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<section id="mlc">
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<span id="global-mlc"></span><h1>MLc<a class="headerlink" href="#mlc" title="Permalink to this heading">¶</a></h1>
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<p>Custom magnitude for local events measured on horizontal components</p>
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<section id="description">
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<h2>Description<a class="headerlink" href="#description" title="Permalink to this heading">¶</a></h2>
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<p>MLc is a custom magnitude for local events based on <a class="reference internal" href="global_ml.html#global-ml"><span class="std std-ref">ML</span></a> but
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with greater flexibility.
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The original implementation is based on specifications by the Hessian Agency for
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Nature Conservation, Environment and Geology, Hessian Earthquake Service.
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More options have been added allowing the magnitude to be configured with
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great flexibility in order to account for many different conditions. The
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general procedures for measuring amplitudes and computing magnitudes are
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outlined in the <a class="reference internal" href="../base/concepts/magnitudes.html#concepts-magnitudes"><span class="std std-ref">“Concepts” section on magnitudes</span></a>.</p>
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<p>The MLc magnitude is very similar to the original <a class="reference internal" href="global_ml.html#global-ml"><span class="std std-ref">ML</span></a>,
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except that</p>
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<ul class="simple">
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<li><p>Amplitude pre-filtering is applied by default.</p></li>
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<li><p>Wood-Anderson simulation is optionally applied and can be deactivated.</p></li>
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<li><p>Measured amplitudes can be scaled accounting for expected units.</p></li>
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<li><p>Measured amplitudes are combined by taking the maximum instead of the average.</p></li>
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<li><p>A parametric <a class="reference internal" href="#mlc-station-magnitude"><span class="std std-ref">magnitude calibration</span></a> function
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applies but a correction in the form log10(A0) can be configured for converting
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measured amplitudes to station magnitudes.</p></li>
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<li><p>Hypocentral instead of epicentral distance is considered by default.</p></li>
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</ul>
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<section id="amplitudes">
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<h3>Amplitudes<a class="headerlink" href="#amplitudes" title="Permalink to this heading">¶</a></h3>
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<p>Some general conditions apply for measuring amplitudes:</p>
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<ul class="simple">
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<li><p>Name amplitude type: MLc.</p></li>
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<li><p>Expected unit of gain-corrected input data: m/s. Activate response correction
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in global bindings in case data are provided in acceleration.</p></li>
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<li><p>Components used for amplitude measurements: both horizontal components
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separately.</p></li>
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</ul>
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<p>The parameters for measuring MLc amplitudes can be adjusted by global
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binding parameters:</p>
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<table class="docutils align-left">
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<colgroup>
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<col style="width: 22.2%" />
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<col style="width: 27.8%" />
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<col style="width: 16.7%" />
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<col style="width: 33.3%" />
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</colgroup>
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<thead>
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<tr class="row-odd"><th class="head"><p>Topic</p></th>
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<th class="head"><p>Parameter</p></th>
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<th class="head"><p>Default</p></th>
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<th class="head"><p>Comment</p></th>
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</tr>
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</thead>
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<tbody>
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<tr class="row-even"><td><p><a class="reference internal" href="../base/filter-grammar.html#filter-grammar"><span class="std std-ref">Filtering</span></a></p></td>
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<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.MLc.preFilter</span></code></p></td>
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<td><p><a class="reference internal" href="../base/filter-grammar.html#filter-bw"><span class="std std-ref">BW(3,0.5,12)</span></a></p></td>
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<td><p>Applied before instrument simulation</p></td>
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</tr>
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<tr class="row-odd"><td><p><a class="reference internal" href="../base/glossary.html#term-Wood-Anderson-seismometer"><span class="xref std std-term">Wood-Anderson simulation</span></a></p></td>
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<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.MLc.applyWoodAnderson</span></code></p></td>
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<td><p>true</p></td>
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<td><p>When WA simulation is inactive, measured amplitudes take the units of the gain of the stream on which they were measured.</p></td>
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</tr>
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<tr class="row-even"><td><p><a class="reference internal" href="../base/glossary.html#term-Wood-Anderson-seismometer"><span class="xref std std-term">Wood-Anderson parameters</span></a></p></td>
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<td><p><a class="reference internal" href="global.html#confval-2"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.WoodAnderson.gain</span></code></a>, <a class="reference internal" href="global.html#confval-3"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.WoodAnderson.T0</span></code></a>, <a class="reference internal" href="global.html#confval-4"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.WoodAnderson.h</span></code></a></p></td>
