.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/glaciology/plot_05_haskell_mantle_viscosity.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_glaciology_plot_05_haskell_mantle_viscosity.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_glaciology_plot_05_haskell_mantle_viscosity.py:


Haskell's mantle viscosity from rebound (1935)
==============================================

Norman Haskell treated the mantle under Fennoscandia as a viscous half-space
and asked how fast a depression the size of the former ice sheet would
recover. Matching the raised shorelines gave a viscosity of about 1e21 Pa s,
still the standard value. The example builds a synthetic uplift history for a
3000 km depression and recovers the viscosity from the slope of its logarithm.

.. GENERATED FROM PYTHON SOURCE LINES 11-33



.. image-sg:: /api/gallery/glaciology/images/sphx_glr_plot_05_haskell_mantle_viscosity_001.png
   :alt: Haskell: 1e21 Pa s, uplift today 6.4 mm/year
   :srcset: /api/gallery/glaciology/images/sphx_glr_plot_05_haskell_mantle_viscosity_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import GRAVITY, SECONDS_PER_YEAR
    from earthsciencekit.glaciology import haskell_viscosity, rebound_uplift_rate, remaining_depression, viscous_relaxation_time

    wavelength, density = 3.0e6, 3300.0
    tau = viscous_relaxation_time(wavelength, 1e21, density, GRAVITY)
    time = np.linspace(0, 10e3, 201) * SECONDS_PER_YEAR
    remaining = remaining_depression(time, 300.0, tau)
    slope = np.polyfit(time, np.log(remaining), 1)[0]
    assert np.isclose(haskell_viscosity(-1 / slope, wavelength, density, GRAVITY), 1e21)
    rate_today = rebound_uplift_rate(time[-1], 300.0, tau) * SECONDS_PER_YEAR * 1e3

    fig, ax = plt.subplots()
    ax.plot(time / SECONDS_PER_YEAR / 1e3, remaining, label=f"relaxation time {tau / SECONDS_PER_YEAR:.0f} years")
    title = f"Haskell: 1e21 Pa s, uplift today {rate_today:.1f} mm/year"
    ax.set(xlabel="time since deglaciation [kyr]", ylabel="uplift still to come [m]", title=title)
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.076 seconds)


.. _sphx_glr_download_api_gallery_glaciology_plot_05_haskell_mantle_viscosity.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/glaciology/plot_05_haskell_mantle_viscosity.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_05_haskell_mantle_viscosity.ipynb <plot_05_haskell_mantle_viscosity.ipynb>`

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

      :download:`Download Python source code: plot_05_haskell_mantle_viscosity.py <plot_05_haskell_mantle_viscosity.py>`

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

      :download:`Download zipped: plot_05_haskell_mantle_viscosity.zip <plot_05_haskell_mantle_viscosity.zip>`


.. only:: html

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

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