.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/geophysics/plot_09_love_numbers.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_geophysics_plot_09_love_numbers.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_geophysics_plot_09_love_numbers.py:


Love numbers (1909)
===================

Kelvin had argued from the ocean tides that the Earth is about as rigid as
steel. Augustus Love described the Earth's yielding to the tidal potential by
two numbers: ``h``, the ratio of the body-tide uplift to the equilibrium tide,
and ``k``, the extra potential of the deformed Earth. A uniform elastic sphere
as rigid as steel has k2 near 0.47; the real Earth, with a fluid core, has
``h2 = 0.61`` and ``k2 = 0.30``. Gravimeters see the tide amplified by
``1 + h - 3 k / 2``, about 1.16.

.. GENERATED FROM PYTHON SOURCE LINES 13-40



.. image-sg:: /api/gallery/geophysics/images/sphx_glr_plot_09_love_numbers_001.png
   :alt: A yielding Earth
   :srcset: /api/gallery/geophysics/images/sphx_glr_plot_09_love_numbers_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.geophysics import love_number_h2, love_number_k2, tidal_gravimetric_factor

    density, gravity, radius = 5514.0, 9.82, 6.371e6
    rigidity = np.logspace(9, 13, 200)
    h2, k2 = love_number_h2(rigidity, density, gravity, radius), love_number_k2(rigidity, density, gravity, radius)
    steel = 8e10
    steel_k2 = love_number_k2(steel, density, gravity, radius)
    assert 0.3 < steel_k2 < 0.6
    assert np.isclose(tidal_gravimetric_factor(0.61, 0.30), 1.16)
    effective = rigidity[np.argmin(np.abs(k2 - 0.30))]
    assert effective > steel

    fig, ax = plt.subplots()
    ax.semilogx(rigidity, h2, label="h2")
    ax.semilogx(rigidity, k2, label="k2")
    ax.semilogx(rigidity, tidal_gravimetric_factor(h2, k2), label="gravimetric factor 1 + h - 3k/2")
    ax.axvline(steel, color="0.5", ls="--", label="steel")
    ax.axhline(0.30, color="C1", ls=":", label="observed k2")
    ax.axhline(0.61, color="C0", ls=":", label="observed h2")
    ax.set(xlabel="rigidity of a uniform Earth [Pa]", ylabel="Love number", title="A yielding Earth")
    ax.legend(fontsize="small")

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.153 seconds)


.. _sphx_glr_download_api_gallery_geophysics_plot_09_love_numbers.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/geophysics/plot_09_love_numbers.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_09_love_numbers.ipynb <plot_09_love_numbers.ipynb>`

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

      :download:`Download Python source code: plot_09_love_numbers.py <plot_09_love_numbers.py>`

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

      :download:`Download zipped: plot_09_love_numbers.zip <plot_09_love_numbers.zip>`


.. only:: html

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

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