.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/geophysics/plot_04_bouguer_mountain_attraction.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_geophysics_plot_04_bouguer_mountain_attraction.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_geophysics_plot_04_bouguer_mountain_attraction.py:


Bouguer's mountain attraction (1749)
====================================

On the French expedition to Peru, Pierre Bouguer measured how far the
volcano Chimborazo pulled a plumb line aside, the first attempt to see a
mountain's gravity. He also measured gravity on the high plateau at Quito and
found it larger than the height alone predicted: the rock under the station
pulls too. Removing that slab of rock (the Bouguer correction) together with
the effect of height (the free-air correction) leaves the attraction of buried
masses, the Bouguer anomaly that gravity surveys still map.

.. GENERATED FROM PYTHON SOURCE LINES 13-46



.. image-sg:: /api/gallery/geophysics/images/sphx_glr_plot_04_bouguer_mountain_attraction_001.png
   :alt: A 3 km mountain pulls the plumb line, Reductions reveal a buried light body
   :srcset: /api/gallery/geophysics/images/sphx_glr_plot_04_bouguer_mountain_attraction_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import EARTH_RADIUS
    from earthsciencekit.geophysics import bouguer_anomaly, bouguer_correction, free_air_correction, normal_gravity, sphere_gravity
    from earthsciencekit.units import convert

    distance = np.linspace(4e3, 2e4, 100)
    pull = sphere_gravity(distance, 0, 3e3, 2670)[..., 0]
    deflection = convert(np.arctan(np.abs(pull) / 9.78), "rad", "degree") * 3600
    assert np.isclose(sphere_gravity(2 * distance[0], 0, 3e3, 2670)[0], pull[0] / 4)
    assert 1 < deflection[0] < 100

    x = np.linspace(-2e4, 2e4, 201)
    height = 1500 * np.exp(-(((x - 6e3) / 8e3) ** 2))
    normal = normal_gravity(np.radians(-1.5))
    buried = sphere_gravity(x, 4e3 + height, 1.5e3, -300)[..., 1]
    observed = normal - free_air_correction(height, normal, EARTH_RADIUS) + bouguer_correction(2670, height) + buried
    anomaly = bouguer_anomaly(observed, normal, height, 2670, EARTH_RADIUS)
    np.testing.assert_allclose(anomaly, buried, atol=1e-12)

    fig, (left, right) = plt.subplots(1, 2, figsize=(10, 4))
    left.plot(distance / 1e3, deflection)
    left.set(xlabel="distance from mountain centre [km]", ylabel="plumb-line deflection [arcsec]", title="A 3 km mountain pulls the plumb line")
    right.plot(x / 1e3, convert(observed - normal, "m/s^2", "mGal"), label="observed - normal")
    right.plot(x / 1e3, convert(anomaly, "m/s^2", "mGal"), label="Bouguer anomaly")
    right.plot(x / 1e3, height / 100, ":", label="topography / 100 [m]")
    right.set(xlabel="profile [km]", ylabel="mGal", title="Reductions reveal a buried light body")
    right.legend()
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.220 seconds)


.. _sphx_glr_download_api_gallery_geophysics_plot_04_bouguer_mountain_attraction.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/geophysics/plot_04_bouguer_mountain_attraction.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_04_bouguer_mountain_attraction.ipynb <plot_04_bouguer_mountain_attraction.ipynb>`

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

      :download:`Download Python source code: plot_04_bouguer_mountain_attraction.py <plot_04_bouguer_mountain_attraction.py>`

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

      :download:`Download zipped: plot_04_bouguer_mountain_attraction.zip <plot_04_bouguer_mountain_attraction.zip>`


.. only:: html

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

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