.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/volcanology/plot_09_patterson_age_of_the_earth.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_09_patterson_age_of_the_earth.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_09_patterson_age_of_the_earth.py:


Patterson's age of the Earth (1956)
===================================

Clair Patterson measured lead in meteorites. The iron meteorite Canyon Diablo
holds almost no uranium, so its lead is primordial; stony meteorites add lead
grown from uranium since they formed. Plotted as 207Pb/204Pb against
206Pb/204Pb they fall on one line whose slope is the radiogenic 207Pb/206Pb
ratio of a 4.55-billion-year age, and terrestrial ocean sediment lies on it
too, so the Earth shares that age.

.. GENERATED FROM PYTHON SOURCE LINES 12-35



.. image-sg:: /api/gallery/volcanology/images/sphx_glr_plot_09_patterson_age_of_the_earth_001.png
   :alt: Meteorite lead isochron
   :srcset: /api/gallery/volcanology/images/sphx_glr_plot_09_patterson_age_of_the_earth_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.units import convert
    from earthsciencekit.volcanology import lead_lead_age, radiogenic_lead_ratio

    primordial = np.array([9.307, 10.294])  # Canyon Diablo 206Pb/204Pb, 207Pb/204Pb
    slope = radiogenic_lead_ratio(convert(4.55, "Ga", "s"))
    growth = np.array([0.0, 10.0, 20.0, 30.0, 40.0])  # synthetic radiogenic 206Pb/204Pb added
    x = primordial[0] + growth
    y = primordial[1] + slope * growth
    fit = np.polyfit(x, y, 1)[0]
    assert np.isclose(convert(lead_lead_age(fit), "s", "Ga"), 4.55)

    fig, ax = plt.subplots()
    ax.plot(x, y, "ko")
    ax.plot(x[0], y[0], "s", color="C3", label="Canyon Diablo (primordial)")
    ax.plot(x, primordial[1] + fit * (x - primordial[0]), label=f"isochron: slope {fit:.3f}, {convert(lead_lead_age(fit), 's', 'Ga'):.2f} Ga")
    ax.set(xlabel="206Pb / 204Pb", ylabel="207Pb / 204Pb", title="Meteorite lead isochron")
    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_volcanology_plot_09_patterson_age_of_the_earth.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_09_patterson_age_of_the_earth.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_09_patterson_age_of_the_earth.ipynb <plot_09_patterson_age_of_the_earth.ipynb>`

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

      :download:`Download Python source code: plot_09_patterson_age_of_the_earth.py <plot_09_patterson_age_of_the_earth.py>`

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

      :download:`Download zipped: plot_09_patterson_age_of_the_earth.zip <plot_09_patterson_age_of_the_earth.zip>`


.. only:: html

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

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