FDEM simulation with anisotropy

[Gary McNeice]

I see in the FDEM documentation a statement that "The inverse problem will not work with full anisotropy". Is it possible to do a forward simulation including conductivity anisotropy?

[Lindsey Heagy]

Hi Gary, 

Thanks for your question! Yes, it is possible to do a forward simulation with anisotropic conductivities. There is one example here: https://github.com/simpeg-research/heagy-2018-fracture-physprops/blob/master/notebooks/3_crosswell_survey.ipynb. See cell 19. 

This example uses a cylindrically symmetric mesh, so only two axes of anisotropy are considered, but for a 3D tensor or OcTree mesh, diagonal anisotropy of the full anisotropic tensor can be considered. For axes-aligned anisotropy (a diagonal tensor), the conductivity values are input as an nC x 3 matrix

sigma = [sigma_x, sigma_y, sigma_z]

for a full tensor, it is nC x 6

sigma = [sigma_xx, sigma_yy, sigma_zz, sigma_xy, sigma_xz, sigma_yz]

(for reference: http://docs.simpeg.xyz/content/api_core/api_InnerProducts.html?highlight=anisotropic#defining-tensor-properties)

I hope this helps getting started! Please feel free to also join the simpeg slack http://slack.simpeg.xyz, if you would like to come chat with other developers and users. 

All the best,

Lindsey 

On Sun, Jun 23, 2019 at 5:54 AM Gary McNeice <gwmc...@gmail.com> wrote:

I see in the FDEM documentation a statement that "The inverse problem will not work with full anisotropy". Is it possible to do a forward simulation including conductivity anisotropy?

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[Gary McNeice]

Thanks for the fast response.

Is it possible to run an anisotropic inversion?

[Lindsey Heagy]

Hi Gary, 

Sorry for my delay... SimPEG can run anisotropic inversions if it is axes aligned / diagonal anisotropy, but the fully anisotropic inversion is not yet up and running (we have an issue tracking this here: https://github.com/simpeg/simpeg/issues/146). If this is something you are interested in contributing to, please feel free to chime in on the issues, and we can provide some pointers as to where code needs to be updated to make this possible. 

Once the derivatives are in place, the inversion will still take some thought with how to appropriately regularize the model as using full anisotropy greatly increases the number of degrees of freedom (6x if you let it invert for each component independently), and we will need a mechanism to enforce that the resultant conductivity matrix is symmetric positive definite. If, for example, you know the principle axes, then you could construct a mapping that takes three input values for the conductivity at each cell and the mapping rotates it to the correct orientation. 

Do you have a specific example in mind? 

All the best,

Lindsey 

On Tue, Jun 25, 2019 at 2:16 PM Gary McNeice <gwmc...@gmail.com> wrote:

Thanks for the fast response.

Is it possible to run an anisotropic inversion?

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