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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_gallery_educational_dlf_design.py>`
        to download the full example code

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

.. _sphx_glr_gallery_educational_dlf_design.py:


Calculating a Digital Linear Filter
===================================

This is an example for the add-on ``fdesign``. The example is taken from the
article Werthmüller et al., 2019. Have a look at the article repository on
`empymod/article-fdesign <https://github.com/emsig/article-fdesign>`_ for
many more examples.

**Reference**

- Werthmüller, D., K. Key, and E. Slob, 2019, **A tool for designing digital
  filters for the Hankel and Fourier transforms in potential, diffusive, and
  wavefield modeling**:  Geophysics, 84(2), F47-F56; DOI:
  `10.1190/geo2018-0069.1 <https://doi.org/10.1190/geo2018-0069.1>`_.

.. GENERATED FROM PYTHON SOURCE LINES 18-23

.. code-block:: Python

    import empymod
    import numpy as np
    import matplotlib.pyplot as plt
    plt.style.use('ggplot')








.. GENERATED FROM PYTHON SOURCE LINES 24-33

.. code-block:: Python


    inp = {'r': np.logspace(0, 10, 1000),
           'r_def': (1, 1, 2),
           'n': 201,
           'name': 'test',
           'full_output': True,
           'fI': (empymod.fdesign.j0_1(5), empymod.fdesign.j1_1(5))}









.. GENERATED FROM PYTHON SOURCE LINES 34-36

1. Rough overview over a wide range
-----------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 36-40

.. code-block:: Python


    filt1, out1 = empymod.fdesign.design(
            spacing=(0.01, 0.2, 10), shift=(-4, 0, 10), save=False, **inp)




.. image-sg:: /gallery/educational/images/sphx_glr_dlf_design_001.png
   :alt: Minimal recovered fields, Filter values of best filter
   :srcset: /gallery/educational/images/sphx_glr_dlf_design_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

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       Filter length   : 201
       Best filter
       > Min field     : 1.67411e-14
       > Spacing       : 0.07333333333
       > Shift         : -2.222222222
       > Base min/max  : 7.080680e-05 / 1.658545e+02

    :: empymod END; runtime = 0:00:01.990649 :: 

    * QC: Overview of brute-force inversion:




.. GENERATED FROM PYTHON SOURCE LINES 41-43

2. First focus
--------------

.. GENERATED FROM PYTHON SOURCE LINES 43-47

.. code-block:: Python


    filt2, out2 = empymod.fdesign.design(
            spacing=(0.04, 0.1, 10), shift=(-3, -0.5, 10), save=False, **inp)




.. image-sg:: /gallery/educational/images/sphx_glr_dlf_design_002.png
   :alt: Minimal recovered fields, Filter values of best filter
   :srcset: /gallery/educational/images/sphx_glr_dlf_design_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

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       Filter length   : 201
       Best filter
       > Min field     : 7.49729e-17
       > Spacing       : 0.06
       > Shift         : -1.333333333
       > Base min/max  : 6.533920e-04 / 1.063427e+02

    :: empymod END; runtime = 0:00:01.972399 :: 

    * QC: Overview of brute-force inversion:




.. GENERATED FROM PYTHON SOURCE LINES 48-50

3. Final focus
--------------

.. GENERATED FROM PYTHON SOURCE LINES 50-55

.. code-block:: Python


    filt, out = empymod.fdesign.design(
            spacing=(0.047, 0.08, 10), shift=(-2.4, -0.75, 10), finish=False,
            save=False, **inp)




.. image-sg:: /gallery/educational/images/sphx_glr_dlf_design_003.png
   :alt: Minimal recovered fields, Filter values of best filter
   :srcset: /gallery/educational/images/sphx_glr_dlf_design_003.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

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       Filter length   : 201
       Best filter
       > Min field     : 1.9984e-16
       > Spacing       : 0.058
       > Shift         : -1.3
       > Base min/max  : 8.251049e-04 / 9.001713e+01

    :: empymod END; runtime = 0:00:01.960396 :: 

    * QC: Overview of brute-force inversion:




.. GENERATED FROM PYTHON SOURCE LINES 56-66

To reproduce exactly the same filter as wer_201_2018:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

::

    filt_orig, out_orig = fdesign.load_filter('wer201', True)
    fdesign.plot_result(filt_orig, out_orig)
    filt_orig, out_orig = fdesign.design(
            spacing=out_orig[0][0], shift=out_orig[0][1], **inp)


.. GENERATED FROM PYTHON SOURCE LINES 69-74

Plot the result
---------------

Plot function
~~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 74-120

.. code-block:: Python


    def plotresult(depth, res, zsrc, zrec):
        x = np.arange(1, 101)*200
        inp = {
            'src': [0, 0, depth[1]-zsrc],
            'rec': [x, x*0, depth[1]-zrec],
            'depth': depth,
            'res': res,
            'ab': 11,
            'freqtime': 1,
            'verb': 1,
        }

        kong241 = empymod.dipole(htarg={'dlf': 'kong_241_2007'}, **inp)
        key201 = empymod.dipole(htarg={'dlf': 'key_201_2012'}, **inp)
        and801 = empymod.dipole(htarg={'dlf': 'anderson_801_1982'}, **inp)
        test = empymod.dipole(htarg={'dlf': filt}, **inp)
        wer201 = empymod.dipole(htarg={'dlf': 'wer_201_2018'}, **inp)
        qwe = empymod.dipole(ht='qwe', **inp)

