.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/volcanology/plot_12_mogi_point_source.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_volcanology_plot_12_mogi_point_source.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_volcanology_plot_12_mogi_point_source.py:


Mogi's point source (1958)
==========================

Kiyoo Mogi modelled a magma chamber as a small pressurized sphere in an elastic
half-space and matched the domes of uplift that surveys measured around
Sakurajima and Kilauea. The uplift is bell-shaped and halves at 0.766 times
the source depth, so the width of a dome locates the chamber and its volume
gives the magma added.

.. GENERATED FROM PYTHON SOURCE LINES 11-34



.. image-sg:: /api/gallery/volcanology/images/sphx_glr_plot_12_mogi_point_source_001.png
   :alt: 1e6 m^3 of magma at 3 km depth
   :srcset: /api/gallery/volcanology/images/sphx_glr_plot_12_mogi_point_source_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.volcanology import mogi_displacement

    depth, volume, nu = 3000.0, 1e6, 0.25
    distance = np.linspace(0, 12000, 1201)
    radial, vertical = mogi_displacement(distance, depth, volume, nu).T
    half_width = distance[np.argmin(np.abs(vertical - vertical[0] / 2))]
    assert np.isclose(half_width / 0.766, depth, rtol=0.005)
    assert np.isclose(distance[np.argmax(radial)], depth / np.sqrt(2), atol=10)

    fig, ax = plt.subplots()
    ax.plot(distance / 1e3, vertical * 100, label="uplift")
    ax.plot(distance / 1e3, radial * 100, label="radial displacement")
    ax.axvline(half_width / 1e3, color="0.5", ls="--", lw=1)
    label = f"half uplift at {half_width / 1e3:.2f} km\n-> depth {half_width / 0.766 / 1e3:.2f} km"
    ax.annotate(label, (half_width / 1e3, vertical[0] * 50), xytext=(10, 0), textcoords="offset points")
    ax.set(xlabel="distance from the summit [km]", ylabel="displacement [cm]", title="1e6 m^3 of magma at 3 km depth")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.089 seconds)


.. _sphx_glr_download_api_gallery_volcanology_plot_12_mogi_point_source.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/volcanology/plot_12_mogi_point_source.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_12_mogi_point_source.ipynb <plot_12_mogi_point_source.ipynb>`

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

      :download:`Download Python source code: plot_12_mogi_point_source.py <plot_12_mogi_point_source.py>`

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

      :download:`Download zipped: plot_12_mogi_point_source.zip <plot_12_mogi_point_source.zip>`


.. only:: html

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

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