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<td><p>2080, 0.8, 0.7</p></td>
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<td><p>Defaults: see <a class="reference internal" href="../base/concepts/magnitudes.html#concepts-magnitudes-wa"><span class="std std-ref">IASPEI recommendation</span></a>.</p></td>
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</tr>
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<tr class="row-odd"><td><p>Amplitude scaling</p></td>
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<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.MLc.amplitudeScale</span></code></p></td>
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<td><p>1</p></td>
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<td><p>Apply for scaling measured amplitudes to units required by the magnitude</p></td>
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</tr>
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<tr class="row-even"><td><p>Amplitude combination</p></td>
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<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.MLc.combiner</span></code></p></td>
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<td><p>max</p></td>
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<td><p>Method for combining amplitudes measured on both horizontal components</p></td>
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</tr>
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</tbody>
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</table>
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<p>Some additional parameters require you to create an amplitude-type profile for
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global binding parameters. Name the profile like the amplitude name, hence MLc
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replacing ‘$name’ in the parameters below:</p>
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<table class="docutils align-left">
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<colgroup>
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<col style="width: 22.2%" />
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<col style="width: 27.8%" />
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<col style="width: 16.7%" />
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<col style="width: 33.3%" />
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</colgroup>
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<thead>
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<tr class="row-odd"><th class="head"><p>Topic</p></th>
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<th class="head"><p>Parameter</p></th>
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<th class="head"><p>Default</p></th>
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<th class="head"><p>Comment</p></th>
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</tr>
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</thead>
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<tbody>
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<tr class="row-even"><td><p>Minimum distance</p></td>
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<td><p><a class="reference internal" href="global.html#confval-amplitudes.-name.minDist"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.$name.minDist</span></code></a></p></td>
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<td><p>0</p></td>
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<td></td>
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</tr>
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<tr class="row-odd"><td><p>Maximum distance</p></td>
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<td><p><a class="reference internal" href="global.html#confval-amplitudes.-name.maxDist"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.$name.maxDist</span></code></a></p></td>
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<td><p>8</p></td>
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<td><p>Cannot be extended beyond default</p></td>
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</tr>
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<tr class="row-even"><td><p>Minimum source depth</p></td>
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<td><p><a class="reference internal" href="global.html#confval-amplitudes.-name.minDepth"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.$name.minDepth</span></code></a></p></td>
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<td><p>0</p></td>
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<td><p>Can be negative</p></td>
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</tr>
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<tr class="row-odd"><td><p>Maximum source depth</p></td>
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<td><p><a class="reference internal" href="global.html#confval-amplitudes.-name.maxDepth"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.$name.maxDepth</span></code></a></p></td>
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<td><p>80</p></td>
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<td><p>Can be extended beyond default</p></td>
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</tr>
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<tr class="row-even"><td><p>Noise window begin</p></td>
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<td><p><a class="reference internal" href="global.html#confval-amplitudes.-name.noiseBegin"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.$name.noiseBegin</span></code></a></p></td>
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<td><p>-30</p></td>
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<td><p>(+++)</p></td>
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</tr>
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<tr class="row-odd"><td><p>Noise window end</p></td>
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<td><p><a class="reference internal" href="global.html#confval-amplitudes.-name.noiseEnd"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.$name.noiseEnd</span></code></a></p></td>
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<td><p>-5</p></td>
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<td><p>(+++)</p></td>
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</tr>
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<tr class="row-even"><td><p>Signal window begin</p></td>
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<td><p><a class="reference internal" href="global.html#confval-amplitudes.-name.signalBegin"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.$name.signalBegin</span></code></a></p></td>
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<td><p>-5</p></td>
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<td><p>(+++)</p></td>
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</tr>
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<tr class="row-odd"><td><p>Signal window end</p></td>
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<td><p><a class="reference internal" href="global.html#confval-amplitudes.-name.signalEnd"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.$name.signalEnd</span></code></a></p></td>
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<td><p>150 (+) or distance/3+30 (++)</p></td>
