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<section id="ml">
<span id="global-ml"></span><h1>ML<a class="headerlink" href="#ml" title="Permalink to this heading"></a></h1>
<p>Standard local (Richter) magnitude</p>
<section id="description">
<h2>Description<a class="headerlink" href="#description" title="Permalink to this heading"></a></h2>
<p>ML is the standard local (Richter) magnitude originally designed for
Southern California by <span id="id1">Richter [<a class="reference internal" href="../base/references.html#id62" title="C.F. Richter. An instrumental earthquake magnitude scale. Bull. Seismol. Soc. Am., 1:1 - 32, 1935. URL: https://resolver.caltech.edu/CaltechAUTHORS:20140804-143558638, doi:10.1785/BSSA0250010001.">57</a>]</span>.</p>
<p>General (default) conditions apply:</p>
<ul class="simple">
<li><p>Amplitude unit in SeisComP: <strong>millimeter</strong> (mm) by simulation of a <a class="reference internal" href="../base/glossary.html#term-Wood-Anderson-seismometer"><span class="xref std std-term">Wood-Anderson seismometer</span></a>.</p></li>
<li><p>Time window, configurable: 150 s by <a class="reference internal" href="scautopick.html#scautopick"><span class="std std-ref">scautopick</span></a> or distance dependent, configurable.</p></li>
<li><p>Distance type: epicentral distance.</p></li>
<li><p>Distance range: 0 - 8 deg, maximum is configurable:
<a class="reference internal" href="global.html#confval-magnitudes.ML.maxDistanceKm"><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.ML.maxDistanceKm</span></code></a>,
measurements beyond 8 deg will be strictly ignored.</p></li>
<li><p>Depth range: 0 - 80 km, configurable for amplitude measurements.</p></li>
</ul>
<section id="amplitudes">
<h3>Amplitudes<a class="headerlink" href="#amplitudes" title="Permalink to this heading"></a></h3>
<p>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.</p>
</section>
<section id="station-magnitudes">
<h3>Station Magnitudes<a class="headerlink" href="#station-magnitudes" title="Permalink to this heading"></a></h3>
<p>The individual station ML is calculated using the following formula:</p>
<div class="math">
<p><img src="../_images/math/2ac00af8e0cff8bc51992386e723083d633de181.png" alt="ML = \log10(A) - \log10(A0)"/></p>
</div><p><em>A</em> 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 (<span id="id2">Richter [<a class="reference internal" href="../base/references.html#id62" title="C.F. Richter. An instrumental earthquake magnitude scale. Bull. Seismol. Soc. Am., 1:1 - 32, 1935. URL: https://resolver.caltech.edu/CaltechAUTHORS:20140804-143558638, doi:10.1785/BSSA0250010001.">57</a>]</span>). 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 <code class="file docutils literal notranslate"><span class="pre">global.cfg</span></code>, e.g.</p>
<div class="highlight-params notranslate"><div class="highlight"><pre><span></span>module.trunk.global.magnitudes.ML.logA0 = &quot;0:-1.3,60:-2.8,100:-3.0,400:-4.5,1000:-5.85&quot;
module.trunk.global.magnitudes.ML.maxDistanceKm = &quot;-1&quot;
</pre></div>
</div>
<p>The <em>logA0</em> configuration string consists of an arbitrary number of
distance-value pairs separated by comma. Within the pairs, the values are
separated by colon. The distance is epicentral distance in km
and the second value corresponds to the <em>log10(A0)</em> term above.</p>
<p>Within each interval the values are computed by linear
interpolation. E.g. for the above default specification, at a
distance of 80 km the <em>log10(A0)</em> value would be</p>
<div class="math">
<p><img src="../_images/math/6e45a883605015d556a6b6fe63821c64d8263242.png" alt="\log10(A0) &amp;= ((-3.0)-(-2.8))*(80-60)/(100-60)-2.8 \\
&amp;= -2.9"/></p>
</div><p>In other words, at 80 km distance the magnitude would be</p>
<div class="math">
<p><img src="../_images/math/d201277e64aa494949afae6e3509d37320084dc7.png" alt="ML &amp;= \log10(A) - (-2.9) \\
&amp;= \log10(A) + 2.9"/></p>
</div><p>which is according to the original Richter formula <span id="id3">[<a class="reference internal" href="../base/references.html#id62" title="C.F. Richter. An instrumental earthquake magnitude scale. Bull. Seismol. Soc. Am., 1:1 - 32, 1935. URL: https://resolver.caltech.edu/CaltechAUTHORS:20140804-143558638, doi:10.1785/BSSA0250010001.">57</a>]</span> if the
amplitude is measured in millimeters.</p>
<p>Several distance-value pairs can be configured for different ranges of
epicenter distance.</p>
</section>
<section id="network-magnitude">
<h3>Network magnitude<a class="headerlink" href="#network-magnitude" title="Permalink to this heading"></a></h3>
<p>By default, the mean is calculated from the station magnitudes to form the
network magnitude.</p>
</section>
<section id="configuration">
<h3>Configuration<a class="headerlink" href="#configuration" title="Permalink to this heading"></a></h3>
<p>Set the configuration and calibration parameters in the global bindings similar
to <a class="reference internal" href="global_mlv.html#global-mlv"><span class="std std-ref">MLv</span></a>.
Instead configuring lots of global bindings profiles or station bindings one
line per parameter can be added to the global module configuration
(<code class="file docutils literal notranslate"><span class="pre">global.cfg</span></code>).</p>
<p>Add ML to the list of computed amplitudes and magnitudes in the configuration of
<a class="reference internal" href="scamp.html#scamp"><span class="std std-ref">scamp</span></a> and <a class="reference internal" href="scmag.html#scmag"><span class="std std-ref">scmag</span></a> and in <a class="reference internal" href="scesv.html#scesv"><span class="std std-ref">scesv</span></a> or <a class="reference internal" href="scolv.html#scolv"><span class="std std-ref">scolv</span></a> for visibility.</p>
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<h3><a href="../index.html">Table of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">ML</a><ul>
<li><a class="reference internal" href="#description">Description</a><ul>
<li><a class="reference internal" href="#amplitudes">Amplitudes</a></li>
<li><a class="reference internal" href="#station-magnitudes">Station Magnitudes</a></li>
<li><a class="reference internal" href="#network-magnitude">Network magnitude</a></li>
<li><a class="reference internal" href="#configuration">Configuration</a></li>
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