.. _global_ml:

##
ML
##

Standard local (Richter) magnitude

Description
===========

ML is the standard local (Richter) magnitude originally designed for
Southern California by :cite:t:`richter-1935`.

Amplitude
---------

The ML amplitude calculation is similar to the original ML. Waveforms from both
horizontal components are time-windowed and restituted to the Wood-Anderson seismograph.
Within the time window the amplitudes are measured on both horizontal components
and combined. The methods for measuring and combining amplitudes are configurable
in the global bindings.


Station Magnitude
-----------------

The individual station ML is calculated using the following formula:

.. math::

   ML = \log10(A) - \log10(A0)

A is the measured ML Wood-Anderson amplitude in millimeters. The second term
is the empirical calibration function, which in turn is a function
of the epicentral distance (:cite:t:`richter-1935`). This calibration
function and distance range can be configured globally or per station using global
bindings or the global module configuration variable
module.trunk.global.magnitudes.ML.logA0 in :file:`global.cfg`, e.g. ::

   module.trunk.global.magnitudes.ML.logA0 = "0 -1.3;60 -2.8;100 -3.0;400 -4.5;1000 -5.85"
   module.trunk.global.magnitudes.ML.maxDistanceKm = "-1"

The *logA0* configuration string consists of an arbitrary number of
distance-value pairs separated by semicolons. The distance is in km
and the second value corresponds to the *log10(A0)* term above.

Within each interval the values are computed by linear
interpolation. E.g. for the above default specification, at a
distance of 80 km the *log10(A0)* value would be

.. math::

   \log10(A0) &= ((-3.0)-(-2.8))*(80-60)/(100-60)-2.8 \\
              &= -2.9

In other words, at 80 km distance the magnitude would be

.. math::

   ML &= \log10(A) - (-2.9) \\
      &= \log10(A) + 2.9

which is according to the original Richter (1935) formula if the
amplitude is measured in millimeters.

Several distance-value pairs can be configured for different ranges of
epicenter distance.


* Amplitude unit in SeisComP: **millimeter** (mm)
* Time window: 150 s by :ref:`scautopick` or distance dependent, configurable
* Default distance range: 0 - 8 deg,  maximum is configurable: :confval:`magnitudes.ML.maxDistanceKm`,
  measurements beyond 8 deg will be strictly ignored.
* Depth range: 0 - 80 km, configurable for amplitude measurements


Network magnitude
-----------------

By default, the mean is calculated from the station magnitudes to form the network
magnitude.


Configuration
-------------

Set the configuration and calibration parameters in the global bindings similar to :ref:`global_mlv`.
Instead configuring lots of global bindings profiles or station bindings one
line per parameter can be added to the global module configuration (:file:`global.cfg`).

Add ML to the list of computed amplitudes and magnitudes in the configuration of
:ref:`scamp` and :ref:`scmag` and in :ref:`scesv` or :ref:`scolv` for visibility.