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<td><p>(<strong>+</strong>) When measured by <a class="reference internal" href="scautopick.html#scautopick"><span class="std std-ref">scautopick</span></a>, (<strong>++</strong>) When measured by <a class="reference internal" href="scamp.html#scamp"><span class="std std-ref">scamp</span></a> or <a class="reference internal" href="scolv.html#scolv"><span class="std std-ref">scolv</span></a> (+++)</p></td>
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</tr>
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<tr class="row-even"><td><p>Minimum <a class="reference internal" href="../base/glossary.html#term-SNR"><span class="xref std std-term">SNR</span></a></p></td>
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<td><p><a class="reference internal" href="global.html#confval-amplitudes.-name.minSNR"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.$name.minSNR</span></code></a></p></td>
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<td><p>not applied</p></td>
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<td><p>Compares the maximum amplitudes measured within the signal and noise windows</p></td>
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</tr>
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<tr class="row-odd"><td><p>Period range</p></td>
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<td><p>NA</p></td>
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<td><p>NA</p></td>
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<td><p>Period is not measured. A configuration will prevent any MLc amplitude from being measured</p></td>
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</tr>
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<tr class="row-even"><td><p>Amplitude saturation</p></td>
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<td><p><a class="reference internal" href="global.html#confval-amplitudes.-name.saturationThreshold"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.$name.saturationThreshold</span></code></a></p></td>
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<td><p>false</p></td>
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<td><p>Apply for avoiding measurements on clipped data</p></td>
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</tr>
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<tr class="row-odd"><td><p>Response correction</p></td>
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<td><p><a class="reference internal" href="global.html#confval-amplitudes.-name.enableResponses"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.$name.enableResponses</span></code></a></p></td>
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<td><p>false</p></td>
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<td><p>Activate for input units other than nm/s and set <a class="reference internal" href="global.html#confval-amplitudes.-name.resp.minFreq"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.$name.resp.minFreq</span></code></a>, <a class="reference internal" href="global.html#confval-amplitudes.-name.resp.maxFreq"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.$name.resp.maxFreq</span></code></a></p></td>
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</tr>
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</tbody>
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</table>
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<p><strong>(+++)</strong> All values defining the time windows for measuring noise and signal
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are relative to P arrival time, read <a class="reference internal" href="../base/time-grammar.html#time-grammar"><span class="std std-ref">Time grammar</span></a>.</p>
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<p>The default values are valid for SW-Germany (<span id="id1">Stange [<a class="reference internal" href="../base/references.html#id100" title="S. Stange. ML determination for local and regional events using a sparse network in Southwestern Germany. J. Seismol., 10:247 – 257, 2006. doi:10.1007/s10950-006-9010-6.">71</a>]</span>).
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The Wood-Anderson simulation will convert input velocity data to ground
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displacement in mm. The input data may be of a different unit after applying
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<code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.MLc.preFilter</span></code>, e.g. when integration is applied, and / or
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when Wood-Anderson simulation is disabled. Configure
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<code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.MLc.amplitudeScale</span></code> for converting the unit of the
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processed data to the unit expected by the
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<a class="reference internal" href="#mlc-station-magnitude"><span class="std std-ref">station magnitude calibration</span></a> for the measured
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amplitude.</p>
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<div class="admonition note">
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<p class="admonition-title">Note</p>
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<p>For comparing MLc amplitudes with <a class="reference internal" href="global_ml.html#global-ml"><span class="std std-ref">ML amplitudes</span></a> set the
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global bindings parameters</p>
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<div class="highlight-properties notranslate"><div class="highlight"><pre><span></span><span class="na">amplitudes.MLc.preFilter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">""</span>
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<span class="na">amplitudes.MLc.combiner</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">average</span>
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</pre></div>
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</div>
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</div>
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</section>
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<section id="station-magnitudes">
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<span id="mlc-station-magnitude"></span><h3>Station magnitudes<a class="headerlink" href="#station-magnitudes" title="Permalink to this heading">¶</a></h3>
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<p>Station magnitudes are computed from measured amplitudes by applying a
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configurable calibration function when the origin is within depths and distance
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constraints. The parameters are configurable in global bindings or by global
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module parameters when applying
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<a class="reference internal" href="../base/concepts/magnitudes.html#concepts-magnitudes-regionalization"><span class="std std-ref">regionalization</span></a>.</p>
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<p>Station corrections are configurable by a magnitude-type profile named MLc in
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global bindings with <a class="reference internal" href="global.html#confval-magnitudes.-name.offset"><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.$name.offset</span></code></a> or the equivalent in
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global module configuration as <code class="xref std std-confval docutils literal notranslate"><span class="pre">module.trunk.NET.STA.magnitudes.MLc.offset</span></code>.
