Use of the 'shape-of-anomaly' data misfit in 3D inversion by planting anomalous densities

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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

SOA=√∑i=1

(α g i−d i)2

Scale factor: d i=α g i

SOA=√∑i=1

(α g i−d i)2

minSOA α=∑i=1

g i d i

∑i=1

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

(g i−d i)2

min of Γ=φ+μθ

compactness

Choose the best:

φ=√∑i=1

(g i−d i)2

min of Γ=SOA+μθ

Exchange for shape-of-anomaly

Γ=φ+μθ Γ=SOA+μθ SOASOA

Synthetic tests

SOA

SOASOA

SOA

SOASOA

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

Outcrop at right place

SOA

Outcrop at right place

~ 6 km

SOA SOA

6 km

In conclusion

SOA SOA

Use of the 'shape-of-anomaly' data misfit in 3D inversion by planting anomalous densities

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Transcript of Use of the 'shape-of-anomaly' data misfit in 3D inversion by planting anomalous densities

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