.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/volcanology/plot_13_nicolaysen_isochron.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_13_nicolaysen_isochron.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_13_nicolaysen_isochron.py:


Nicolaysen's isochron (1961)
============================

Louis Nicolaysen showed how to date a rock without knowing how much daughter
it started with. Minerals that crystallized together share the initial
87Sr/86Sr but take up different amounts of rubidium. As 87Rb decays they move
along lines of slope one, so at any time they lie on a straight isochron whose
slope gives the age and whose intercept gives the initial ratio.

.. GENERATED FROM PYTHON SOURCE LINES 11-39



.. image-sg:: /api/gallery/volcanology/images/sphx_glr_plot_13_nicolaysen_isochron_001.png
   :alt: Rb-Sr mineral isochron
   :srcset: /api/gallery/volcanology/images/sphx_glr_plot_13_nicolaysen_isochron_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 isochron_fit

    rate = 1.42e-11 / convert(1, "year", "s")  # 87Rb decay constant, 1/s
    age, initial = convert(1.2, "Ga", "s"), 0.7045
    rubidium = np.array([0.15, 0.9, 2.1, 4.0, 6.5])
    scatter = np.array([2, -3, 1, 3, -2]) * 1e-5  # deterministic analytical noise
    strontium = initial + rubidium * np.expm1(rate * age) + scatter
    fit_age, fit_initial = isochron_fit(rubidium, strontium, rate)
    assert np.isclose(convert(fit_age, "s", "Ga"), 1.2, rtol=2e-3) and np.isclose(fit_initial, initial, atol=1e-4)

    fig, ax = plt.subplots()
    ax.plot(rubidium, np.full_like(rubidium, initial), "o", mfc="none", color="0.5", label="at crystallization")
    ax.plot(rubidium, strontium, "ko", label="today")
    line = np.array([0, 7.0])
    ax.plot(
        line,
        fit_initial + line * np.expm1(rate * fit_age),
        label=f"isochron: {convert(fit_age, 's', 'Ga'):.3f} Ga, initial {fit_initial:.4f}",
    )
    ax.set(xlabel="87Rb / 86Sr", ylabel="87Sr / 86Sr", title="Rb-Sr mineral isochron")
    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_13_nicolaysen_isochron.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_13_nicolaysen_isochron.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_13_nicolaysen_isochron.ipynb <plot_13_nicolaysen_isochron.ipynb>`

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

      :download:`Download Python source code: plot_13_nicolaysen_isochron.py <plot_13_nicolaysen_isochron.py>`

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

      :download:`Download zipped: plot_13_nicolaysen_isochron.zip <plot_13_nicolaysen_isochron.zip>`


.. only:: html

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

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