Use of the 'shape-of-anomaly' data misfit in 3D inversion by planting anomalous densities
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Use of the “shape-of-anomaly” data misfit in 3D inversion by planting anomalous densities Leonardo Uieda Valéria C. F. Barbosa
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E-poster presentation given at the 2012 SEG Annual Meeting in Las Vegas. Abstract: We present an improvement to the method of 3D gravity gradient inversion by planting anomalous densities. This method estimates a density-contrast distribution defined on a grid of right-rectangular prisms. Instead of solving large equation systems, the method uses a systematic search algorithm to grow the solution, one prism at a time, around user-specified prisms called “seeds”. These seeds have known density contrasts and the solution is constrained to be concentrated around the seeds as well as have their density contrasts. Thus, prior geologic and geophysical information are incorporated into the inverse problem through the seeds. However, this leads to a strong dependence of the solution on the correct location, density contrast, and number of seeds used. Our improvement to this method consists of using the “shape-of-anomaly” data-misfit function in conjunction with the l2-norm data-misfit function. The shape-of-anomaly function measures the different in shape between the observed and predicted data and is insen- sitive to differences in amplitude. Tests on synthetic and real data show that the improved method not only has an increased robustness with respect to the number of seeds and their locations, but also provides a better fit of the observed data.
Transcript of Use of the 'shape-of-anomaly' data misfit in 3D inversion by planting anomalous densities
Use of the “shape-of-anomaly” data misfit in
3D inversion by planting anomalous densities
Leonardo Uieda
Valéria C. F. Barbosa
Difference in shape
Scale factor: d i=α g i
Scale factor: d i=α g i
SOA=√∑i=1
N
(α g i−d i)2
Scale factor: d i=α g i
SOA=√∑i=1
N
(α g i−d i)2
minSOA α=∑i=1
N
g i d i
∑i=1
N
g i2
d , g α SOA
Predicted (model)
Observed
Planting anomalous densities
g i (observed)
mesh
seed
d i (predicted)
Choose the best:
φ=√∑i=1
N
(g i−d i)2
min of Γ=φ+μθ
&
compactness
Choose the best:
φ=√∑i=1
N
(g i−d i)2
min of Γ=SOA+μθ
&
Exchange for shape-of-anomaly
Γ=φ+μθ Γ=SOA+μθ SOASOA
Γ=φ+μθ Γ=SOA+μθ SOASOA
Γ=φ+μθ Γ=SOA+μθ SOASOA
Γ=φ+μθ Γ=SOA+μθ SOASOA
Γ=φ+μθ Γ=SOA+μθ SOASOA
Γ=φ+μθ Γ=SOA+μθ SOASOA
Γ=φ+μθ Γ=SOA+μθ SOASOA
Γ=φ+μθ Γ=SOA+μθ SOASOA
Γ=φ+μθ Γ=SOA+μθ SOASOA
Γ=φ+μθ Γ=SOA+μθ SOASOA
Γ=φ+μθ Γ=SOA+μθ SOASOA
Γ=φ+μθ Γ=SOA+μθ SOASOA
Synthetic tests
SOA
SOA
SOASOA
SOASOA
SOA
SOA
SOASOA
SOA
SOA
SOASOA
Redenção granite
Bouguer anomaly
Outcrop
Oliveira et al.(2008)
Bouguer anomaly
~ 6 km
Oliveira et al.(2008)
Bouguer anomaly
Seed at 3km ~ 6 km
SOA Known outcrop
SOA
Outcrop at wrong place
Known outcrop
SOA
Outcrop at wrong place
~ 9 km
Known outcrop
SOA
SOA
Outcrop at right place
SOA
Outcrop at right place
~ 6 km
5
SOA SOA
5
SOA SOA
6 km
In conclusion
SOA SOA
SOA SOA
SOA SOA
SOA SOA
