.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/seismology/plot_16_prem_travel_time.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_16_prem_travel_time.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_16_prem_travel_time.py:


Dziewonski and Anderson's PREM (1981)
=====================================

Adam Dziewonski and Don Anderson fitted one spherically symmetric Earth model,
PREM, to travel times, normal modes and the Earth's mass and moment of inertia.
Integrating slowness through such a table predicts arrival times. The rounded
P-wave values below follow PREM. A vertical ray from the surface through the
centre to the antipode takes about 20 minutes, close to the tabulated PKIKP
time of about 1212 s.

.. GENERATED FROM PYTHON SOURCE LINES 12-34



.. image-sg:: /api/gallery/seismology/images/sphx_glr_plot_16_prem_travel_time_001.png
   :alt: Rounded PREM profile, Integrated slowness
   :srcset: /api/gallery/seismology/images/sphx_glr_plot_16_prem_travel_time_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    surface to antipode: 1231 s; to the core: 259 s






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.seismology import vertical_travel_time

    depth_km = np.array([0, 15, 15, 24.4, 24.4, 220, 220, 400, 400, 670, 670, 2891, 2891, 5150, 5150, 6371])
    vp_km_s = np.array([5.8, 5.8, 6.8, 6.8, 8.11, 7.99, 8.56, 8.91, 9.13, 10.27, 10.75, 13.72, 8.06, 10.36, 11.03, 11.26])
    time = vertical_travel_time(depth_km * 1e3, vp_km_s * 1e3)
    antipode = 2 * time[-1]
    assert np.isclose(antipode, 1212, rtol=0.03)
    print(f"surface to antipode: {antipode:.0f} s; to the core: {time[11]:.0f} s")

    fig, axes = plt.subplots(1, 2, figsize=(10, 4), sharey=True)
    axes[0].plot(vp_km_s, depth_km)
    axes[0].set(xlabel="P speed [km/s]", ylabel="depth [km]", title="Rounded PREM profile")
    axes[1].plot(time, depth_km)
    axes[1].set(xlabel="one-way vertical time [s]", title="Integrated slowness")
    axes[0].invert_yaxis()
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.167 seconds)


.. _sphx_glr_download_api_gallery_seismology_plot_16_prem_travel_time.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_16_prem_travel_time.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_16_prem_travel_time.ipynb <plot_16_prem_travel_time.ipynb>`

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

      :download:`Download Python source code: plot_16_prem_travel_time.py <plot_16_prem_travel_time.py>`

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

      :download:`Download zipped: plot_16_prem_travel_time.zip <plot_16_prem_travel_time.zip>`


.. only:: html

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

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