        plt.figure(figsize=(8, 3.5))
        plt.subplot(121)
        plt.semilogy(x, qwe.amp(), c='0.5', label='QWE')
        plt.semilogy(x, kong241.amp(), 'k--', label='Kong241')
        plt.semilogy(x, key201.amp(), 'k:', label='Key201')
        plt.semilogy(x, and801.amp(), 'k-.', label='And801')
        plt.semilogy(x, test.amp(), 'r', label='This filter')
        plt.semilogy(x, wer201.amp(), 'b', label='Wer201')
        plt.legend()
        plt.xticks([0, 5e3, 10e3, 15e3, 20e3])
        plt.xlim([0, 20e3])

        plt.subplot(122)
        plt.semilogy(x, np.abs((kong241-qwe)/qwe), 'k--', label='Kong241')
        plt.semilogy(x, np.abs((key201-qwe)/qwe), 'k:', label='Key201')
        plt.semilogy(x, np.abs((and801-qwe)/qwe), 'k-.', label='And801')
        plt.semilogy(x, np.abs((test-qwe)/qwe), 'r', label='This filter')
        plt.semilogy(x, np.abs((wer201-qwe)/qwe), 'b', label='Wer201')
        plt.legend()
        plt.xticks([0, 5e3, 10e3, 15e3, 20e3])
        plt.xlim([0, 20e3])
        plt.ylim([1e-14, 1])

        plt.show()









.. GENERATED FROM PYTHON SOURCE LINES 121-123

Plot the individual models
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 123-128

.. code-block:: Python


    plotresult([-1e50, 2000], [2e14, 1/3.2, 1], 50, 0)  # KONG model
    plotresult([0, 1000, 2000, 2100], [1/1e-12, 1/3.3, 1, 100, 1], 10, 0)  # KEY m.
    plotresult([0, 1, 1000, 1100], [2e14, 10, 10, 500, 10], 0.5, 0.2)  # LAND model




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /gallery/educational/images/sphx_glr_dlf_design_004.png
         :alt: dlf design
         :srcset: /gallery/educational/images/sphx_glr_dlf_design_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /gallery/educational/images/sphx_glr_dlf_design_005.png
         :alt: dlf design
         :srcset: /gallery/educational/images/sphx_glr_dlf_design_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /gallery/educational/images/sphx_glr_dlf_design_006.png
         :alt: dlf design
         :srcset: /gallery/educational/images/sphx_glr_dlf_design_006.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none

    * WARNING :: Hankel-quadrature did not converge at least once;
                 => desired `atol` and `rtol` might not be achieved.
    * WARNING :: Hankel-quadrature did not converge at least once;
                 => desired `atol` and `rtol` might not be achieved.




.. GENERATED FROM PYTHON SOURCE LINES 129-131

.. code-block:: Python


    empymod.Report()





.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table style='border: 1.5px solid;'>
      <tr>
         <td style='text-align: center; font-weight: bold; font-size: 1.2em; border: 1px solid;' colspan='6'>Fri Mar 01 20:17:30 2024 UTC</td>
      </tr>
      <tr>
        <td style='text-align: right; border: 1px solid;'>OS</td>
        <td style='text-align: left; border: 1px solid;'>Linux</td>
        <td style='text-align: right; border: 1px solid;'>CPU(s)</td>
        <td style='text-align: left; border: 1px solid;'>2</td>
        <td style='text-align: right; border: 1px solid;'>Machine</td>
        <td style='text-align: left; border: 1px solid;'>x86_64</td>
      </tr>
      <tr>
        <td style='text-align: right; border: 1px solid;'>Architecture</td>
        <td style='text-align: left; border: 1px solid;'>64bit</td>
        <td style='text-align: right; border: 1px solid;'>RAM</td>
        <td style='text-align: left; border: 1px solid;'>7.5 GiB</td>
        <td style='text-align: right; border: 1px solid;'>Environment</td>
        <td style='text-align: left; border: 1px solid;'>Python</td>
      </tr>
      <tr>
        <td style='text-align: right; border: 1px solid;'>File system</td>
        <td style='text-align: left; border: 1px solid;'>ext4</td>
      </tr>
      <tr>
         <td style='text-align: center; border: 1px solid;' colspan='6'>Python 3.11.6 (main, Feb  1 2024, 16:47:41) [GCC 11.4.0]</td>
      </tr>
      <tr>
        <td style='text-align: right; border: 1px solid;'>numpy</td>
        <td style='text-align: left; border: 1px solid;'>1.26.4</td>
        <td style='text-align: right; border: 1px solid;'>scipy</td>
        <td style='text-align: left; border: 1px solid;'>1.12.0</td>
        <td style='text-align: right; border: 1px solid;'>numba</td>
        <td style='text-align: left; border: 1px solid;'>0.59.0</td>
      </tr>
      <tr>
        <td style='text-align: right; border: 1px solid;'>empymod</td>
        <td style='text-align: left; border: 1px solid;'>2.3.0</td>
        <td style='text-align: right; border: 1px solid;'>IPython</td>
        <td style='text-align: left; border: 1px solid;'>8.22.1</td>
        <td style='text-align: right; border: 1px solid;'>matplotlib</td>
        <td style='text-align: left; border: 1px solid;'>3.8.3</td>
      </tr>
    </table>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 21.561 seconds)

**Estimated memory usage:**  12 MB


.. _sphx_glr_download_gallery_educational_dlf_design.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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