This repository contains python and jupyter notebooks demonstrating how to use clustering inversion to solve the inverse problem of a fully anisotropic conductivity layered earth, measured by the electrical soundings. The purpose of this work is to demonstrate a repeatable method of applying clustering inversion to an anisotropic quantity when incorporating petrophysical information.
To run these codes the only requirements are:
numpyscipyjupyter
The code implementation of the electrical potential due to a layered half-space
is found in the anisotropic_potential.py. In it are the necessary steps to
model the voltage for given combindations of A, B, M, and N electrodes, using a
semi-analytic form. This formulation is analytic in the wavenumber domain, at
which point it uses a real ifft. The jacobian of the kernel is calculated using
a reverse mode operation that has a cost of roughly 2x the forward operation.
There are four notebooks that correspond to the examples presented in the
formal report of this method. The Inversion`_cross.ipynb corresponds to the
main example used throughout the work. The three other notebooks,
Inversion1_star_cross.ipynb, Inversion2.ipynb, and Inversion3.ipynb
then correspond to the three repeated examples which show the generality of the
approach to different amount of data and with different true models.
The Plotting.ipynb notebook contains all of the figures prepared for the
manuscript.
All output models and data for each of the four different cases can be found in the Models directory. These will also be recreated by running the Inversion notebooks.