.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/upward_derivative.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_gallery_upward_derivative.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_gallery_upward_derivative.py:


Upward derivative of a regular grid
===================================

.. GENERATED FROM PYTHON SOURCE LINES 11-96



.. image-sg:: /gallery/images/sphx_glr_upward_derivative_001.png
   :alt: Magnetic anomaly, Upward derivative
   :srcset: /gallery/images/sphx_glr_upward_derivative_001.png
   :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none


    Upward derivative:
     <xarray.DataArray (northing: 157, easting: 95)>
    array([[ 0.08118127,  0.04840311,  0.04986904, ..., -0.04998174,
            -0.04946451, -0.08324109],
           [ 0.04715736,  0.00822274,  0.00748728, ..., -0.02351687,
            -0.02195097, -0.06526992],
           [ 0.04793475,  0.00739243,  0.00510616, ..., -0.03223078,
            -0.03044794, -0.07926779],
           ...,
           [-0.15958524, -0.04712847, -0.05012313, ...,  0.09228404,
             0.08211778,  0.26426587],
           [-0.14767232, -0.04100584, -0.04493305, ...,  0.08538301,
             0.07280294,  0.24507784],
           [-0.22975479, -0.14307243, -0.15089174, ...,  0.28623612,
             0.25756289,  0.38850882]])
    Coordinates:
      * northing  (northing) float64 4.175e+06 4.176e+06 ... 4.253e+06 4.253e+06
      * easting   (easting) float64 -3.24e+05 -3.235e+05 ... -2.774e+05 -2.769e+05






|

.. code-block:: default

    import matplotlib.pyplot as plt
    import numpy as np
    import pyproj
    import verde as vd
    import xrft

    import harmonica as hm

    # Fetch the sample total-field magnetic anomaly data from Great Britain
    data = hm.datasets.fetch_britain_magnetic()

    # Slice a smaller portion of the survey data to speed-up calculations for this
    # example
    region = [-5.5, -4.7, 57.8, 58.5]
    inside = vd.inside((data.longitude, data.latitude), region)
    data = data[inside]

    # Since this is a small area, we'll project our data and use Cartesian
    # coordinates
    projection = pyproj.Proj(proj="merc", lat_ts=data.latitude.mean())
    easting, northing = projection(data.longitude.values, data.latitude.values)
    coordinates = (easting, northing, data.altitude_m)

    # Grid the scatter data using an equivalent layer
    eql = hm.EquivalentSources(depth=1000, damping=1).fit(
        coordinates, data.total_field_anomaly_nt
    )

    grid_coords = vd.grid_coordinates(
        region=vd.get_region(coordinates), spacing=500, extra_coords=1500
    )
    grid = eql.grid(grid_coords, data_names=["magnetic_anomaly"])
    grid = grid.magnetic_anomaly

    # Pad the grid to increase accuracy of the FFT filter
    pad_width = {
        "easting": grid.easting.size // 3,
        "northing": grid.northing.size // 3,
    }
    grid = grid.drop_vars("upward")  # drop extra coordinates due to bug in xrft.pad
    grid_padded = xrft.pad(grid, pad_width)

    # Compute the upward derivative of the grid
    deriv_upward = hm.derivative_upward(grid_padded)

    # Unpad the derivative grid
    deriv_upward = xrft.unpad(deriv_upward, pad_width)

    # Show the upward derivative
    print("\nUpward derivative:\n", deriv_upward)

    # Plot original magnetic anomaly and the upward derivative
    fig, (ax1, ax2) = plt.subplots(
        nrows=1, ncols=2, figsize=(9, 8), sharex=True, sharey=True
    )

    # Plot the magnetic anomaly grid
    grid.plot(
        ax=ax1,
        cmap="seismic",
        cbar_kwargs={"label": "nT", "location": "bottom", "shrink": 0.8, "pad": 0.08},
    )
    ax1.set_title("Magnetic anomaly")

    # Plot the upward derivative
    scale = np.quantile(np.abs(deriv_upward), q=0.98)  # scale the colorbar
    deriv_upward.plot(
        ax=ax2,
        vmin=-scale,
        vmax=scale,
        cmap="seismic",
        cbar_kwargs={"label": "nT/m", "location": "bottom", "shrink": 0.8, "pad": 0.08},
    )
    ax2.set_title("Upward derivative")

    # Scale the axes
    for ax in (ax1, ax2):
        ax.set_aspect("equal")

    # Set ticklabels with scientific notation
    ax1.ticklabel_format(axis="x", style="sci", scilimits=(-2, 2))
    ax1.ticklabel_format(axis="y", style="sci", scilimits=(-2, 2))

    plt.tight_layout()
    plt.show()


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

   **Total running time of the script:** ( 0 minutes  10.893 seconds)


.. _sphx_glr_download_gallery_upward_derivative.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



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

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



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

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


.. only:: html

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

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