.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/plate_tectonics/plot_13_morgan_hotspot_tracks.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_13_morgan_hotspot_tracks.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_13_morgan_hotspot_tracks.py:


Morgan's hotspot tracks (1971)
==============================

W. Jason Morgan proposed that fixed plumes rising from the deep mantle feed
chains such as Hawaii-Emperor. A plate rotating over them leaves volcanoes
whose age grows linearly along small circles about the plate's Euler pole.
Chains at different distances from the pole move at different speeds but
record the same rotation. Positions and ages here are synthetic.

.. GENERATED FROM PYTHON SOURCE LINES 11-35



.. image-sg:: /api/gallery/plate_tectonics/images/sphx_glr_plot_13_morgan_hotspot_tracks_001.png
   :alt: Ages along two hotspot tracks
   :srcset: /api/gallery/plate_tectonics/images/sphx_glr_plot_13_morgan_hotspot_tracks_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import EARTH_RADIUS
    from earthsciencekit.plate_tectonics import hotspot_age
    from earthsciencekit.units import convert

    omega = convert(convert(8.6, "cm/year", "m/s"), "m/s", "m/s") / (EARTH_RADIUS * np.sin(np.deg2rad(70)))
    rotation = np.deg2rad(np.linspace(0, 25, 26))
    fig, ax = plt.subplots()
    ages = []
    for colatitude, name in [(70, "Hawaii-like chain"), (40, "chain nearer the pole")]:
        length = rotation * EARTH_RADIUS * np.sin(np.deg2rad(colatitude))
        age = hotspot_age(length, omega, EARTH_RADIUS, np.deg2rad(colatitude))
        ages.append(age)
        ax.plot(length / 1e3, convert(age, "s", "year") / 1e6, "o-", ms=3, label=name)
    np.testing.assert_allclose(ages[0], ages[1])
    midway = hotspot_age(2.4e6, omega, EARTH_RADIUS, np.deg2rad(70))
    assert np.isclose(convert(midway, "s", "year") / 1e6, 27.9, atol=0.1)
    ax.set(xlabel="distance along chain [km]", ylabel="volcano age [million years]", title="Ages along two hotspot tracks")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.083 seconds)


.. _sphx_glr_download_api_gallery_plate_tectonics_plot_13_morgan_hotspot_tracks.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_13_morgan_hotspot_tracks.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_13_morgan_hotspot_tracks.ipynb <plot_13_morgan_hotspot_tracks.ipynb>`

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

      :download:`Download Python source code: plot_13_morgan_hotspot_tracks.py <plot_13_morgan_hotspot_tracks.py>`

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

      :download:`Download zipped: plot_13_morgan_hotspot_tracks.zip <plot_13_morgan_hotspot_tracks.zip>`


.. only:: html

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

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