.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/plate_tectonics/plot_02_airy_isostasy.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_api_gallery_plate_tectonics_plot_02_airy_isostasy.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

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

.. _sphx_glr_api_gallery_plate_tectonics_plot_02_airy_isostasy.py:


Airy's isostasy (1855)
======================

George Airy explained why the Himalaya deflect a plumb line less than their
visible mass predicts: mountains float on denser rock on light roots. A root
of depth ``r`` under an elevation ``h`` balances the pressure at the base of
the deepest column.

.. GENERATED FROM PYTHON SOURCE LINES 10-34



.. image-sg:: /api/gallery/plate_tectonics/images/sphx_glr_plot_02_airy_isostasy_001.png
   :alt: Light roots under high mountains
   :srcset: /api/gallery/plate_tectonics/images/sphx_glr_plot_02_airy_isostasy_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import GRAVITY
    from earthsciencekit.plate_tectonics import airy_root

    crust, mantle, thickness = 2800.0, 3300.0, 35e3
    elevation = np.array([0, 1, 2, 3, 4, 5]) * 1e3
    root = airy_root(elevation, crust, mantle)
    compensation = thickness + root.max()
    pressure = GRAVITY * (crust * (elevation + thickness + root) + mantle * (compensation - thickness - root))
    np.testing.assert_allclose(pressure, pressure[0])
    assert np.isclose(float(airy_root(4e3, crust, mantle)), 22.4e3)

    fig, ax = plt.subplots()
    ax.bar(np.arange(elevation.size), (elevation + thickness + root) / 1e3, bottom=-(thickness + root) / 1e3, color="tan", label="crust")
    ax.axhline(-thickness / 1e3, color="0.5", ls="--", label="normal Moho")
    ax.axhline(-compensation / 1e3, color="k", lw=0.8, label="compensation depth")
    ax.set_xticks(np.arange(elevation.size), [f"{h / 1e3:.0f}" for h in elevation])
    ax.set(xlabel="elevation [km]", ylabel="height above sea level [km]", title="Light roots under high mountains")
    ax.legend(loc="lower left")

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.082 seconds)


.. _sphx_glr_download_api_gallery_plate_tectonics_plot_02_airy_isostasy.py:

.. only:: html

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

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/plate_tectonics/plot_02_airy_isostasy.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_airy_isostasy.ipynb <plot_02_airy_isostasy.ipynb>`

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

      :download:`Download Python source code: plot_02_airy_isostasy.py <plot_02_airy_isostasy.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_airy_isostasy.zip <plot_02_airy_isostasy.zip>`


.. only:: html

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

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