral methods.

5. Reconstruction of basement relief The automatic depth-estimation methods A huge amount of aeromagnetic data has been collected by governmental agencies 1) CompuDepth (O’Brien, 1972) 2) Werner deconvolution (Hartman et al., 1971) 3) Naudy’s method (Naudy, 1971) 4) Euler deconvolution (Thompson, 1982)

6. Reconstruction of basement relief The automatic depth-estimation methods Thompson (1982) 1) Euler deconvolution Reid et al. (1990) and Werner (1953) Hartman et al. (1971) 2) Werner deconvolution Ku and Sharp (1983) Hansen and Simmonds (1993) To estimate the depths and the horizontal coordinates of simple equivalent sources (e.g., single pole, dipole, and line of dipoles) Two geologic settings are usually considered

7. Reconstruction of basement relief The automatic depth-estimation methods The Euler deconvolution and the Werner deconvolution Two geologic settings are usually considered

8. Reconstruction of basement relief The automatic depth-estimation methods The Euler deconvolution and the Werner deconvolution Two geologic settings are usually considered The first geologic setting Highly magnetized rocks 1) The basement relief is inferred by the intrusion-position estimates Sedimentation process Erosion process Weakly magnetized rock

9. Reconstruction of basement relief The automatic depth-estimation methods The Euler deconvolution and the Werner deconvolution Two geologic settings are usually considered The second geologic setting Erosion process 2) The basement relief is inferred by the fault-position estimates. Sedimentation process Faulting process Basement rock

10. Reconstruction of basement relief The automatic depth-estimation methods What are the advantages and disadvantages of Euler and Werner deconvolutions? Advantages • These methods do not require a priori knowledge about the anomalous source magnetization. • High-speed processing methods Disadvantages • The misuse and abuse of these methods

11. 0 20 40 60 80 100 120 140 0 2 Depth (km) 4 6 Wrong faults 8 0 20 40 60 80 100 120 140 Reconstruction of basement relief An example of the misuse and abuse of Euler deconvolution Total-field anomaly and its gradients Each structural index is related to the nature or geometry of the source

12. Reconstruction of basement relief The automatic depth-estimation methods What are the advantages and disadvantages of Euler and Werner deconvolutions? Disadvantages • The misuse and abuse of these methods • The poor performance of these methods to interpret interfering anomalies produced by multiple sources that are separated vertically from each other by short distances. • The large number of estimated solutions

13. Reconstruction of basement relief The automatic depth-estimation methods The undesirable broad spray of Euler solutions It is a vision of hell !

14. Reconstruction of basement relief Three groups of methods can be used to map the basement relief: 1) The automatic depth-estimation methods; 2) The spectral methods; and 3) The nonspectral methods.

15. Reconstruction of basement relief The spectral methods The spectral methods lead to two subgroups: 1) The statistical spectral method and 2) The spectral inversion methods for depth-to-basement estimation

16. Reconstruction of basement relief The statistical spectral method (Spector and Grant, 1970) To estimate average depths of ensembles of shallow- or deep-seated sources. Magnetic anomaly nT 5 10 15 20 25 30 x (km) h1 Shallow-seated sources Depth h2 Ensemble of 3D vertical prisms Deep-seated sources (e.g., the basement relief)

17. P ( k ) Reconstruction of basement relief The spectral methods The statistical spectral method Spector and Grant (1970) For sources with infinite thicknesses (e.g., basement relief) the average radial power spectrum, of the reduced-to-the-pole magnetic data measured on the observation plane, z: z h - - = × × | k 2 ( ) | P ( k ) Q ( k ) e S 2 In this method we want to estimate from P(k) the average depth h2 of the ensemble of deep-seated sources (e.g., basement relief).

18. » - a 2 ( h z ) 2 Reconstruction of basement relief Spector and Grant’s (1970) method The natural logarithm of the average radial power density spectrum, P(k) varies linearly with k. Deep-seated sources (low-wavenumber) ln { P(k)} Shallow-seated sources (high-wavenumber) a k

19. Reconstruction of basement relief The spectral methods The statistical spectral method Spector and Grant (1970) What are the advantages and disadvantages of Spector and Grant’s method? Advantages • The simplicity in implementation • The low computational load • The ability in taking interferences into account. Disadvantages • It does not provide a detailed depth-to-basement estimate • It presumes nonoverlapping spectra of the anomalies produced by the shallow and the deep-seated sources.