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The latter is not supported by <a class="reference internal" href="scconfig.html#scconfig"><span class="std std-ref">scconfig</span></a> but it reduces the amount of
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required bindings.</p>
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<p>The calibration function is considered in one of the forms</p>
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<ul>
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<li><p>Parametric when <code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.calibrationType</span></code> = “parametric”<a href="#id2"><span class="problematic" id="id3">`</span></a>:</p>
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<div class="math">
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<p><img src="../_images/math/f3e2c61cf74e64278c41c2c01028f3b9fe5d1c8e.svg" alt="MLc = \log_{10}(A) + c_7 * e^{c8 * r} + c_6 * h + c_3 * \log_{10}(r / c_5) + c_2 * (r + c_4) + c_1 + c_0(station)"/></p>
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</div><p>where</p>
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<ul class="simple">
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<li><p><em>A</em>: displacement amplitude measured in unit of mm or as per configuration</p></li>
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<li><p><em>c1 - c8</em>: general calibration parameters</p></li>
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<li><p><em>c0</em>: station-specific correction</p></li>
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<li><p><em>r</em>: Hypocentral (default) or epicentral distance as configured by
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<code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.distMode</span></code></p></li>
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<li><p>h: (source depth - <code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.parametric.H</span></code>) when
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source depth > <code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.parametric.H</span></code> but 0 otherwise.</p></li>
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</ul>
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<p>The default values are valid for SW-Germany (<span id="id4">Stange [<a class="reference internal" href="../base/references.html#id100" title="S. Stange. ML determination for local and regional events using a sparse network in Southwestern Germany. J. Seismol., 10:247 – 257, 2006. doi:10.1007/s10950-006-9010-6.">71</a>]</span>). <em>c6</em>,
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<em>H</em> have been added for supporting dependency on depth (<span id="id5">Rhoades <em>et al.</em> [<a class="reference internal" href="../base/references.html#id93" title="D.A. Rhoades, A. Christophersen, S. Bourguignon, J. Ristau, and J. Salichon. A Depth‐Dependent Local Magnitude Scale for New Zealand Earthquakes Consistent with Moment Magnitude. Bull. Seismol. Soc. Am., 111(2):1056–1066, 2020. doi:10.1785/0120200252.">65</a>]</span>)
|
||
and <em>c7</em>, <em>c8</em> for observations at short distances (<span id="id6">Luckett <em>et al.</em> [<a class="reference internal" href="../base/references.html#id71" title="R. Luckett, L. Ottemöller, A. Butcher, and B. Baptie. Extending local magnitude ml to short distances. Geophys. J. Int., 216:1145–1156, 2019. doi:10.1093/gji/ggy484.">61</a>]</span>).</p>
|
||
</li>
|
||
<li><p>log10(A0)-based non-parametric when <code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.calibrationType</span></code> = “A0”<a href="#id7"><span class="problematic" id="id8">`</span></a>:</p>
|
||
<div class="math">
|
||
<p><img src="../_images/math/ccab4425809584f06dd1ddcaf88fa0b15cb94841.svg" alt="MLc = \log_{10}(A) - \log_{10}(A_0)"/></p>
|
||
</div><p>where</p>
|
||
<ul class="simple">
|
||
<li><p><img class="math" src="../_images/math/93675c26b872cb6c8401f3a9d037d0e7383ae06b.svg" alt="log_{10}(A_0)"/>: distance-dependent correction value. Read
|
||
<a class="reference internal" href="global_mlv.html#global-mlv"><span class="std std-ref">MLv</span></a> for the details.</p></li>
|
||
</ul>
|
||
</li>
|
||
</ul>
|
||
<div class="admonition note">
|
||
<p class="admonition-title">Note</p>
|
||
<ul class="simple">
|
||
<li><p>The magnitude calibration function can be regionalized by adjusting global
|
||
module configuration parameters in MLc region profiles of
|
||
<code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.region.*</span></code> and in a <em>MLc</em> Magnitude type profile
|
||
