.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/seismology/plot_08_zoeppritz_reflection.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_08_zoeppritz_reflection.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_08_zoeppritz_reflection.py:


Zoeppritz's reflection coefficients (1919)
==========================================

Karl Zoeppritz derived how a plane wave divides at a boundary between two
elastic media. At normal incidence his equations reduce to the impedance
contrast: the pressure transmission can exceed one, yet the reflected and
transmitted energy fractions always sum to one.

.. GENERATED FROM PYTHON SOURCE LINES 10-34



.. image-sg:: /api/gallery/seismology/images/sphx_glr_plot_08_zoeppritz_reflection_001.png
   :alt: Energy is shared, never created
   :srcset: /api/gallery/seismology/images/sphx_glr_plot_08_zoeppritz_reflection_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    sediment/basement: R = 0.459, T = 1.459






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.seismology import reflection_coefficient, seismic_impedance, transmission_coefficient

    ratio = np.logspace(-2, 2, 201)
    r = reflection_coefficient(1, ratio)
    t = transmission_coefficient(1, ratio)
    reflected, transmitted = r * r, t * t / ratio
    np.testing.assert_allclose(reflected + transmitted, 1, atol=1e-14)

    # A sediment-on-basement contact.
    z1, z2 = seismic_impedance(2200, 2500), seismic_impedance(2700, 5500)
    print(f"sediment/basement: R = {reflection_coefficient(z1, z2):.3f}, T = {transmission_coefficient(z1, z2):.3f}")

    fig, ax = plt.subplots()
    ax.semilogx(ratio, reflected, label="reflected energy")
    ax.semilogx(ratio, transmitted, label="transmitted energy")
    ax.axvline(z2 / z1, color="k", ls=":", label="sediment on basement")
    ax.set(xlabel="impedance ratio Z2/Z1", ylabel="incident energy fraction", title="Energy is shared, never created")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.152 seconds)


.. _sphx_glr_download_api_gallery_seismology_plot_08_zoeppritz_reflection.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_08_zoeppritz_reflection.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_08_zoeppritz_reflection.ipynb <plot_08_zoeppritz_reflection.ipynb>`

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

      :download:`Download Python source code: plot_08_zoeppritz_reflection.py <plot_08_zoeppritz_reflection.py>`

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

      :download:`Download zipped: plot_08_zoeppritz_reflection.zip <plot_08_zoeppritz_reflection.zip>`


.. only:: html

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

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