adaptive learning gravity inversion for 3d salt body imaging fernando j. s. silva dias valéria c....
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![Page 1: Adaptive learning gravity inversion for 3D salt body imaging Fernando J. S. Silva Dias Valéria C. F. Barbosa National Observatory João B. C. Silva Federal](https://reader036.vdocuments.us/reader036/viewer/2022062423/56649edb5503460f94bea779/html5/thumbnails/1.jpg)
Adaptive learning gravity inversion for
3D salt body imagingFernando J. S. Silva Dias
Valéria C. F. Barbosa National Observatory
João B. C. SilvaFederal University of Pará
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• Introduction and Objective
• Methodology
• Real Data Inversion Result
• Conclusions
• Synthetic Data Inversion Result
Content
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Introduction
Brazilian sedimentary
basin
Seismic and gravity data are combined to interpret salt bodies
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IntroductionWhere is the base of the salt body ?
Top of the salt body
It is much harder to “see” what lies beneath salt bodies.
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Oezsen (2004)
We adapted the 3D gravity inversion through an adaptive learning procedure (Silva Dias et al., 2007) to estimate the
shape of salt bodies.
Starich et al. (1994) Yarger et al. (2001)
Huston et al. (2004)
Methods that reconstruct 3D (or 2D) salt bodies from gravity data
Interactive gravity forward modeling:
Gravity inversion methods
Bear et al. (1995)
Krahenbuhl and Li (2006)
Jorgensen and Kisabeth (2000)
Routh et al. (2001) Moraes and Hansen (2001)
Objective
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Methodology
• Forward modeling of gravity anomalies
• Inverse Problem
• Adaptive Learning Procedure
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Gravity anomaly
x
y
z
3D salt body
Source Region
Forward modeling of gravity anomalies
y
xD
epth
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y
z
Dep
th
x
Source Region
dy
dzdx
The source region is divided into an mx × my× mz grid
of M 3D vertical juxtaposed prisms
Forward modeling of gravity anomalies
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x
Observed gravity anomaly
y
z
Dep
th
Source Region
To estimate the 3D density-contrast distribution
y
x
Forward modeling of gravity anomalies
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The vertical component of the gravity field produced by the
density-contrast distribution (r’):
)(g ir )'(rV
i
''
'3
i dvzz
rr
Methodology
The discrete forward modeling operator for the gravity anomaly can be expressed by:
g A p
''
')( 3
jVi
iiij dv
zzA
rrr
where(N x 1) (M x 1)(NxM)
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Methodology
2
Ago 1N
g
The unconstrained Inverse Problem
The linear inverse problem can be formulated by
minimizing
ill-posed problem
p
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x
y
z Source Region
Dep
thMethodology
Concentration of salt mass about specified
geometric elements (axes and points)
3D salt body
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z
Dep
th
3D salt body
Homogeneous salt body embedded in homogeneous sediments
Methodology
First-guess skeletal outline of the salt body
Only one target density contrast
g/cm3
homogeneous sediments
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Homogeneous salt body embedded in a heterogeneous sedimentary pack
zHeterogeneous
sedimentary pack
Dep
th
3D salt body
Methodology
A reversal 3D density-contrast distribution
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z
Dep
th Heterogeneous salt body
Methodology
Homogeneous sediments
g/cm3g/cm3
g/cm3
g/cm3
Heterogeneous salt body embedded in homogeneous sediments
First-guess skeletal outline of a particular homogeneous section of the salt body
A reversal 3D density-contrast distribution
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MethodologyIterative inversion method consists of two nested iterative loops:
The outer loop: adaptive learning procedure
The inner loop: Iterative inversion method fits the gravity data satisfies two constraints:
• Density contrast values: zero or a nonnull value.
• Concentration of the estimated nonnull density contrast
about a set of geometric elements (axes and points)
• Coarse interpretation model
• first-guess geometric elements (axes and points)
• corresponding target density contrasts
x
y
z
x
y
z
pjtargetg/
cm3
x
z
y
• refined interpretation model
• new geometric elements (points)
• corresponding target density contrasts
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The inversion method of the inner loop estimates
iteratively the constrained parameter correction Δp by
Minimizing
Subject to
Methodology
Δp2 )( k
W )( k1/2
p
and updates the density-contrast estimates by
2 Ago 1
NΔp )(po +
)( k )( k
)()()1( ˆˆ kkk pΔpp o
≡
)(
3
ˆ k-1j
jjj
p
dwWp
)( k1/2 )( k1/2
={ }Prior reference vector
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}{min1 N
jdE
d j
MjNzezyeyxd Ejjj ,,1,,,1)()((2/1222
xe )j
Methodology
z
y
x
xe
)
ye, , ze)
jd
The method defines dj as the
distance from the center of the
j th prism to the
closest geometric elementclosest geometric element
d j
Inner loop
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Adaptive Learning Procedure
• Interpretation model
• Geometric elements
• Associated target density contrasts
Outer Loop
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static geologic
reference model
x
y
z
OUTER LOOP:First Iteration OUTER LOOP: Second Iteration
New geometric elements (points) and associated target density contrasts
Dynamic geologic reference model
Adaptive Learning Procedure
INNER LOOP:
First density-contrast distribution estimate
New interpretation model
Each 3D prism is divided
First interpretation model first-guess geometric elements and associated
target density contrasts
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Inversion of Synthetic Data
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Noise-corrupted gravity anomaly
Synthetic example with a variable density contrast
-1 0 1 2 3 4 5 6 7
y (km)
1
2
3
4
5
6
7
8
9x
(km
)
-0.1
0.1
0.3
0.5
mGal
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Homogeneous salt dome with density of 2.2 g/cm3 embedded in five sedimentary layers
Synthetic example with a variable density contrast
with density varying with depth from 1.95 to 2.39 g/cm3.D
epth
3D salt body
1.5 km Nil zone
1.95 g/cm3
2.39 g/cm3
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Synthetic example with a variable density contrast
Density contrast (g/cm3)
Dep
th (
km)
The true reversal 3D density-contrast distribution
abovebelow
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The blue axes are the first-guess skeletal outlines: static geologic reference model
Synthetic example with a variable density contrast
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Synthetic example with a variable density contrast
True Salt Body
Estimated Salt
Body
Interpretation model at the fourth iteration: 80×72×40 grid of 3D prisms.