e.g., in <code class="file docutils literal notranslate"><span class="pre">global.cfg</span></code>.</p></li>
|
||
</ul>
|
||
</div>
|
||
<p>Configurable parameters:</p>
|
||
<table class="docutils align-left">
|
||
<colgroup>
|
||
<col style="width: 22.2%" />
|
||
<col style="width: 27.8%" />
|
||
<col style="width: 16.7%" />
|
||
<col style="width: 33.3%" />
|
||
</colgroup>
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>Topic</p></th>
|
||
<th class="head"><p>Parameter</p></th>
|
||
<th class="head"><p>Default</p></th>
|
||
<th class="head"><p>Comment</p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>Distance type</p></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.distMode</span></code></p></td>
|
||
<td><p>hypocentral</p></td>
|
||
<td><p>epicentral or hyocentral can be selected</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>Minimum distance</p></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.minDist</span></code></p></td>
|
||
<td><p>-1</p></td>
|
||
<td></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>Maximum distance</p></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.maxDist</span></code></p></td>
|
||
<td><p>8</p></td>
|
||
<td><p>Measurements beyond 8 deg are strictly ignored</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>Minimum source depth</p></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.minDepth</span></code></p></td>
|
||
<td><p>-10</p></td>
|
||
<td></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>Maximum source depth</p></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.maxDepth</span></code></p></td>
|
||
<td><p>80</p></td>
|
||
<td><p>Can be extended beyond default</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>Period range</p></td>
|
||
<td><p>NA</p></td>
|
||
<td><p>NA</p></td>
|
||
<td><p>Period is not measured. A configuration will prevent any MLc magnitude from being computed</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>Amplitude type</p></td>
|
||
<td></td>
|
||
<td><p>MLc</p></td>
|
||
<td><p>Configurable by <a class="reference internal" href="../base/concepts/magnitudes.html#concepts-magnitudes-aliases"><span class="std std-ref">amplitude and magnitude alias</span></a></p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>Amplitude unit</p></td>
|
||
<td></td>
|
||
<td><p>mm</p></td>
|
||
<td><p>other units can be assumed by amplitude scaling with <code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.MLc.amplitudeScale</span></code></p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>Magnitude calibration type</p></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.calibrationType</span></code></p></td>
|
||
<td><p>parametric</p></td>
|
||
<td><p>parametric and A0 (non-parametric) are available</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>Linear magnitude correction</p></td>
|
||
<td><p><a class="reference internal" href="global.html#confval-magnitudes.-name.multiplier"><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.$name.multiplier</span></code></a></p></td>
|
||
<td><p>1.0</p></td>
|
||
<td><p>Configure station corrections more conveniently configurable in global module configuration as <code class="xref std std-confval docutils literal notranslate"><span class="pre">module.trunk.NET.STA.magnitudes.MLc.multiplier</span></code></p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>Constant magnitude correction</p></td>
|
||
<td><p><a class="reference internal" href="global.html#confval-magnitudes.-name.offset"><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.$name.offset</span></code></a></p></td>
|
||
<td><p>0.0</p></td>
|
||
<td><p>Configure station corrections more conveniently configurable in global module configuration as <code class="xref std std-confval docutils literal notranslate"><span class="pre">module.trunk.NET.STA.magnitudes.MLc.offset</span></code></p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td></td>
|
||
<td></td>
|
||
<td></td>
|
||
<td></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p><strong>parametric</strong> calibration</p></td>
|
||
<td></td>
|
||
<td></td>
|
||
<td><p>Parameters are used for <code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.calibrationType</span></code> = parametric</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.parametric.c0</span></code></p></td>
|
||
<td><p>0.0</p></td>
|
||
<td></td>
|
||
</tr>
|
||
<tr class="row-even"><td></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.parametric.c1</span></code></p></td>
|
||
<td><p>0.69</p></td>
|
||
<td></td>
|
||
</tr>
|
||
<tr class="row-odd"><td></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.parametric.c2</span></code></p></td>
