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<section id="mlv">
<span id="global-mlv"></span><h1>MLv<a class="headerlink" href="#mlv" title="Permalink to this heading"></a></h1>
<p>Local (Richter) magnitude measured on the vertical component</p>
<section id="description">
<h2>Description<a class="headerlink" href="#description" title="Permalink to this heading"></a></h2>
<p>MLv is the local (Richter) magnitude (<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>) computed from amplitudes measured on the
vertical component.</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: 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>Default distance range: 0 - 8 deg, maximum is configurable
<a class="reference internal" href="global.html#confval-magnitudes.MLv.maxDistanceKm"><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLv.maxDistanceKm</span></code></a>, measurements beyond 8 deg will be
strictly ignored.</p></li>
<li><p>Depth range: no limitation.</p></li>
</ul>
<section id="amplitudes">
<h3>Amplitudes<a class="headerlink" href="#amplitudes" title="Permalink to this heading"></a></h3>
<p>The MLv amplitude calculation is very similar to the original <a class="reference internal" href="global_ml.html#global-ml"><span class="std std-ref">ML</span></a>,
except that the amplitude is measured on the vertical component. The methods
for measuring 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 MLv is calculated up to the epicentral distance
<a class="reference internal" href="global.html#confval-magnitudes.MLv.maxDistanceKm"><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLv.maxDistanceKm</span></code></a> using the following formula:</p>
<div class="math">
<p><img src="../_images/math/f73f0c80f57e4c0aa9f75af47267f7aa55522b40.png" alt="MLv = \log10(A) - \log10(A0)"/></p>
</div><p>A is the MLv Wood-Anderson amplitude in millimeters. The second term
is the empirical calibration function, which in turn is a function
of the epicentral distance (see <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 can be configured globally or per station using global
bindings or the global module configuration variable
module.trunk.global.magnitudes.MLv.logA0 in <code class="file docutils literal notranslate"><span class="pre">global.cfg</span></code>, e.g.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">module</span><span class="o">.</span><span class="n">trunk</span><span class="o">.</span><span class="k">global</span><span class="o">.</span><span class="n">magnitudes</span><span class="o">.</span><span class="n">MLv</span><span class="o">.</span><span class="n">logA0</span> <span class="o">=</span> <span class="s2">&quot;0:-1.3,60:-2.8,100:-3.0,400:-4.5,1000:-5.85&quot;</span>
<span class="n">module</span><span class="o">.</span><span class="n">trunk</span><span class="o">.</span><span class="k">global</span><span class="o">.</span><span class="n">magnitudes</span><span class="o">.</span><span class="n">MLv</span><span class="o">.</span><span class="n">maxDistanceKm</span> <span class="o">=</span> <span class="s2">&quot;-1&quot;</span>
</pre></div>
</div>
<p>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 <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/e43775c444e67a786957a45f52e1b6a4b4d757a8.png" alt="MLv &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>
</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 trimmed mean is calculated from the station magnitudes to form
the <a class="reference internal" href="../base/glossary.html#term-network-magnitude"><span class="xref std std-term">network magnitude</span></a>. Outliers beyond the outer 12.5% percentiles are
removed before forming the mean.</p>
</section>
<section id="configuration">
<h3>Configuration<a class="headerlink" href="#configuration" title="Permalink to this heading"></a></h3>
<p>Several distance-value pairs can be configured for different ranges of
epicentral distance.
The calibration function and maximum distance can be configured globally,
per network or per station using the configuration variables. 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>), e.g.</p>
<p>global:</p>
<div class="highlight-params notranslate"><div class="highlight"><pre><span></span>module.trunk.global.magnitudes.MLv.logA0 = &quot;0:-1.3,60:-2.8,100:-3.0,400:-4.5,1000:-5.85&quot;
module.trunk.global.magnitudes.MLv.maxDistanceKm = -1
</pre></div>
</div>
<p>or per network:</p>
<div class="highlight-params notranslate"><div class="highlight"><pre><span></span>module.trunk.GR.magnitudes.MLv.logA0 = &quot;0:-1.3,60:-2.8,100:-3.0,400:-4.5,1000:-5.85&quot;
module.trunk.GR.magnitudes.MLv.maxDistanceKm = -1
</pre></div>
</div>
<p>or per station:</p>
<div class="highlight-params notranslate"><div class="highlight"><pre><span></span>module.trunk.GR.MOX.magnitudes.MLv.logA0 = &quot;0:-1.3,60:-2.8,100:-3.0,400:-4.5,1000:-5.85&quot;
module.trunk.GR.MOX.magnitudes.MLv.maxDistanceKm = -1
</pre></div>
</div>
<p>Set the configuration and calibration parameters in the global bindings. By
default MLv is computed by <a class="reference internal" href="scautopick.html#scautopick"><span class="std std-ref">scautopick</span></a> and is visible in GUIs.</p>
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<h3><a href="../index.html">Table of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">MLv</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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