3D depth-to-basement and density contrast estimates using gravity and borehole data Cristiano Mendes Martins Valéria C. F. Barbosa National Observatory João B. C. Silva Federal University of Pará

Contents Objective Methodology Real Data Inversion Result Conclusions Synthetic Data Inversion Result

Objective z Depth Gravity data Estimate x y N E a 3D basement relief of a sedimentary basin Basement relief Homogeneous lower medium from gravity data and depth-to-basement information at few points: x y N E

The   and  Objective a 3D basement relief of a sedimentary basin Homogeneous lower medium Heterogeneous upper medium 1,0 2,0 3,0 4,0 5,0 6,0 -0,6 -0,2 0,0 Depth  (g/cm 3 ) -0,4 Rao et al. (1994)   z z       0  0   Estimate from gravity data and depth-to-basement information at few points: Parabolic decay of density contrast with depth

Methodology

Methodology y x z y x Gravity observations g o M R  Basement relief Depth

Methodology y x Gravity observations g o M R  z Depth y x Sedimentary pack Basement relief

Methodology y x z y x Gravity observations g o M R  Basement relief Prisms’ thicknesses are the parameters to be estimated Depth pjpj dx dy Sedimentary pack

Methodology The vertical component of the gravity field produced by M prisms:  .,...,1,' ' ' 2 3 Mizdds zz z g M j jj p i ij jo o SjSj i j            rr   Chakravarthi et al. (2002)  ) ( i r j   3 z jo o     The constrained nonlinear inversion obtains a 3D depth-to-basement estimate by minimizing: 2 Rp subject to and 2 2 ),,( 1  o M pgg o 2 B B zpW 

Methodology 2 Rp subject to and 2 2 ),,( 1  o M pg g o The constrained nonlinear inversion obtains a 3D depth-to-basement estimate by minimizing: The first-order Tikhonov regularizing function The borehole information about the basement depth The data misfit function 0   2 B B zpW  B z g o g  2

2 B B zpW  0 ),(    ^ Methodology To estimate the parameters defining the parabolic decay of the density contrast with depth   z z       0  0   2 Rp 2. We obtain a 3D depth-to-basement estimate by: 1. We fix a pair of (  ,  ) We get the pair (  ,   ) in the following way: subject to 2 2 ),,( 1  o M pg g o 3. We evaluate the functional: 4. We repeat this procedure for different pairs (  ,  ) to produce a discrete mapping of  (  ,  ) minimizing B z p ^

INVERSION OF SYNTHETIC DATA

Simulated 3D sedimentary basin Horizontal coordinate y (km) Horizontal coordinate x (km) mGal Noise-corrupted gravity anomaly

Simulated 3D sedimentary basin The true depths of the simulated basement relief Region I Region II

Simulated 3D sedimentary basin Region I Region II Horizontal coordinate y (km) Horizontal coordinate x (km) Region IRegion II The true depths of the simulated basement relief Gravity data

Simulated 3D sedimentary basin To estimate the parameters defining the parabolic decay of the density contrast with depth Depth (km) Region I Region II   (g/cm 3 ) Parabolic laws of density contrast variation with depth   z z       0  0   We evaluate the functional: 2 B B zpW  0 ),(    ^

Region I Region II To estimate the parameters defining the parabolic decay of the density contrast with depth Simulated 3D sedimentary basin We evaluate the functional: 2 B B zpW  0 ),(    ^ B z p ^

To estimate the parameters defining the parabolic decay of the density contrast with depth The contour maps of functional km Region I Region II Simulated 3D sedimentary basin 2 B B zpW  0 ),(    ^ + +

Estimated basement relief

Simulated 3D sedimentary basin True basement relief Estimated basement relief Horizontal coordinate x (km) Horizontal coordinate y (km)

INVERSION OF REAL GRAVITY DATA

Real Gravity Data Brazil Salvador Brasília Rio de Janeiro São Paulo Study area The onshore and part of the shallow offshore Almada Basin on Brazil’s coast.

Real Gravity Data GRAVITY ANOMALY Almada Basin (Brazil)

14 o 30’S 14 o 45’S 39 o 05’ W mGal Real Gravity Data The gravity data from Almada Basin (Brazil) corrected for the seawater and Moho effects. I Actual coastline Shallow offshoreOnshore IIIII

Real Gravity Data The parameters defining the parabolic decay of the density contrast with depth for Almada Basin (Brazil) The contour map of functional: km Functional    for the regions I-II  0 (g/cm 3 )  (g/cm 3 /km) Functional    for the regions II-III 2 B B zpW  0 ),(    ^

Real Gravity Data The 3D depth-to-basement estimate of Almada Basin (Brazil) A B C D E 14 o 30’S 14 o 45’S 39 o 05’ W km

Real Gravity Data The 3D depth-to-basement estimates of Almada Basin (Brazil) Estimated basement relief Gravity anomaly

Conclusions

Conclusions Estimates the 3D basement relief and the density contrast It is impossible to determine the density and the volume of the source from gravity data only. The gravity inversion method How did we overcome the fundamental ambiguity involving the product of the physical property by the volume ? depth-to-basement information at few points gravity data density volume

Inversion method for simultaneously estimating 3D basement relief and density contrast of a sedimentary basin using gravity data and depth control at few points The estimated basement relief is not just a scaled version of the gravity data The method works well even in the case of complex geologic setting Conclusions

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Extra Figures

The contour maps of functional Region I B B zpW  0 ),(    ^ Depth (km) Horizontal coordinate x (km) N True basement S Horizontal coordinate x (km) Horizontal coordinate y (km) Gravity data Region IRegion II