439 lines
19 KiB
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439 lines
19 KiB
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<!-- 2020-11-12 jeu. 10:28 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Ground Motion Measurements</title>
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<meta name="author" content="Dehaeze Thomas" />
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Ground Motion Measurements</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#org98d0be2">1. Experimental Setup</a></li>
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<li><a href="#org7e6d21c">2. Measurement Analysis</a>
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<ul>
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<li><a href="#orgb4815e7">2.1. Load data</a></li>
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<li><a href="#org76505c6">2.2. Time domain plots of the measured voltage</a></li>
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<li><a href="#orge77c65d">2.3. Computation of the ASD of the measured voltage</a></li>
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<li><a href="#org7f9c12d">2.4. Scaling to take into account the sensibility of the geophone and the voltage amplifier</a></li>
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<li><a href="#org7f5940d">2.5. Time domain plots of the ground motion</a></li>
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<li><a href="#org02ba5d0">2.6. Computation of the ASD of the velocity and displacement</a></li>
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<li><a href="#org1e033f3">2.7. Save</a></li>
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<li><a href="#org8d373fd">2.8. Comparison with other measurements of ground motion</a>
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<ul>
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<li><a href="#orgad95d8a">2.8.1. Load the measurement data</a></li>
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<li><a href="#orgd5a5c4f">2.8.2. Compute PSD of the measurements</a></li>
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<li><a href="#org4688ea2">2.8.3. Compare PSD of Cern, ID09 and ID31</a></li>
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</ul>
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</li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org98d0be2" class="outline-2">
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<h2 id="org98d0be2"><span class="section-number-2">1</span> Experimental Setup</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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The goal here is to compare the ground motion at the location of the micro-station (ID31 beamline at ESRF) with other measurements of the ground motion.
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</p>
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<p>
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This will also permit to confirm that the device use for the measurement (geophones, amplifiers, ADC) are working well and that the data processing is correct.
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</p>
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<p>
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One L22 geophone is put on the ID31 floor.
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The signal is then filtered with a first order low pass filter with a cut-off frequency of \(1kHz\).
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Then the signal is amplified by a Voltage Amplifier with the following settings:
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</p>
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<ul class="org-ul">
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<li>AC/DC option set to DC</li>
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<li>Amplification of 60dB (1000)</li>
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<li>Low pass filter at the output with a cut-off frequency of \(1kHz\)</li>
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</ul>
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<p>
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On figure <a href="#orgb7f8464">1</a> is an overview of multiple measurements made at famous location.
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</p>
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<div id="orgb7f8464" class="figure">
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<p><img src="./img/ground_motion_measurements.png" alt="ground_motion_measurements.png" width="800px" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Power spectral density of ground vibration in the vertical direction at multiple locations (<a href="https://vibration.desy.de/">source</a>)</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org7e6d21c" class="outline-2">
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<h2 id="org7e6d21c"><span class="section-number-2">2</span> Measurement Analysis</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="orgcc23e80"></a>
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</p>
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<div class="note" id="org6e1fb83">
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<p>
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All the files (data and Matlab scripts) are accessible <a href="data/ground_meas_id31.zip">here</a>.
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</p>
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</div>
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</div>
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<div id="outline-container-orgb4815e7" class="outline-3">
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<h3 id="orgb4815e7"><span class="section-number-3">2.1</span> Load data</h3>
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<div class="outline-text-3" id="text-2-1">
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<div class="org-src-container">
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<pre class="src src-matlab">data = load(<span class="org-string">'mat/data_028.mat'</span>, <span class="org-string">'data'</span>); data = data.data;
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org76505c6" class="outline-3">
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<h3 id="org76505c6"><span class="section-number-3">2.2</span> Time domain plots of the measured voltage</h3>
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<div class="outline-text-3" id="text-2-2">
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-type">figure</span>;
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hold on;
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plot(data(<span class="org-type">:</span>, 3), data(<span class="org-type">:</span>, 1));
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hold off;
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xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
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xlim([0, 100]);
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</pre>
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</div>
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<div id="org32fab28" class="figure">
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<p><img src="figs/ground_motion_id31_time.png" alt="ground_motion_id31_time.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Measurement of the ground motion - Time domain</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orge77c65d" class="outline-3">
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<h3 id="orge77c65d"><span class="section-number-3">2.3</span> Computation of the ASD of the measured voltage</h3>
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<div class="outline-text-3" id="text-2-3">
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<div class="org-src-container">
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<pre class="src src-matlab">dt = data(2, 3) <span class="org-type">-</span> data(1, 3);
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Fs = 1<span class="org-type">/</span>dt;
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win = hanning(ceil(10<span class="org-type">*</span>Fs));
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">[px_dc, f] = pwelch(data(<span class="org-type">:</span>, 1), win, [], [], Fs);
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-type">figure</span>;
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hold on;
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plot(f, sqrt(px_dc));
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hold off;
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<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
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<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
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xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$'</span>)
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xlim([0.1, 500]);
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</pre>
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</div>
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<div id="org46dd80c" class="figure">
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<p><img src="figs/ground_motion_id31_asd_volt.png" alt="ground_motion_id31_asd_volt.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Amplitude Spectral Density of the measured Voltage</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org7f9c12d" class="outline-3">
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<h3 id="org7f9c12d"><span class="section-number-3">2.4</span> Scaling to take into account the sensibility of the geophone and the voltage amplifier</h3>
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<div class="outline-text-3" id="text-2-4">
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<p>
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The Geophone used are L22. Their sensibility is shown on figure <a href="#org8006b4c">4</a>.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">S0 = 88; <span class="org-comment">% Sensitivity [V/(m/s)]</span>
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f0 = 2; <span class="org-comment">% Cut-off frequency [Hz]</span>
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S = S0<span class="org-type">*</span>(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>f0)<span class="org-type">/</span>(1<span class="org-type">+</span>s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>f0);
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">freqs = logspace(<span class="org-type">-</span>1, 2, 1000);
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<span class="org-type">figure</span>;
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hold on;
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plot(f, abs(squeeze(freqresp(S, f, <span class="org-string">'Hz'</span>))));
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hold off;
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<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
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xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Magnitude $\left[\frac{V}{m/s}\right]$'</span>);
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xlim([0.1, 100]);
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</pre>
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</div>
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<div id="org8006b4c" class="figure">
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<p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Sensibility of the Geophone</p>
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</div>
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<p>
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We also take into account the gain of the electronics which is here set to be \(60dB\).