20. Reconstruction of basement relief The spectral methods The spectral methods lead to two subgroups: 1) The statistical spectral method and 2) The spectral inversion methods for depth-to-basement estimation

21. Magnetic data Gravity data Pilkington and Crossley (1986) Pilkington (2006) Caratori Tontini et al. (2008) Oldenburg (1974) Guspí (1993) Reconstruction of basement relief The spectral inversion method for depth-to-basement estimation It is based on Parker’s (1973) forward calculation technique. - n 1 | k | å ¥ - = p k | | z n e F { d } 2 m F { p } o = n ! n 1 Examples of successful spectral inversion of

22. - n 1 | k | å z ¥ - = p k | | n e F { d } 2 m F { p } o = n ! n 1 Reconstruction of basement relief What are the advantages and disadvantages of the spectral inversion method? Advantages The rapid computation of the potential-field response It provides a detailed depth-to-basement estimate Disadvantage The average depth of the interface z0 must be known. Ill-posed problem How do these methods stabilize the solution? The solutions are stabilized either by applying a low-pass filter to the data or by employing a damping parameter.

23. Reconstruction of basement relief Three groups of methods can be used to map the basement relief: 1) The automatic depth-estimation methods; 2) The spectral methods; and 3) The nonspectral methods.

24. Reconstruction of basement relief The nonspectral methods Gravity and magnetic inversions in the space domain The nonspectral method does not use Parker’s (1973) formula

25. Reconstruction of basement relief x Potential-field data y o M d Î R dy dx The nonspectral methods Gravity and magnetic inversion in the space domain Prisms’ thicknesses are the parameters to be estimated x Sedimentary pack y pj Depth Basement relief z

26. l Y m f ( p ) ( p ) ( p ) ( ) Y = - o ( p ) W d d ( p ) d L Reconstruction of basement relief The nonspectral methods Tikhonov regularization method (Tikhonov and Arsenin, 1977) The unconstrained nonlinear inversion obtains a 3D depth-to-basement estimate by minimizing: Ill-posed problem = + The regularizing function Parameter vector The data-misfit function

27. Reconstruction of basement relief = p + l Y m f ( p ) ( p ) ( p ) Examples of successful nonspectral inversion of Gravity and Magnetic data are: The nonspectral methods Gravity and magnetic inversion in the space domain There are different nonspectral inversions methods Richardson and MacInnes (1989) Barbosa et al. (1997, 1999) Gallardo-Delgado (2003) Nunes et al. (2008) Martins et al. (2009). How do these methods differ? The methods differ in the particular regularizing function used.

28. Reconstruction of basement relief The nonspectral methods Gravity and magnetic inversion in the space domain Two regularizing functions: • The first-order Tikhonov regularization ( the smoothing regularization) • The total variation (TV) regularization ( the nonsmoothing regularization)

29. Reconstruction of basement relief The nonspectral methods Gravity and magnetic inversion in the space domain Results using synthetic gravity data by applying the smoothing and TV regularizations

30. Reconstruction of basement relief -6 25 -14 20 -22 Horizontal coordinate x (km) 15 -30 10 -38 5 -46 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 -54 Horizontal coordinate y (km) mGal The nonspectral methods First synthetic test Simulated 3D sedimentary basin Noise-corrupted gravity anomaly

31. Reconstruction of basement relief The nonspectral methods The true depths of the simulated basement relief

32. Reconstruction of basement relief Estimated basement relief by using the smoothing regularization The nonspectral methods True basement relief Estimated basement relief by using the smoothing regularization

33. Reconstruction of basement relief The nonspectral methods Second synthetic test 3D fault-bounded sedimentary basin The true depths of the simulated basement relief

