103 lines
3.2 KiB
ReStructuredText
103 lines
3.2 KiB
ReStructuredText
.. _global_ml:
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##
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ML
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##
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Standard local (Richter) magnitude
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Description
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===========
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ML is the standard local (Richter) magnitude originally designed for
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Southern California by :cite:t:`richter-1935`.
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General (default) conditions apply:
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* Amplitude unit in SeisComP: **millimeter** (mm) by simulation of a :term:`Wood-Anderson seismometer`.
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* Time window, configurable: 150 s by :ref:`scautopick` or distance dependent, configurable.
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* Distance type: epicentral distance.
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* Distance range: 0 - 8 deg, maximum is configurable:
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:confval:`magnitudes.ML.maxDistanceKm`,
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measurements beyond 8 deg will be strictly ignored.
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* Depth range: 0 - 80 km, configurable for amplitude measurements.
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Amplitudes
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----------
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The ML amplitude calculation is similar to the original ML. Waveforms from both
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horizontal components are time-windowed and restituted to the Wood-Anderson
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seismograph. Within the time window the amplitudes are measured on both
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horizontal components and combined. The methods for measuring and combining
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amplitudes are configurable in the global bindings.
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Station Magnitudes
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------------------
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The individual station ML is calculated using the following formula:
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.. math::
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ML = \log10(A) - \log10(A0)
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*A* is the measured ML Wood-Anderson amplitude in millimeters. The second term
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is the empirical calibration function, which in turn is a function
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of the epicentral distance (:cite:t:`richter-1935`). This calibration
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function and distance range can be configured globally or per station using
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global bindings or the global module configuration variable
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module.trunk.global.magnitudes.ML.logA0 in :file:`global.cfg`, e.g.
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.. code-block:: params
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module.trunk.global.magnitudes.ML.logA0 = "0:-1.3,60:-2.8,100:-3.0,400:-4.5,1000:-5.85"
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module.trunk.global.magnitudes.ML.maxDistanceKm = "-1"
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The *logA0* configuration string consists of an arbitrary number of
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distance-value pairs separated by comma. Within the pairs, the values are
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separated by colon. The distance is epicentral distance in km
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and the second value corresponds to the *log10(A0)* term above.
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Within each interval the values are computed by linear
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interpolation. E.g. for the above default specification, at a
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distance of 80 km the *log10(A0)* value would be
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.. math::
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\log10(A0) &= ((-3.0)-(-2.8))*(80-60)/(100-60)-2.8 \\
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&= -2.9
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In other words, at 80 km distance the magnitude would be
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.. math::
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ML &= \log10(A) - (-2.9) \\
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&= \log10(A) + 2.9
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which is according to the original Richter formula :cite:p:`richter-1935` if the
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amplitude is measured in millimeters.
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Several distance-value pairs can be configured for different ranges of
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epicenter distance.
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Network magnitude
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-----------------
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By default, the mean is calculated from the station magnitudes to form the
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network magnitude.
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Configuration
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-------------
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Set the configuration and calibration parameters in the global bindings similar
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to :ref:`global_mlv`.
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Instead configuring lots of global bindings profiles or station bindings one
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line per parameter can be added to the global module configuration
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(:file:`global.cfg`).
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Add ML to the list of computed amplitudes and magnitudes in the configuration of
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:ref:`scamp` and :ref:`scmag` and in :ref:`scesv` or :ref:`scolv` for visibility.
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