.. _sphx_glr__examples_02_simple_inversion:

Examples: Single-frequency inversion
------------------------------------




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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="This example discusses details of settings various settings for modeling or inversion using the single-frequency tdManager">

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  .. image:: /_examples/02_simple_inversion/images/thumb/sphx_glr_plot_01_inversion_settings_thumb.png
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  :ref:`sphx_glr__examples_02_simple_inversion_plot_01_inversion_settings.py`

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      <div class="sphx-glr-thumbnail-title">Setting modeling and inversion settings</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="CRTomo implements a last-square inversion with regularization based on the Thikonov appraoch. Herey a cost function is minimized, consisting of a data misfit \Psi_d and a model misfit \Psi_m. Both terms are weighted against each other using a regularization parameter $\lambda$.">

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  .. image:: /_examples/02_simple_inversion/images/thumb/sphx_glr_plot_02_data_errors_thumb.png
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  :ref:`sphx_glr__examples_02_simple_inversion_plot_02_data_errors.py`

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      <div class="sphx-glr-thumbnail-title">Data error handling in CRTomo</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Especially for synthetic modeling/inversion studies it is important to add data noise to the data.">

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  .. image:: /_examples/02_simple_inversion/images/thumb/sphx_glr_plot_03_adding_data_noise_thumb.png
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  :ref:`sphx_glr__examples_02_simple_inversion_plot_03_adding_data_noise.py`

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      <div class="sphx-glr-thumbnail-title">Adding data noise to measurements</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Full processing of one frequency of one timestep of the data from Weigand and Kemna 2017 (Biogeosciences).">

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  .. image:: /_examples/02_simple_inversion/images/thumb/sphx_glr_plot_05_single_freq_inversion_CR_thumb.png
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  :ref:`sphx_glr__examples_02_simple_inversion_plot_05_single_freq_inversion_CR.py`

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      <div class="sphx-glr-thumbnail-title">A single-frequency inversion (CR container)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Full processing of one frequency of one timestep of the data from Weigand and Kemna 2017 (Biogeosciences).">

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  .. image:: /_examples/02_simple_inversion/images/thumb/sphx_glr_plot_06_single_freq_inversion_sEIT_thumb.png
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  :ref:`sphx_glr__examples_02_simple_inversion_plot_06_single_freq_inversion_sEIT.py`

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      <div class="sphx-glr-thumbnail-title">A single-frequency inversion (sEIT container)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example aims to provide a full discussion of a single-frequency complex resistivity simulation study. A simulation study usually consists of the following steps:">

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  .. image:: /_examples/02_simple_inversion/images/thumb/sphx_glr_plot_07_synthetic_modinv_study_thumb.png
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  :ref:`sphx_glr__examples_02_simple_inversion_plot_07_synthetic_modinv_study.py`

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      <div class="sphx-glr-thumbnail-title">Single frequency synthetic study</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In principle an individual data error can be assigned to each data point. However, since data errors are not easily determined in geoelectrical applications, it is common to employ various data error models that exploit empirically observed relationships between the data errors and the measurements themselves.">

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  .. image:: /_examples/02_simple_inversion/images/thumb/sphx_glr_plot_09_individual_errors_thumb.png
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  :ref:`sphx_glr__examples_02_simple_inversion_plot_09_individual_errors.py`

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      <div class="sphx-glr-thumbnail-title">Using individual data errors in CRTomo</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Generating regularization decouplins">

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  .. image:: /_examples/02_simple_inversion/images/thumb/sphx_glr_plot_10_generating_decouplings_thumb.png
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  :ref:`sphx_glr__examples_02_simple_inversion_plot_10_generating_decouplings.py`

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      <div class="sphx-glr-thumbnail-title">Generating regularization decouplins</div>
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    </div>


.. toctree::
   :hidden:

   /_examples/02_simple_inversion/plot_01_inversion_settings
   /_examples/02_simple_inversion/plot_02_data_errors
   /_examples/02_simple_inversion/plot_03_adding_data_noise
   /_examples/02_simple_inversion/plot_05_single_freq_inversion_CR
   /_examples/02_simple_inversion/plot_06_single_freq_inversion_sEIT
   /_examples/02_simple_inversion/plot_07_synthetic_modinv_study
   /_examples/02_simple_inversion/plot_09_individual_errors
   /_examples/02_simple_inversion/plot_10_generating_decouplings