|
||
<td><p>0.00095</p></td>
|
||
<td></td>
|
||
</tr>
|
||
<tr class="row-even"><td></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.parametric.c3</span></code></p></td>
|
||
<td><p>1.11</p></td>
|
||
<td></td>
|
||
</tr>
|
||
<tr class="row-odd"><td></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.parametric.c4</span></code></p></td>
|
||
<td><p>0.0</p></td>
|
||
<td></td>
|
||
</tr>
|
||
<tr class="row-even"><td></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.parametric.c5</span></code></p></td>
|
||
<td><p>1.0</p></td>
|
||
<td></td>
|
||
</tr>
|
||
<tr class="row-odd"><td></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.parametric.c6</span></code></p></td>
|
||
<td><p>0.0</p></td>
|
||
<td><p>see <span id="id9">Rhoades <em>et al.</em> [<a class="reference internal" href="../base/references.html#id93" title="D.A. Rhoades, A. Christophersen, S. Bourguignon, J. Ristau, and J. Salichon. A Depth‐Dependent Local Magnitude Scale for New Zealand Earthquakes Consistent with Moment Magnitude. Bull. Seismol. Soc. Am., 111(2):1056–1066, 2020. doi:10.1785/0120200252.">65</a>]</span></p></td>
|
||
</tr>
|
||
<tr class="row-even"><td></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.parametric.H</span></code></p></td>
|
||
<td><p>40.0</p></td>
|
||
<td><p>see <span id="id10">Rhoades <em>et al.</em> [<a class="reference internal" href="../base/references.html#id93" title="D.A. Rhoades, A. Christophersen, S. Bourguignon, J. Ristau, and J. Salichon. A Depth‐Dependent Local Magnitude Scale for New Zealand Earthquakes Consistent with Moment Magnitude. Bull. Seismol. Soc. Am., 111(2):1056–1066, 2020. doi:10.1785/0120200252.">65</a>]</span></p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.parametric.c7</span></code></p></td>
|
||
<td><p>0.0</p></td>
|
||
<td><p>see <span id="id11">Luckett <em>et al.</em> [<a class="reference internal" href="../base/references.html#id71" title="R. Luckett, L. Ottemöller, A. Butcher, and B. Baptie. Extending local magnitude ml to short distances. Geophys. J. Int., 216:1145–1156, 2019. doi:10.1093/gji/ggy484.">61</a>]</span></p></td>
|
||
</tr>
|
||
<tr class="row-even"><td></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.parametric.c8</span></code></p></td>
|
||
<td><p>0.0</p></td>
|
||
<td><p>see <span id="id12">Luckett <em>et al.</em> [<a class="reference internal" href="../base/references.html#id71" title="R. Luckett, L. Ottemöller, A. Butcher, and B. Baptie. Extending local magnitude ml to short distances. Geophys. J. Int., 216:1145–1156, 2019. doi:10.1093/gji/ggy484.">61</a>]</span></p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td></td>
|
||
<td></td>
|
||
<td></td>
|
||
<td></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p><strong>non-parametric</strong> calibration</p></td>
|
||
<td></td>
|
||
<td></td>
|
||
<td><p>Parameters are used for <code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.calibrationType</span></code> = A0</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td></td>
|
||
<td><p><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.MLc.A0.logA0</span></code></p></td>
|
||
<td><p>0:-1.3,60:-2.8,100:-3.0,400:-4.5,1000:-5.85</p></td>
|
||
<td><p>from <a class="reference internal" href="global_ml.html#global-ml"><span class="std std-ref">ML magnitude</span></a></p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</section>
|
||
<section id="network-magnitude">
|
||
<h3>Network magnitude<a class="headerlink" href="#network-magnitude" title="Permalink to this heading">¶</a></h3>
|
||
<p>The network magnitude is computed from station magnitudes automatically by
|
||
<a class="reference internal" href="scmag.html#scmag"><span class="std std-ref">scmag</span></a> or interactively by <a class="reference internal" href="scolv.html#scolv"><span class="std std-ref">scolv</span></a>.
|
||
Originally the median was computed from all station MLc to form the
|
||
<a class="reference internal" href="../base/glossary.html#term-network-magnitude"><span class="xref std std-term">network magnitude</span></a> MLc. Here, the trimmed mean is applied. Outliers
|
||
beyond the outer 12.5% percentiles are removed before forming the mean. The
|
||
method can be adjusted in <a class="reference internal" href="scmag.html#scmag"><span class="std std-ref">scmag</span></a> by <a class="reference internal" href="scmag.html#confval-magnitudes.average"><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.average</span></code></a>.</p>
|
||
</section>
|
||
<section id="moment-magnitude">
|
||
<h3>Moment magnitude<a class="headerlink" href="#moment-magnitude" title="Permalink to this heading">¶</a></h3>
