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https://github.com/leouieda/seg2012

Code and slides for "Use of the 'shape-of-anomaly' data misfit in 3D inversion by planting anomalous densities" presented at the 2012 SEG Annual Meeting
https://github.com/leouieda/seg2012

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Code and slides for "Use of the 'shape-of-anomaly' data misfit in 3D inversion by planting anomalous densities" presented at the 2012 SEG Annual Meeting

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Source code for the expanded abstract and presentation.

Presented at the 2012 SEG Annual Meeting.

Results were generated using open-source software [Fatiando a
Terra](http://fatiando.org)

Published expanded abstract:
[doi:10.1190/segam2012-0383.1](
http://library.seg.org/doi/abs/10.1190/segam2012-0383.1)

Also available for download on my
[personal page](http://fatiando.org/people/uieda/).

Slides available on figshare:
[doi:10.6084/m9.figshare.156864](http://dx.doi.org/10.6084/m9.figshare.156864)

Citation:

Uieda, L., and V. C. F. Barbosa (2012), Use of the "shape-of-anomaly" data
misfit in 3D inversion by planting anomalous densities, SEG Technical Program
Expanded Abstracts, pp. 1-6, doi:10.1190/segam2012-0383.1

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

**Leonardo Uieda and Valéria C. F. Barbosa**

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 insensitive 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.