.. _global_ml:

##
ML
##

ML is the Richter (1935) magnitude.

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

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::

   mag = \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 (see Richter, 1935). This calibration
function can be configured globally or per station using the config
variable module.trunk.global.ML.logA0, e.g.

module.trunk.global.ML.logA0 = "0 -1.3;60 -2.8;400 -4.5;1000 -5.85"

The logA0 configuration string consists of an arbitrary number of
distance-value pairs separated by semicolons. The distance is in km
and the 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 100 km the logA0 value would be
((-4.5)-(-2.8))*(100-60)/(400-60)-2.8 = -3.0 -- in other words, at 100 km
distance the magnitude would be

.. math::

   mag = \log10(A) - (-3) = \log10(A) + 3

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 SeisComP3: **millimeter** (mm)
* Time window: 150 s by :ref:`scautopick` or distance dependent
* Default distance range: 0 - 8 deg
* Depth range: 0 - 80 km

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

Set the configuration and calibration parameters in the global bindings. Add ML to the list of
computed amplitudes and magnitudes in the configuration of :ref:`scamp` and :ref:`scmag`
and in :ref:`scesv` for visibility.