|
||
<p>MLc can be scaled to a moment magnitude, Mw(MLc), by a magnitude-type profile in
|
||
global module configuration. Read the
|
||
<a class="reference internal" href="../base/tutorials/amplitudes-magnitudes.html#tutorials-mags-moment"><span class="std std-ref">Tutorial on moment magnitudes</span></a> for the details.</p>
|
||
</section>
|
||
<section id="aliases">
|
||
<h3>Aliases<a class="headerlink" href="#aliases" title="Permalink to this heading">¶</a></h3>
|
||
<p>Amplitude and magnitude aliases can be created by <a class="reference internal" href="global.html#confval-magnitudes.aliases"><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.aliases</span></code></a>
|
||
and <a class="reference internal" href="global.html#confval-amplitudes.aliases"><code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.aliases</span></code></a>, respectively, in global module configuration
|
||
in order to derive other magnitude types from
|
||
original amplitudes and magnitudes. The actual amplitude and magnitude
|
||
parameters of the aliases will be configured in global bindings or by
|
||
magnitude-type profiles in global module configuration. Read the
|
||
<a class="reference internal" href="../base/tutorials/amplitudes-magnitudes.html#tutorials-magnitude-aliases"><span class="std std-ref">Tutorial on magnitude aliases</span></a> for the
|
||
details.</p>
|
||
</section>
|
||
<section id="regionalization">
|
||
<h3>Regionalization<a class="headerlink" href="#regionalization" title="Permalink to this heading">¶</a></h3>
|
||
<p>Regionalization may be achieved by a magnitude-type profile in global module
|
||
configuration. Read the
|
||
<a class="reference internal" href="../base/tutorials/amplitudes-magnitudes.html#tutorials-magnitude-region"><span class="std std-ref">Tutorial on regionalization</span></a> for the details.</p>
|
||
</section>
|
||
</section>
|
||
<section id="examples">
|
||
<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this heading">¶</a></h2>
|
||
<p>The flexibility of the amplitude and magnitude processing allows for MLc to be
|
||
applied in various use cases. Examples are given below.</p>
|
||
<ul>
|
||
<li><p><strong>Default:</strong> Pre-filtered and gain-corrected amplitudes, Wood-Anderson
|
||
corrected and measured in mm for Southwestern Germany, <span id="id13">Stange [<a class="reference internal" href="../base/references.html#id100" title="S. Stange. ML determination for local and regional events using a sparse network in Southwestern Germany. J. Seismol., 10:247 – 257, 2006. doi:10.1007/s10950-006-9010-6.">71</a>]</span>:</p>
|
||
<div class="math">
|
||
<p><img src="../_images/math/d949c4542df9586bfdd0006602e3f0b3a56fbc5b.svg" alt="MLc = \log_{10}(A) + 1.11 * \log_{10}(r) + 0.00095 * r + 0.69 + c_0"/></p>
|
||
</div></li>
|
||
<li><p>Wood-Anderson-corrected displacement amplitudes measured in mm for
|
||
Southern California, <span id="id14">Hutton and Boore [<a class="reference internal" href="../base/references.html#id54" title="L.K. Hutton and D.M. Boore. The ML scale in southern California. Bull. Seismol. Soc. Am,, 77(6):2074–2094, 1987. URL: https://resolver.caltech.edu/CaltechAUTHORS:20140905-113510505.">53</a>]</span>:</p>
|
||
<div class="math">
|
||
<p><img src="../_images/math/fe3a90edfdebbbcc8730ea60fd0048e251cda93c.svg" alt="MLc = \log_{10}(A) + 1.110 * \log_{10}(r / 100) + 0.00189 * (r - 100) + 3.0"/></p>
|
||
</div></li>
|
||
<li><p>Pre-filtered velocity amplitudes in units of mym/s (requiring to set
|
||
<code class="xref std std-confval docutils literal notranslate"><span class="pre">amplitudes.MLc.amplitudeScale</span></code>), no Wood-Anderson correction,
|
||
for West Bohemia, e.g. <span id="id15">Hiemer and Roessler [<a class="reference internal" href="../base/references.html#id53" title="S. Hiemer and D. Roessler. Monitoring the West Bohemian earthquake swarm in 2008/2009 by a temporary small-aperture seismic array. J. Seismol., 16:169-182, 2012. doi:10.1007/s10950-011-9256-5.">52</a>]</span>:</p>
|
||
<div class="math">
|
||
<p><img src="../_images/math/b21da4311b2f4882dbbadbcb617d04c5e5e35e7b.svg" alt="MLc = \log_{10}(A) - log_{10}(2\Pi) + 2.1 * \log_{10}(r) - 1.7 + c_0"/></p>
|
||
</div></li>
|
||
</ul>
|
||
<figure class="align-center" id="id18">
|
||
<a class="reference internal image-reference" href="../_images/magnitude-calibrations_MLc_s_MLc_hb.png"><img alt="../_images/magnitude-calibrations_MLc_s_MLc_hb.png" src="../_images/magnitude-calibrations_MLc_s_MLc_hb.png" style="width: 18cm;" /></a>
|
||
<figcaption>
|
||
<p><span class="caption-text">MLc magnitudes for measured amplitude of 1 mm with default magnitude
