.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/volcanology/plot_03_boltwood_uranium_lead_ages.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_03_boltwood_uranium_lead_ages.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_03_boltwood_uranium_lead_ages.py:


Boltwood's uranium-lead ages (1907)
===================================

Boltwood noticed that uranium minerals always contain lead, and more of it in
older rocks. Taking lead as the end of the uranium decay series, he turned the
lead-to-uranium ratio of minerals into ages of hundreds of millions to billions
of years, the first radiometric ages. With a known decay constant the age is
``log(1 + D/P) / lambda``; Boltwood's simpler ratio-over-rate is the first term
of that logarithm and overestimates old ages.

.. GENERATED FROM PYTHON SOURCE LINES 12-35



.. image-sg:: /api/gallery/volcanology/images/sphx_glr_plot_03_boltwood_uranium_lead_ages_001.png
   :alt: Lead accumulates in uranium minerals
   :srcset: /api/gallery/volcanology/images/sphx_glr_plot_03_boltwood_uranium_lead_ages_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import LAMBDA_U238
    from earthsciencekit.units import convert
    from earthsciencekit.volcanology import radiometric_age

    ratio = np.linspace(0, 0.6, 121)  # radiogenic 206Pb atoms per 238U atom
    age = convert(radiometric_age(ratio, LAMBDA_U238), "s", "Ma")
    linear = convert(ratio / LAMBDA_U238, "s", "Ma")
    assert np.all(age <= linear) and np.isclose(age[1], linear[1], rtol=3e-3)
    assert np.isclose(convert(radiometric_age(np.e - 1, LAMBDA_U238), "s", "Ma"), 1e-6 / 1.55125e-10)  # one mean life

    minerals = np.array([0.05, 0.12, 0.2, 0.3])  # synthetic Pb/U ratios
    fig, ax = plt.subplots()
    ax.plot(ratio, age, label="log(1 + D/P) / lambda")
    ax.plot(ratio, linear, "--", label="D / (P lambda), Boltwood's form")
    ax.plot(minerals, convert(radiometric_age(minerals, LAMBDA_U238), "s", "Ma"), "ko", label="synthetic minerals")
    ax.set(xlabel="206Pb / 238U", ylabel="age [Ma]", title="Lead accumulates in uranium minerals")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.094 seconds)


.. _sphx_glr_download_api_gallery_volcanology_plot_03_boltwood_uranium_lead_ages.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_03_boltwood_uranium_lead_ages.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_03_boltwood_uranium_lead_ages.ipynb <plot_03_boltwood_uranium_lead_ages.ipynb>`

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

      :download:`Download Python source code: plot_03_boltwood_uranium_lead_ages.py <plot_03_boltwood_uranium_lead_ages.py>`

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

      :download:`Download zipped: plot_03_boltwood_uranium_lead_ages.zip <plot_03_boltwood_uranium_lead_ages.zip>`


.. only:: html

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

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