.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/seismology/plot_13_knopoff_q.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_13_knopoff_q.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_13_knopoff_q.py:


Knopoff's Q (1964)
==================

Leon Knopoff reviewed the evidence that rocks dissipate a nearly constant
fraction of wave energy per cycle, whatever the frequency. With a constant
quality factor Q, amplitude decays as exp(-pi f t / Q), so high frequencies
die first. The log ratio of two spectra is then a straight line in frequency
whose slope gives Q, the spectral-ratio method.

.. GENERATED FROM PYTHON SOURCE LINES 11-36



.. image-sg:: /api/gallery/seismology/images/sphx_glr_plot_13_knopoff_q_001.png
   :alt: Constant Q = 200, Spectral ratio recovers Q = 200
   :srcset: /api/gallery/seismology/images/sphx_glr_plot_13_knopoff_q_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.seismology import attenuated_amplitude

    Q = 200.0
    frequency = np.linspace(0.5, 20, 100)
    near, far = 5.0, 50.0
    log_ratio = np.log(attenuated_amplitude(1, frequency, far, Q) / attenuated_amplitude(1, frequency, near, Q))
    slope = np.polyfit(frequency, log_ratio, 1)[0]
    Q_hat = -np.pi * (far - near) / slope
    assert np.isclose(Q_hat, Q)

    travel = np.linspace(0, 60, 200)
    fig, axes = plt.subplots(1, 2, figsize=(10, 3.5))
    for f in [1, 5, 20]:
        axes[0].plot(travel, attenuated_amplitude(1, f, travel, Q), label=f"{f} Hz")
    axes[0].set(xlabel="travel time [s]", ylabel="relative amplitude", title=f"Constant Q = {Q:.0f}")
    axes[0].legend()
    axes[1].plot(frequency, log_ratio)
    axes[1].set(xlabel="frequency [Hz]", ylabel="ln(A far / A near)", title=f"Spectral ratio recovers Q = {Q_hat:.0f}")
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.210 seconds)


.. _sphx_glr_download_api_gallery_seismology_plot_13_knopoff_q.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_13_knopoff_q.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_13_knopoff_q.ipynb <plot_13_knopoff_q.ipynb>`

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

      :download:`Download Python source code: plot_13_knopoff_q.py <plot_13_knopoff_q.py>`

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

      :download:`Download zipped: plot_13_knopoff_q.zip <plot_13_knopoff_q.zip>`


.. only:: html

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

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