|
||
calibration (<em>MLc_s</em>, <span id="id16">Stange [<a class="reference internal" href="../base/references.html#id100" title="S. Stange. ML determination for local and regional events using a sparse network in Southwestern Germany. J. Seismol., 10:247 – 257, 2006. doi:10.1007/s10950-006-9010-6.">71</a>]</span>) and calibration values for Southern
|
||
California (<em>MLc_hb</em>, <span id="id17">Hutton and Boore [<a class="reference internal" href="../base/references.html#id54" title="L.K. Hutton and D.M. Boore. The ML scale in southern California. Bull. Seismol. Soc. Am,, 77(6):2074–2094, 1987. URL: https://resolver.caltech.edu/CaltechAUTHORS:20140905-113510505.">53</a>]</span>).</span><a class="headerlink" href="#id18" title="Permalink to this image">¶</a></p>
|
||
</figcaption>
|
||
</figure>
|
||
</section>
|
||
<section id="setup">
|
||
<h2>Setup<a class="headerlink" href="#setup" title="Permalink to this heading">¶</a></h2>
|
||
<ol class="arabic">
|
||
<li><p><strong>Set the configuration and calibration parameters</strong> in the global bindings
|
||
similar
|
||
to <a class="reference internal" href="global_ml.html#global-ml"><span class="std std-ref">ML</span></a>. Instead of 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>) which takes the form</p>
|
||
<div class="highlight-properties notranslate"><div class="highlight"><pre><span></span><span class="na">module.trunk.NET.STA.amplitudes.MLc.preFilter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">value</span>
|
||
<span class="na">module.trunk.NET.STA.magnitudes.MLc.parametric.c0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">value</span>
|
||
</pre></div>
|
||
</div>
|
||
</li>
|
||
<li><p>Add MLc to the list of default amplitudes and magnitudes if MLc is to be
|
||
computed by automatic modules, e.g. of <a class="reference internal" href="scamp.html#scamp"><span class="std std-ref">scamp</span></a>, <a class="reference internal" href="scmag.html#scmag"><span class="std std-ref">scmag</span></a>.</p></li>
|
||
<li><p>Configure <a class="reference internal" href="scmag.html#scmag"><span class="std std-ref">scmag</span></a> (<a class="reference internal" href="scmag.html#confval-magnitudes.average"><code class="xref std std-confval docutils literal notranslate"><span class="pre">magnitudes.average</span></code></a> in <code class="file docutils literal notranslate"><span class="pre">scmag.cfg</span></code>)
|
||
for choosing the method to form the
|
||
network magnitude from station magnitudes, e.g.</p>
|
||
<div class="highlight-properties notranslate"><div class="highlight"><pre><span></span><span class="na">magnitudes.average</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">MLc:median</span>
|
||
</pre></div>
|
||
</div>
|
||
</li>
|
||
<li><p>Add MLc to the list of magnitudes preferred by <a class="reference internal" href="scevent.html#scevent"><span class="std std-ref">scevent</span></a>
|
||
(<a class="reference internal" href="scevent.html#confval-eventAssociation.magTypes"><code class="xref std std-confval docutils literal notranslate"><span class="pre">eventAssociation.magTypes</span></code></a> in <code class="file docutils literal notranslate"><span class="pre">scevent.cfg</span></code>) in order to let
|
||
MLc become the preferred magnitude.</p></li>
|
||
<li><p>Set defaults/visibility of MLc in <a class="reference internal" href="../base/glossary.html#term-GUI"><span class="xref std std-term">GUI</span></a> modules, e.g. <a class="reference internal" href="scolv.html#scolv"><span class="std std-ref">scolv</span></a>
|
||
or <a class="reference internal" href="scesv.html#scesv"><span class="std std-ref">scesv</span></a>.</p></li>
|
||
</ol>
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<h3><a href="../index.html">Table of Contents</a></h3>
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||
<ul>
|
||
<li><a class="reference internal" href="#">MLc</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="#moment-magnitude">Moment magnitude</a></li>
|
||
<li><a class="reference internal" href="#aliases">Aliases</a></li>
|
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<li><a class="reference internal" href="#regionalization">Regionalization</a></li>
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</ul>
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|
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<li><a class="reference internal" href="#examples">Examples</a></li>
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<li><a class="reference internal" href="#setup">Setup</a></li>
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