.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/seismology/plot_14_aki_seismic_moment.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_14_aki_seismic_moment.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_14_aki_seismic_moment.py:


Aki's seismic moment (1966)
===========================

From the long-period Love waves of the 1964 Niigata earthquake, Keiiti Aki
measured the seismic moment, rigidity times fault area times average slip.
Unlike magnitudes read off one instrument, moment is a physical quantity that
does not saturate for great earthquakes. The fault dimensions below are of the
order Aki inferred (about 100 km by 20 km, a few metres of slip).

.. GENERATED FROM PYTHON SOURCE LINES 11-34



.. image-sg:: /api/gallery/seismology/images/sphx_glr_plot_14_aki_seismic_moment_001.png
   :alt: Moment grows as length cubed
   :srcset: /api/gallery/seismology/images/sphx_glr_plot_14_aki_seismic_moment_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    moment of order 3.2e+20 N m






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.seismology import seismic_moment

    rigidity = 4e10
    niigata = seismic_moment(rigidity, 100e3 * 20e3, 4.0)
    assert 1e20 < niigata < 1e21
    print(f"moment of order {niigata:.1e} N m")

    # Self-similar ruptures: width is half the length and slip grows with length.
    length = np.logspace(3, 6, 100)
    moment = seismic_moment(rigidity, length * length / 2, 5e-5 * length)
    np.testing.assert_allclose(np.diff(np.log10(moment)) / np.diff(np.log10(length)), 3)

    fig, ax = plt.subplots()
    ax.loglog(length / 1e3, moment, label="self-similar ruptures")
    ax.loglog(100, niigata, "o", label="Niigata-sized rupture")
    ax.set(xlabel="rupture length [km]", ylabel="seismic moment [N m]", title="Moment grows as length cubed")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.151 seconds)


.. _sphx_glr_download_api_gallery_seismology_plot_14_aki_seismic_moment.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_14_aki_seismic_moment.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_14_aki_seismic_moment.ipynb <plot_14_aki_seismic_moment.ipynb>`

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

      :download:`Download Python source code: plot_14_aki_seismic_moment.py <plot_14_aki_seismic_moment.py>`

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

      :download:`Download zipped: plot_14_aki_seismic_moment.zip <plot_14_aki_seismic_moment.zip>`


.. only:: html

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

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