.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/plate_tectonics/plot_15_parsons_sclater_depth_age.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_15_parsons_sclater_depth_age.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_15_parsons_sclater_depth_age.py:


Parsons and Sclater's depth-age law (1977)
==========================================

Barry Parsons and John Sclater fitted ocean depth and heat flow against
sea-floor age. Out to about 70 million years the depth grows as
``2500 + 350 sqrt(t)`` metres (``t`` in million years), which the cooling
half-space reproduces; older floor flattens, as their cooling-plate fit shows.
Surface heat flow falls as one over the square root of age.

.. GENERATED FROM PYTHON SOURCE LINES 11-38



.. image-sg:: /api/gallery/plate_tectonics/images/sphx_glr_plot_15_parsons_sclater_depth_age_001.png
   :alt: plot 15 parsons sclater depth age
   :srcset: /api/gallery/plate_tectonics/images/sphx_glr_plot_15_parsons_sclater_depth_age_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.plate_tectonics import halfspace_heat_flux, ocean_depth
    from earthsciencekit.units import convert

    age_myr = np.linspace(0, 160, 321)
    age = convert(age_myr * 1e6, "year", "s")
    depth = ocean_depth(age, 2500, 3300, 1000, 3e-5, 1e-6, 273, 1553)
    empirical = np.where(age_myr < 70, 2500 + 350 * np.sqrt(age_myr), 6400 - 3200 * np.exp(-age_myr / 62.8))
    young = age_myr < 70
    np.testing.assert_allclose(depth[young], empirical[young], rtol=0.01)
    flux = halfspace_heat_flux(age[1:], 1e-6, 3.3, 273, 1553)
    np.testing.assert_allclose(flux * np.sqrt(age_myr[1:]), flux[0] * np.sqrt(age_myr[1]))

    fig, (left, right) = plt.subplots(1, 2, figsize=(9, 4))
    left.plot(age_myr, depth / 1e3, label="half-space model")
    left.plot(age_myr, empirical / 1e3, "--", label="Parsons and Sclater fit")
    left.invert_yaxis()
    left.set(xlabel="age [million years]", ylabel="ocean depth [km]")
    left.legend()
    right.plot(age_myr[1:], flux * 1e3)
    right.set(xlabel="age [million years]", ylabel="heat flow [mW/m^2]", ylim=(0, 400))
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.170 seconds)


.. _sphx_glr_download_api_gallery_plate_tectonics_plot_15_parsons_sclater_depth_age.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_15_parsons_sclater_depth_age.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_15_parsons_sclater_depth_age.ipynb <plot_15_parsons_sclater_depth_age.ipynb>`

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

      :download:`Download Python source code: plot_15_parsons_sclater_depth_age.py <plot_15_parsons_sclater_depth_age.py>`

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

      :download:`Download zipped: plot_15_parsons_sclater_depth_age.zip <plot_15_parsons_sclater_depth_age.zip>`


.. only:: html

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

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