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Synthetic example with a variable density contrast
Estimated Salt BodyFitted anomaly
-1 0 1 2 3 4 5 6 7y (km)
1
2
3
4
5
6
7
8
9
x(k
m)
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Real Gravity Data
Galveston Island salt dome
Texas
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Localization of Galveston Island salt dome
Study area
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Localization of Galveston Island salt dome
Study area
Location map of the study area (after Fueg, 1995; Moraes and Hansen, 2001)
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Galveston Island salt dome
(UTM15)km E
NBouguer anomaly maps
(UTM15) km E N
314 320 326 332
3134
3136
3138
3140
3142
3144
3146
3148
3150
3152
-1.4-0.212.2mGalFueg’s (1995)
density models
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Galveston Island salt domeD
epth
(km
)
0.08 0.00 (g/cm3)
0.20 (g/cm3)
0.10 (g/cm3)
0.06 (g/cm3)
0.02 (g/cm3)
- 0.04 (g/cm3)
- 0.08 (g/cm3)
- 0.13 (g/cm3)
0.15
0.5
0.8
1.2
1.5
2.0
3.4
Dep
th (
km)
0.08 0.00 (g/cm3)
0.20 (g/cm3)
0.10 (g/cm3)
0.06 (g/cm3)
0.02 (g/cm3)
- 0.04 (g/cm3)
- 0.08 (g/cm3)
- 0.18 (g/cm3)
0.15
0.5
0.8
1.2
1.5
2.0
3.2
2.6
3.83.9 - 0.23 (g/cm3)
- 0.13 (g/cm3)
First static geologic reference model based on Fueg’s (1995) density models
The first geologic hypothesis about the salt dome
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Galveston Island salt domeThe first estimated reversal 3D density-contrast distribution
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Dep
th (
km)
0.04 0.00 (g/cm3)
0.19 (g/cm3)
0.08 (g/cm3)
- 0.04 (g/cm3)
0.31
0.35
1.2
2.0
2.2 - 0.13 (g/cm3)
Galveston Island salt dome
(UTM15) km E N
314 320 326 332
3134
3136
3138
3140
3142
3144
3146
3148
3150
3152
-1.4-0.212.2mGal
The second geologic hypothesis about the salt dome
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Galveston Island salt domeThe second estimated reversal 3D density-contrast distribution
Density contrast (g/cm3)
-0.13 -0.042 0.045 0.13 0.22
Overhang
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Conclusions
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Adaptive learning gravity inversion for 3D salt body imaging
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Thank You
We thank Dr. Roberto A. V. Moraes and Dr. Richard O. Hansen for providing the
real gravity data
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Extra Figures
1 CPU ATHLON with one core and 2.4 GHertz and 1 MB of cache L22GB of DDR1 memory
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Large source surrounding a small sourceThe red dots are the first-guess skeletal outlines:
static geologic reference model
(a)
(b)
Silva Dias et al. Fig. 8
Estimated density contrast (g/cm3)0.1 0.2 0.3 0.4 0.5
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(a)
(b)
Silva Dias et al. Fig. 8
Estimated density contrast (g/cm3)0.1 0.2 0.3 0.4 0.5
Large source surrounding a small sourceFifth iteration
interpretation model: 48×48×24 grid of 3D prisms.
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Multiple buried sources at different depths The points are the first-guess skeletal outlines:
static geologic reference model
density contrast (g/cm3)
0.15 g/cm3
0.3g/cm3
0.4 g/cm3
Third iteration Interpretation model: 28×48×24 grid of 3D prisms.
Silva Dias et al. Fig. 8
(d)
(e)
0.15 0.2 0.3 0.4Estimated density contrast (g/cm3)
Silva Dias et al. Fig. 8
(d)
(e)
0.15 0.2 0.3 0.4Estimated density contrast (g/cm3)
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Methodology
Penalization Algorithm:
)(ˆ kjp
jp target
0 (g/cm3)
jp target 0 (g/cm3)
• For positive target density contrast
• For negative target density contrast
)(ˆ kjp
)(ˆ kjp )(ˆ k
jp
jjwp
)( k1/2
=
target
jp or 0 (g/cm3)
)(ˆ kpΔ)(kp o )1(ˆ kp
( k )
op
j
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Methodology
Penalization Algorithm:
jp target
0 (g/cm3)
jp target
0 (g/cm3)
• For positive target density contrast
• For negative target density contrast
)(ˆ kjp
)()()1( ˆˆ kkk pΔpp o
pjtarget
2
pjtarget
2
)(ˆ kjp)(ˆ k
jp
)(ˆ kjp
target
jp( k )
op
j
( k )
op
j
0 (g/cm3)
)(
3
ˆ k-1
j
j
jj p
dwp
)( k1/2
=)(ˆ k
jp
)(ˆ kjp