.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/seismology/plot_06_love_waves.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_seismology_plot_06_love_waves.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_seismology_plot_06_love_waves.py:


Love waves (1911)
=================

Augustus Love showed that horizontal shear waves can be trapped in a slow
surface layer over a faster half-space, which a homogeneous Earth cannot do.
Their speed depends on period: short waves travel at the speed of the layer,
long waves at the speed of the half-space. That dispersion measures the
thickness of the crust. The layer here is a 35 km crust over mantle.

.. GENERATED FROM PYTHON SOURCE LINES 11-35



.. image-sg:: /api/gallery/seismology/images/sphx_glr_plot_06_love_waves_001.png
   :alt: Long Love waves feel the mantle
   :srcset: /api/gallery/seismology/images/sphx_glr_plot_06_love_waves_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.seismology import love_wave_angular_frequency, s_wave_speed

    h = 35e3
    b1, b2 = 3.5e3, 4.5e3
    m1, m2 = 2800 * b1**2, 3300 * b2**2
    assert np.isclose(s_wave_speed(m1, 2800), b1)
    speed = np.linspace(b1 * 1.001, b2 * 0.999, 400)
    period = 2 * np.pi / love_wave_angular_frequency(speed, h, b1, b2, m1, m2)
    assert np.all(np.diff(period) > 0)

    fig, ax = plt.subplots()
    for thickness in [20e3, 35e3, 50e3]:
        omega = love_wave_angular_frequency(speed, thickness, b1, b2, m1, m2)
        ax.semilogx(2 * np.pi / omega, speed / 1e3, label=f"crust {thickness / 1e3:.0f} km")
    ax.axhline(b1 / 1e3, color="k", ls=":")
    ax.axhline(b2 / 1e3, color="k", ls=":")
    ax.set(xlabel="period [s]", ylabel="phase speed [km/s]", title="Long Love waves feel the mantle")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.115 seconds)


.. _sphx_glr_download_api_gallery_seismology_plot_06_love_waves.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/seismology/plot_06_love_waves.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_06_love_waves.ipynb <plot_06_love_waves.ipynb>`

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

      :download:`Download Python source code: plot_06_love_waves.py <plot_06_love_waves.py>`

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

      :download:`Download zipped: plot_06_love_waves.zip <plot_06_love_waves.zip>`


.. only:: html

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

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