.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "content/examples/20-published/plot_effective_medium_theory.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_content_examples_20-published_plot_effective_medium_theory.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_content_examples_20-published_plot_effective_medium_theory.py:


Effective Medium Theory Mapping
===============================

This example uses Self Consistent Effective Medium Theory to estimate the
electrical conductivity of a mixture of two phases of materials. Given
the electrical conductivity of each of the phases (:math:`\sigma_0`,
:math:`\sigma_1`), the :class:`simpeg.maps.SelfConsistentEffectiveMedium`
map takes the concentration of phase-1 (:math:`\phi_1`) and maps this to an
electrical conductivity.

This mapping is used in chapter 2 of:

Heagy, Lindsey J.(2018, in prep) *Electromagnetic methods for imaging
subsurface injections.* University of British Columbia

:author: `@lheagy <https://github.com/lheagy>`_

.. GENERATED FROM PYTHON SOURCE LINES 20-28

.. code-block:: Python


    import numpy as np
    import matplotlib.pyplot as plt
    from simpeg import maps
    from matplotlib import rcParams

    rcParams["font.size"] = 12








.. GENERATED FROM PYTHON SOURCE LINES 29-35

Conductivities
---------------

Here we consider a mixture composed of fluid (3 S/m) and conductive
particles which we will vary the conductivity of.


.. GENERATED FROM PYTHON SOURCE LINES 35-40

.. code-block:: Python


    sigma_fluid = 3
    sigma1 = np.logspace(1, 5, 5)  # look at a range of particle conductivities
    phi = np.linspace(0.0, 1, 1000)  # vary the volume of particles








.. GENERATED FROM PYTHON SOURCE LINES 41-48

Construct the Mapping
---------------------

We set the conductivity of the phase-0 material to the conductivity of the
fluid. The mapping will then take a concentration (by volume), of phase-1
material and compute the effective conductivity


.. GENERATED FROM PYTHON SOURCE LINES 48-51

.. code-block:: Python


    scemt = maps.SelfConsistentEffectiveMedium(sigma0=sigma_fluid, sigma1=1)








.. GENERATED FROM PYTHON SOURCE LINES 52-58

Loop over a range of particle conductivities
--------------------------------------------

We loop over the values defined as `sigma1` and compute the effective
conductivity of the mixture for each concentration in the `phi` vector


.. GENERATED FROM PYTHON SOURCE LINES 58-65

.. code-block:: Python


    sige = np.zeros([phi.size, sigma1.size])

    for i, s in enumerate(sigma1):
        scemt.sigma1 = s
        sige[:, i] = scemt * phi





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    /home/vsts/work/1/s/simpeg/maps/_property_maps.py:1456: UserWarning:

    Maximum number of iterations reached





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Plot the effective conductivity
-------------------------------

The plot shows the effective conductivity of 5 difference mixtures. In all
cases, the conductivity of the fluid, :math:`\sigma_0`, is 3 S/m. The
conductivity of the particles is indicated in the legend


.. GENERATED FROM PYTHON SOURCE LINES 73-83

.. code-block:: Python


    fig, ax = plt.subplots(1, 1, figsize=(7, 4), dpi=350)

    ax.semilogy(phi, sige)
    ax.grid(which="both", alpha=0.4)
    ax.legend(["{:1.0e} S/m".format(s) for s in sigma1])
    ax.set_xlabel(r"Volume fraction of proppant $\phi$")
    ax.set_ylabel("Effective conductivity (S/m)")

    plt.tight_layout()



.. image-sg:: /content/examples/20-published/images/sphx_glr_plot_effective_medium_theory_001.png
   :alt: plot effective medium theory
   :srcset: /content/examples/20-published/images/sphx_glr_plot_effective_medium_theory_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 2.027 seconds)

**Estimated memory usage:**  9 MB


.. _sphx_glr_download_content_examples_20-published_plot_effective_medium_theory.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_effective_medium_theory.ipynb <plot_effective_medium_theory.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_effective_medium_theory.py <plot_effective_medium_theory.py>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_