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. SilvaFederal University of Pará

Contents• Objective

• Methodology

• Real Data Inversion Result

• Conclusions

• Synthetic Data Inversion Result

Objective

zDep

thD

epth

Gravity dataGravity data

Estimate

x yN 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 yN 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

Dep

th

(g/cm3)-0,4

Rao et al. (1994)

20

30

zz

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

go MR

Basement relief

Dep

thD

epth

Methodology

y

x Gravity observations

go MR

z

Dep

thD

epth

y

xSedimentary

pack

Basement relief

Methodology

y

x

z

y

x Gravity observations

go MR

Basement relief

Prisms’ thicknesses are the parameters to be estimated

Dep

thD

epth

pj

dxdy

Sedimentary pack

MethodologyThe vertical component of the gravity field

produced by M prisms:

.,...,1,'

'1 03

'

2

3

Mizddszz

zg

M

jjj

p

i

ij

jo

o

Sji

j

rr

Chakravarthi et al. (2002)

)(ir

j

3

z jo

o

The constrained nonlinear inversion obtains a 3D depth-to-basement estimate by minimizing:

2Rp

subject to

and

2

2

),,(1

oM pgg o

2BB zpW

Methodology

2Rp

subject to

and

22

),,(1 oM pggo

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 function0

2BB zpW Bz

go g 2

2BB zpW

0 ),( ^

MethodologyTo estimate the parameters defining the parabolic

decay of the density contrast with depth

20

30

zz

0

0

2Rp

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 22

),,(1

oM pggo

3. We evaluate the functional:

4. We repeat this procedure for different pairs (, ) to

produce a discrete mapping of (, )

minimizing

0

(g/c

m3 )

(g/cm3/km)0.03 0.04 0.05 0.06 0.07

-0.42

-0.41

-0.4

-0.39

-0.38

km2

0.00.61.62.63.64.65.66.67.68.6

Bzp̂

INVERSION OF

SYNTHETIC DATA

Simulated 3D sedimentary basin

Horizontal coordinate

y (km)

Hor

izon

tal c

oord

inat

e x

(km

)

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

5

10

15

20

25

-54

-46

-38

-30

-22

-14

-6

mGal

Noise-corrupted gravity anomaly

Simulated 3D sedimentary basinThe true depths of the

simulated basement relief

Region I

Region II

Simulated 3D sedimentary basin

Region IRegion II Horizontal coordinate y (km)

Hor

izon

tal

coor

dina

te x

(km

)

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

5

10

15

20

25

- 45

Region I Region IIThe 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

Dep

th (k

m)

Region I

Region II

(g/cm3)

8.07.06.05.04.03.02.01.00.0

-0.2-0.4-0.6-0.8 0.0

Parabolic laws of density contrast variation with depth 2

0

30

zz

0

0

We evaluate the functional:

2BB zpW

0 ),( ^

Region IRegion II

To estimate the parameters defining the parabolic decay of the density contrast with depth

Simulated 3D sedimentary basin

We evaluate the functional:

2BB zpW

0 ),( ^ Bzp̂

km20.00.81.62.43.24.04.85.66.47.28.08.89.6

(g/cm3/km)

0 (

g/cm

3 )

0.08 0.09 0.10 0.11 0.12-0.630

-0.615

-0.600

-0.585

-0.570

To estimate the parameters defining the parabolic decay of the density contrast with depth

The contour maps of functional

0 (

g/cm

3 )

(g/cm3/km)

0.03 0.04 0.05 0.06 0.07-0.42

-0.41

-0.4

-0.39

-0.38

km2

0.0

0.6

1.6

2.6

3.6

4.6

5.66.6

7.68.6

Region I Region II

Simulated 3D sedimentary basin

2BB zpW

0 ),( ^

+ +

Simulated 3D sedimentary basin

Estimated basement relief

Simulated 3D sedimentary basin

True basement relief

Estimated basement relief

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

5

10

15

20

25

Hor

izon

tal

coor

dina

te x

(km

)Horizontal coordinate y (km)

INVERSION OF

REAL GRAVITY DATA

Real Gravity Data

Brazil

Salvador

Brasília

Rio de JaneiroSão

Paulo

Study area

The onshore and part of the shallow offshore Almada Basin on Brazil’s coast.

Real Gravity Data

mGal-10010203040506070809014o 30’S

14o 45’S

39o 15’ W 39o 05’ W

GRAVITY ANOMALY Almada Basin (Brazil)

14o 30’S

14o 45’S

39o 05’ W

-85.0

-70.0

-55.0

-40.0

-25.0

-10.0

-3.8

0.0

mGal

Real Gravity DataThe gravity data from Almada Basin (Brazil)

corrected for the seawater and Moho effects. I

Actual coastline

Shallow offshoreOnshore

II III

Real Gravity DataThe parameters defining the parabolic decay of the density contrast with depth for Almada Basin (Brazil)

14o 30’S

14o 45’S

39o 05’ W

-85.0

-70.0

-55.0

-40.0

-25.0

-10.0

-3.8

0.0

mGal

I II IIIThe contour map of functional:

km20.420.570.720.871.021.171.321.471.621.771.92

(g/cm3/km)

0,030 0,035 0,040 0,045 0,050

- 0,58

-0,57

-0,56

-0,55

-0,54

0

(g/c

m3 )

Functional for the regions I-II

0,035 0,040 0,045 0,050 0,055-0,58

-0,57

-0,56

-0,55

-0,54

0

(g/c

m3 )

(g/cm3/km)

km2

0.28

0.31

0.34

0.36

0.40

0.43

0.46

0.48

0.52

0.55

Functional for the regions II-III

2BB zpW

0 ),( ^

Real Gravity DataThe 3D depth-to-basement estimate of

Almada Basin (Brazil)

A

B

C

D

E14o 30’S

14o45’S

39o 05’ W

km7.06.25.44.63.83.02.21.40.80.40.1

Real Gravity DataThe 3D depth-to-basement estimates of

Almada Basin (Brazil)

-85

-70

-55

-40

-25

-10

-3.8

0.0

mGal

14o 30’S

14o 45’S

39o 05’ W

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

Thank You I cordially invite you to attend the upcoming

Extra Figures

km20.00.81.62.43.24.04.85.66.47.28.08.89.6

(g/cm3/km)

0 (

g/cm

3 )

0.08 0.09 0.10 0.11 0.12-0.630

-0.615

-0.600

-0.585

-0.570

The contour maps of functional

Region I

+

22

33

44

55

11

2BB zpW 0 ),( ^

0 5 10 15 20 25 30

8

6

4

2

0

Dep

th (k

m)

Horizontal coordinate x (km)

N

True basement

S

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

5

10

15

20

25

Hor

izon

tal

coor

dina

te x

(km

)

Horizontal coordinate y (km)

Gravity dataRegion I Region II