34. Reconstruction of basement relief The nonspectral methods True basement relief Estimated basement relief by using the TV regularization Estimated basement relief by using the smoothing regularization

35. Reconstruction of basement relief The nonspectral methods What are the advantages and disadvantages of the nonspectral inversion methods? Advantages • It provides a detailed depth-to-basement estimate • The estimated topography is independent of the initial guess • The estimated topography is not just a scaled version of the observed data • It allows introducing geological information about the actual basement relief on the solution Disadvantage The high computational load

36. Reconstruction of salt dome Strategies for the reconstruction of 3D (or 2D) salt bodies from gravity data are 1) The interactive gravity forward modeling The interactive gravity forward modeling Some examples of published methods are: 2) The gravity inversion methods Starich et al. (1994) Integrated seismic interpretation and 3D gravity forward modeling Yarger et al. (2001) 2D salt modeling using gravity data to supplement the 2D seismic interpretation Huston et al. (2004) Integrated well and seismic data to support gravity modeling Oezsen (2004) Integrated gravity data into an iterative velocity-depth model

37. Reconstruction of salt dome Strategies for the reconstruction of 3D (or 2D) salt bodies from gravity data are Methods that estimate the geometry of isolated salt bodies by approximating them by 2D bodies with polygonal cross sections or 3D polyhedral bodies The gravity inversion methods x True 2D salt body Moraes and Hansen (2001) Depth Silva and Barbosa (2004) Wildman e Gazonas (2009) 2D estimated polygonal cross section Luo (2010)

38. Reconstruction of salt dome Strategies for the reconstruction of 3D (or 2D) salt bodies from gravity data are The gravity inversion methods Methods that estimate a 3D (2D) density-contrast distribution Bear et al. (1995) Jorgensen and Kisabeth (2000) Nagihara and Hall (2001) Routh et al. (2001) Krahenbuhl and Li (2006; 2009) Silva Dias et al. (2008; 2009)

39. Reconstruction of salt dome Source Region Methods that estimate a 3D density-contrast distribution dy The source region is divided into an mx× my× mzgrid of M 3D vertical juxtaposed prisms dz x dx y Depth z

40. Reconstruction of salt dome Observed gravity anomaly Source Region The estimated 3D density-contrast distribution is expected to reconstruct a 3D salt dome x x y y Depth z

41. Reconstruction of salt dome l Y m f ( p ) ( p ) ( p ) To estimate the 3D (or 2D) density-contrast distribution Tikhonov regularization method (Tikhonov and Arsenin, 1977) The unconstrained inversion obtains a 3D (2D) density-contrast distribution by minimizing: Ill-posed problem = + The regularizing function Parameter vector The data-misfit function

42. Reconstruction of salt dome Source Region Concentrationof salt mass aboutspecifiedgeometric elements (axes and points) x y Depth 3D salt body z

43. Reconstruction of salt dome 2D synthetic test Gravity data Density contrast - 0.2 g/cm3 Simulated salt dome

44. Reconstruction of salt dome Concentrationof salt mass aboutspecifiedgeometric elements Geometric elements (axes) that presumably describe the salt body’s framework. Silva and Barbosa (2006) Gravity data Salt dome Axes

45. Reconstruction of salt dome Concentrationof salt mass aboutspecifiedgeometric elements The evolution of the density distribution estimates along the iterations Iteration 1

46. Reconstruction of salt dome Concentrationof salt mass aboutspecifiedgeometric elements The evolution of the density distribution estimates along the iterations Iteration 2

47. Reconstruction of salt dome Concentrationof salt mass aboutspecifiedgeometric elements The evolution of the density distribution estimates along the iterations Iteration 3

48. Reconstruction of salt dome Concentrationof salt mass aboutspecifiedgeometric elements The evolution of the density distribution estimates along the iterations Iteration 4

49. Reconstruction of salt dome Concentrationof salt mass aboutspecifiedgeometric elements The evolution of the density distribution estimates along the iterations Iteration 5

50. Reconstruction of salt dome Concentrationof salt mass aboutspecifiedgeometric elements The evolution of the density distribution estimates along the iterations Iteration 6