.. _sec-use-case-local:

Low-Magnitude Events
====================

While the MT packages generally ships with Green's functions supporting
observation of large (M>5) events inverting waveforms of lower-magnitude events
for moment tensors is supported as well by :ref:`scmtv` and :ref:`scautomt`.
Since inversion for moment tensors of such events is generally challenging a few
requirement must be met:

* High-quality, low-noise waveforms,
* :ref:`Green's functions <scautomt-gf>` for an appropriate Earth's model
  sampled at a rate high enough to represent the frequency content of the
  inverted waveforms.
* Appropriate travel-time tables for :cite:t:`LOCSAT` ideally corresponding to
  the Green's functions. Define the travel-time tables in the
  :ref:`description file of the Green's functions <data-files>`.
* Create of use an inversion profile specifically configured for smaller events.
  :ref:`scmtv` ships with two example profiles, *FWF3*, *M3* which are
  specifically designed for M<3 events. These profiles can be used for reference
  but eventually tailoring may be required.

  .. note::

     * In the list of recommended configuration parameters below, *full* stands
       for the wavetype and must be adjusted accordingly.
     * The parameters of the standard profile *FWF3* are used in the
       recommendations and the examples below and can be used as starting point
       and also applied to :ref:`scautomt`:

       .. code-block:: param

          automt.profiles.FWF3.name = "Full WF, <M3, GF >2 sps"
          automt.profiles.FWF3.magnitudes = -INF;3.0
          automt.profiles.FWF3.minItemFit = 60
          automt.profiles.FWF3.maxShift = 2
          automt.profiles.FWF3.shiftStep = 1
          automt.profiles.FWF3.minDist = 0
          automt.profiles.FWF3.minSNR.full = 3
          automt.profiles.FWF3.maxShift.full = 1
          automt.profiles.FWF3.wZ.full = 1
          automt.profiles.FWF3.wR.full = 1
          automt.profiles.FWF3.wT.full = 1
          automt.profiles.FWF3.wNormalize.full = true
          automt.profiles.FWF3.periods.full = 1-2
          automt.profiles.FWF3.signalBegin.full = P-1
          automt.profiles.FWF3.signalEnd.full = S+5

  **Recommendations for inversion profiles:**

  * Use full-waveform inversion for time windows covering P and S waves if S-P
    travel time are well represented by Green's functions. Otherwise create
    separate time windows. In order to consider P and S waves equally on 3
    components, you may consider P wave time windows in the configuration of
    full waveforms and S phases by configuring body waves with P and S but a
    time window only around S phases. The latter is reasonable since inversion
    of body waves P and S considers vertical and horizontal components
    separately.
  * Consider small periods (large frequencies) representing the signal's
    frequency content. The periods must be supported by the Green's functions.
    Configure similar: :confval:`automt.profiles.$name.periods.full` = 1-2.
  * Define precise time windows considering the period range for inversion.
    Larger periods require larger time windows. Configure similar:
    :confval:`automt.profiles.$name.signalBegin.full` = P-1 and
    :confval:`automt.profiles.$name.signalEnd.full` = S+5.
  * Allow only small time shifts of source time and for individual wave
    snippets. Configure :confval:`automt.profiles.$name.maxShift` and
    :confval:`automt.profiles.$name.maxShift.full`.
  * Require reasonable *Fit* of snippets (items). Configure:
    :confval:`automt.profiles.$name.minItemFit`.
  * Consider high-quality waveforms only. Configure:
    :confval:`automt.profiles.$name.minSNR.full`.


.. _sec-use-case-local-scmtv:

Interactive inversion
---------------------

The recommended steps to take for interactive inversion in :ref:`scmtv` are
demonstrated with a Mw=2.7 event, observations up to 1.6 degree epicentral
distance in central Germany and the inversion profile *FWF3*:

#. Load the waveforms of an event of interest
#. Unless automatically done, you should now load the set of custom Green's
   functions with high sample rates. The data is resampled to the sample rate of
   the Green's functions.

   .. figure:: media/local-initial.png
      :width: 12cm
      :align: center

      Initial solution for an ML=3.0 event, Green's functions for the IASP91
      Earth's model sampled at 16 Hz. Data processing is based on the standard
      M3-M4 inversion profile.

#. Choose an inversion profile and perform a single inversion. You should test
   and adjust the profile parameters and eventually store the profile parameters
   accordingly in the configuration of :ref:`scmtv`

   .. figure:: media/local-initial_fwf5.png
      :width: 12cm
      :align: center

      Initial solution of the same event after loading the standard FWF5
      inversion profile. The fit is still poor since waveforms must still be
      aligned with Green's functions and noisy data are to be removed.

#. Remove all wave snippets with low *Fit*, let's say <40% and trigger a single
   inversion. If the solution is well-posed, you may add more wave snippets with
   larger *Fit*, let's say >60% and invert again.

   .. figure:: media/local-fwf5-snippets.png
      :width: 12cm
      :align: center

      Solution after removing snippets with *Fit* <40% and inverting. The
      overall *Fit* has improved significantly but the trace alignment is still
      imperfect.

#. Manually shift the wave snippets to match the Green's functions and invert
   again. You may trim the data to discard noise. During shifting and trimming
   you may activate *Norm. Single* for a better view on the matched data.

   .. figure:: media/local-final.png
      :width: 12cm
      :align: center

      Final solution after shifting and trimming data. More snippets, previously
      with low *Fit* could be re-activated and matched contributing to a stable
      solution with high *Fit* and DC (double-couple) percentage. The final Mw
      is 2.7.

#. When sufficient wave snippets are matched and the solution is stable you may
   press *Apply all* and commit the solution.

   .. figure:: media/local-commit.png
      :width: 12cm
      :align: center

      After applying the solution you may press the *Commit* button to store
      the results or generate bulletins and reports.


.. _sec-use-case-local-scautomt:

Automatic inversion
-------------------

Once the inversion has been
:ref:`tested and verified interactively <sec-use-case-local-scmtv>` you may
copy the inversion profile parameters to the module configuration of
:ref:`scautomt` and run the module without interaction. Before, you may finally
test the module in a :ref:`playback <sec-scautomt-playbacks>`.