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
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