.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/seismology/plot_02_rayleigh_surface_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_02_rayleigh_surface_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_02_rayleigh_surface_waves.py:


Rayleigh's surface waves (1885)
===============================

Lord Rayleigh found a wave bound to the free surface of an elastic solid,
slower than the shear wave and decaying with depth. Its speed solves a cubic
that depends only on Poisson's ratio: about 0.92 of the shear speed in a
Poisson solid. Because it spreads in two dimensions rather than three, it
carries the largest motions on distant seismograms.

.. GENERATED FROM PYTHON SOURCE LINES 11-31



.. image-sg:: /api/gallery/seismology/images/sphx_glr_plot_02_rayleigh_surface_waves_001.png
   :alt: Surface waves trail the shear wave
   :srcset: /api/gallery/seismology/images/sphx_glr_plot_02_rayleigh_surface_waves_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.seismology import poisson_ratio, rayleigh_wave_speed

    vs = 1.0
    vp = np.sqrt(np.linspace(4 / 3 + 1e-3, 100, 400)) * vs
    ratio = rayleigh_wave_speed(vp, vs) / vs
    nu = poisson_ratio(vp, vs)
    assert np.isclose(rayleigh_wave_speed(np.sqrt(3), 1), np.sqrt(2 - 2 / np.sqrt(3)))
    assert np.all(ratio < 1) and np.all(np.diff(ratio[np.argsort(nu)]) > 0)

    fig, ax = plt.subplots()
    ax.plot(nu, ratio)
    ax.plot(0.25, np.sqrt(2 - 2 / np.sqrt(3)), "o", label="Poisson solid: 0.9194")
    ax.set(xlabel="Poisson's ratio", ylabel="Rayleigh speed / shear speed", title="Surface waves trail the shear wave")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.083 seconds)


.. _sphx_glr_download_api_gallery_seismology_plot_02_rayleigh_surface_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_02_rayleigh_surface_waves.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_rayleigh_surface_waves.ipynb <plot_02_rayleigh_surface_waves.ipynb>`

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

      :download:`Download Python source code: plot_02_rayleigh_surface_waves.py <plot_02_rayleigh_surface_waves.py>`

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

      :download:`Download zipped: plot_02_rayleigh_surface_waves.zip <plot_02_rayleigh_surface_waves.zip>`


.. only:: html

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

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