.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/plate_tectonics/plot_12_walcott_lithospheric_flexure.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_12_walcott_lithospheric_flexure.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_12_walcott_lithospheric_flexure.py:


Walcott's lithospheric flexure under loads (1970)
=================================================

Richard Walcott measured how the lithosphere bends under volcanic islands,
ice sheets and sediment, and estimated its rigidity from the bending. A line
load on an elastic plate digs a moat that crosses zero at ``3 pi alpha / 4``
and lifts a bulge at ``pi alpha`` whose height is ``exp(-pi)`` of the central
deflection. The load here is a synthetic Hawaiian-scale ridge.

.. GENERATED FROM PYTHON SOURCE LINES 11-35



.. image-sg:: /api/gallery/plate_tectonics/images/sphx_glr_plot_12_walcott_lithospheric_flexure_001.png
   :alt: Moat and bulge, alpha = 74 km
   :srcset: /api/gallery/plate_tectonics/images/sphx_glr_plot_12_walcott_lithospheric_flexure_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 flexural_deflection, flexural_parameter, flexural_rigidity

    rigidity = flexural_rigidity(7e10, 30e3, 0.25)
    contrast, load = 3300 - 1000, 2e13
    alpha = float(flexural_parameter(rigidity, contrast, GRAVITY))
    x = np.linspace(-600e3, 600e3, 2401)
    w = flexural_deflection(x, load, rigidity, contrast, GRAVITY)
    w0 = float(flexural_deflection(0, load, rigidity, contrast, GRAVITY))
    assert abs(float(flexural_deflection(3 * np.pi * alpha / 4, load, rigidity, contrast, GRAVITY))) < 1e-9 * w0
    assert np.isclose(float(flexural_deflection(np.pi * alpha, load, rigidity, contrast, GRAVITY)), -np.exp(-np.pi) * w0)

    fig, ax = plt.subplots()
    ax.plot(x / 1e3, -w / 1e3)
    ax.axvline(np.pi * alpha / 1e3, color="0.5", ls="--", label="bulge at pi alpha")
    ax.axhline(0, color="k", lw=0.5)
    ax.set(xlabel="distance from load [km]", ylabel="surface height [km]", title=f"Moat and bulge, alpha = {alpha / 1e3:.0f} km")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.079 seconds)


.. _sphx_glr_download_api_gallery_plate_tectonics_plot_12_walcott_lithospheric_flexure.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_12_walcott_lithospheric_flexure.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_12_walcott_lithospheric_flexure.ipynb <plot_12_walcott_lithospheric_flexure.ipynb>`

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

      :download:`Download Python source code: plot_12_walcott_lithospheric_flexure.py <plot_12_walcott_lithospheric_flexure.py>`

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

      :download:`Download zipped: plot_12_walcott_lithospheric_flexure.zip <plot_12_walcott_lithospheric_flexure.zip>`


.. only:: html

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

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