.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/plate_tectonics/plot_16_nuvel1_euler_circuit.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_16_nuvel1_euler_circuit.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_16_nuvel1_euler_circuit.py:


NUVEL-1 relative plate motions (1990)
=====================================

Charles DeMets, Richard Gordon, Donald Argus and Seth Stein fitted spreading
rates, transform azimuths and earthquake slip vectors for all the major
plates at once. The fit requires every circuit of relative Euler vectors to
close: the motion of A relative to C is A-B plus B-C. At a triple junction the
three relative velocities then form a closed triangle. The Euler vectors here
are synthetic.

.. GENERATED FROM PYTHON SOURCE LINES 12-62



.. image-sg:: /api/gallery/plate_tectonics/images/sphx_glr_plot_16_nuvel1_euler_circuit_001.png
   :alt: The velocity triangle closes
   :srcset: /api/gallery/plate_tectonics/images/sphx_glr_plot_16_nuvel1_euler_circuit_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 compose_euler_vectors, euler_velocity_x, euler_velocity_y, euler_velocity_z
    from earthsciencekit.units import convert


    def euler_vector(latitude, longitude, degrees_per_myr):
        rate = convert(degrees_per_myr, "degree", "rad") / convert(1e6, "year", "s")
        lat, lon = np.deg2rad(latitude), np.deg2rad(longitude)
        return rate * np.array([np.cos(lat) * np.cos(lon), np.cos(lat) * np.sin(lon), np.sin(lat)])


    def velocity(omega, r):
        return np.array(
            [
                euler_velocity_x(omega[1], omega[2], r[1], r[2]),
                euler_velocity_y(omega[2], omega[0], r[2], r[0]),
                euler_velocity_z(omega[0], omega[1], r[0], r[1]),
            ]
        )


    omega_ab = euler_vector(48.7, -78.2, 0.78)
    omega_bc = euler_vector(-10.0, -60.0, 0.5)
    omega_ac = compose_euler_vectors(omega_ab, omega_bc)
    np.testing.assert_allclose(compose_euler_vectors(omega_ac, -omega_ac), 0)

    lat, lon = np.deg2rad(20.0), np.deg2rad(-110.0)
    r = EARTH_RADIUS * np.array([np.cos(lat) * np.cos(lon), np.cos(lat) * np.sin(lon), np.sin(lat)])
    east = np.array([-np.sin(lon), np.cos(lon), 0])
    north = np.array([-np.sin(lat) * np.cos(lon), -np.sin(lat) * np.sin(lon), np.cos(lat)])
    legs = {"A relative to B": velocity(omega_ab, r), "B relative to C": velocity(omega_bc, r), "C relative to A": velocity(-omega_ac, r)}
    np.testing.assert_allclose(sum(legs.values()), 0, atol=1e-20)

    fig, ax = plt.subplots()
    corners = [np.zeros(2)]
    for name, v in legs.items():
        step = convert(np.array([east @ v, north @ v]), "m/s", "cm/year")
        ax.annotate("", corners[-1] + step, corners[-1], arrowprops={"arrowstyle": "->", "lw": 2})
        ax.text(*(corners[-1] + step / 2), name, ha="center", va="bottom")
        corners.append(corners[-1] + step)
    assert np.allclose(corners[-1], 0, atol=1e-12)
    ax.plot(*np.array(corners).T, "o", color="k", ms=4)
    ax.set(xlabel="east [cm/year]", ylabel="north [cm/year]", title="The velocity triangle closes", aspect="equal")
    ax.margins(0.25)

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.068 seconds)


.. _sphx_glr_download_api_gallery_plate_tectonics_plot_16_nuvel1_euler_circuit.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_16_nuvel1_euler_circuit.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_16_nuvel1_euler_circuit.ipynb <plot_16_nuvel1_euler_circuit.ipynb>`

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

      :download:`Download Python source code: plot_16_nuvel1_euler_circuit.py <plot_16_nuvel1_euler_circuit.py>`

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

      :download:`Download zipped: plot_16_nuvel1_euler_circuit.zip <plot_16_nuvel1_euler_circuit.zip>`


.. only:: html

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

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