.. _sphx_glr_gallery_gravmag_euler_moving_window.py:


.. _gallery_euler_mw:

Euler deconvolution with a moving window
----------------------------------------

Euler deconvolution attempts to estimate the coordinates of simple (idealized)
sources from the input potential field data. There is a strong assumption that
the sources have simple geometries, like spheres, vertical pipes, vertical
planes, etc. So it wouldn't be much of a surprise if the solutions aren't great
when sources are complex.

Let's test the Euler deconvolution using a moving window scheme, a very common
approach used in all industry software. This is implemented in
:class:`fatiando.gravmag.euler.EulerDeconvMW`.






.. image:: /gallery/gravmag/images/sphx_glr_euler_moving_window_001.png
    :align: center


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

 Out::

    Centers of the model spheres:
    [-1000 -1000  1500]
    [1000 1500 1000]
    Kept Euler solutions after the moving window scheme:
    [[ 1005.02117863  1555.11042642   998.68593456]
     [ 1042.92870628  1479.25104857   982.8034785 ]
     [ -903.03736426  -826.2551998   1580.03357152]
     [ -996.30379977  -940.33986512  1459.01039032]
     [ 1159.1957134   1006.77185575  1199.42292819]
     [ 1465.17965473   408.39773001  1920.31472105]
     [  991.40325194  1468.18742261  1020.67590594]
     [ -966.01139554  -775.38064946  1465.22351287]
     [-1041.3450269   -971.09938734  1500.22185195]
     [ -284.04967711  -382.06786678  2243.58685856]
     [  -35.58602726  -108.90046998  1540.68712849]
     [ 1058.8441761   1516.37801553   994.86866767]
     [  999.08320679  1580.06304764  1051.97367365]
     [ -933.90137199  -995.14775353  1406.97615438]
     [  381.76290333  1131.68128707   992.51158521]
     [  914.43334205  1475.15646829   978.0510579 ]
     [ 1277.82392557  1876.41150747   931.05131937]
     [-1017.82794862 -1140.04437429  1560.46288409]
     [ -991.58404782 -1012.73293178  1556.74635058]
     [ -349.91796733   355.56106336  1792.13495774]]




|


.. code-block:: python

    from __future__ import print_function
    from fatiando.gravmag import sphere, transform, euler
    from fatiando import gridder, utils, mesher
    import matplotlib.pyplot as plt

    # Make some synthetic magnetic data to test our Euler deconvolution.
    # The regional field
    inc, dec = -45, 0
    # Make a model of two spheres magnetized by induction only
    model = [
        mesher.Sphere(x=-1000, y=-1000, z=1500, radius=1000,
                      props={'magnetization': utils.ang2vec(2, inc, dec)}),
        mesher.Sphere(x=1000, y=1500, z=1000, radius=1000,
                      props={'magnetization': utils.ang2vec(1, inc, dec)})]

    print("Centers of the model spheres:")
    print(model[0].center)
    print(model[1].center)

    # Generate some magnetic data from the model
    shape = (100, 100)
    area = [-5000, 5000, -5000, 5000]
    x, y, z = gridder.regular(area, shape, z=-150)
    data = sphere.tf(x, y, z, model, inc, dec)

    # We also need the derivatives of our data
    xderiv = transform.derivx(x, y, data, shape)
    yderiv = transform.derivy(x, y, data, shape)
    zderiv = transform.derivz(x, y, data, shape)

    # Now we can run our Euler deconv solver on a moving window over the data.
    # Each window will produce an estimated point for the source.
    # We use a structural index of 3 to indicate that we think the sources are
    # spheres.

    # Run the Euler deconvolution on moving windows to produce a set of solutions
    # by running the solver on 10 x 10 windows of size 1000 x 1000 m
    solver = euler.EulerDeconvMW(x, y, z, data, xderiv, yderiv, zderiv,
                                 structural_index=3, windows=(10, 10),
                                 size=(1000, 1000))
    # Use the fit() method to obtain the estimates
    solver.fit()

    # The estimated positions are stored as a list of [x, y, z] coordinates
    # (actually a 2D numpy array)
    print('Kept Euler solutions after the moving window scheme:')
    print(solver.estimate_)

    # Plot the solutions on top of the magnetic data. Remember that the true depths
    # of the center of these sources is 1500 m and 1000 m.

    plt.figure(figsize=(6, 5))
    plt.title('Euler deconvolution with a moving window')
    plt.contourf(y.reshape(shape), x.reshape(shape), data.reshape(shape), 30,
                 cmap="RdBu_r")
    plt.scatter(solver.estimate_[:, 1], solver.estimate_[:, 0],
                s=50, c=solver.estimate_[:, 2], cmap='cubehelix')
    plt.colorbar(pad=0).set_label('Depth (m)')
    plt.xlim(area[2:])
    plt.ylim(area[:2])
    plt.tight_layout()
    plt.show()

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



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



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