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">G0_db = 60; <span class="org-comment">% [dB]</span>
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G0 = 10<span class="org-type">^</span>(G0_db<span class="org-type">/</span>20); <span class="org-comment">% [abs]</span>
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</pre>
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</div>
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<p>
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We divide the PSD measured (in \(\text{V^2}/\sqrt{Hz}\)) by the square of the gain of the voltage amplifier to obtain the PSD of the voltage across the geophone.
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We further divide the result by the square of the magnitude of sensibility of the Geophone to obtain the PSD of the velocity in \((m/s)^2/Hz\).
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">psd_gv = px_dc<span class="org-type">./</span>abs(squeeze(freqresp(G0<span class="org-type">*</span>S, f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
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</pre>
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</div>
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<p>
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Finally, we obtain the PSD of the ground motion in \(m^2/Hz\) by dividing by the square of the frequency in \(rad/s\).
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">psd_gm = psd_gv<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f)<span class="org-type">.^</span>2;
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org7f5940d" class="outline-3">
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<h3 id="org7f5940d"><span class="section-number-3">2.5</span> Time domain plots of the ground motion</h3>
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<div class="outline-text-3" id="text-2-5">
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<p>
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We can inverse the dynamics of the geophone to convert the measured voltage into the estimated ground motion.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">est_vel = lsim(inv(G0<span class="org-type">*</span>S)<span class="org-type">*</span>(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span>)<span class="org-type">/</span>(1<span class="org-type">+</span>s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span>), data(<span class="org-type">:</span>, 1), data(<span class="org-type">:</span>, 3)); <span class="org-comment">% Estimated velocity above 1Hz</span>
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est_vel = est_vel <span class="org-type">-</span> mean(est_vel(data(<span class="org-type">:</span>,3)<span class="org-type">></span>10)); <span class="org-comment">% The mean value of the velocity if removed</span>
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est_dis = lsim(1<span class="org-type">/</span>(1<span class="org-type">+</span>s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span>), est_vel, data(<span class="org-type">:</span>, 3)); <span class="org-comment">% The velocity is integrated above 1Hz</span>
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</pre>
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</div>
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<div id="org3674cd1" class="figure">
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<p><img src="figs/time_domain_velocity.png" alt="time_domain_velocity.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Time domain velocity (<a href="./figs/time_domain_velocity.png">png</a>, <a href="./figs/time_domain_velocity.pdf">pdf</a>)</p>
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</div>
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<div id="org39fbab6" class="figure">
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<p><img src="figs/time_domain_displacement.png" alt="time_domain_displacement.png" />
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</p>
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<p><span class="figure-number">Figure 6: </span>Time domain absolute displacement (<a href="./figs/time_domain_displacement.png">png</a>, <a href="./figs/time_domain_displacement.pdf">pdf</a>)</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org02ba5d0" class="outline-3">
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<h3 id="org02ba5d0"><span class="section-number-3">2.6</span> Computation of the ASD of the velocity and displacement</h3>
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<div class="outline-text-3" id="text-2-6">
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<p>
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The ASD of the measured velocity is shown on figure <a href="#orgddc47d6">7</a>.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-type">figure</span>;
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hold on;
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plot(f, sqrt(psd_gv));
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hold off;
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<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
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<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
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xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
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xlim([0.1, 500]);
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</pre>
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</div>
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<div id="orgddc47d6" class="figure">
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<p><img src="figs/ground_motion_id31_asd_velocity.png" alt="ground_motion_id31_asd_velocity.png" />
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</p>
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<p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the Velocity</p>
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</div>
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<p>
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We also plot the ASD in displacement (figure <a href="#org9eb24d7">8</a>);
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-type">figure</span>;
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hold on;
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plot(f, sqrt(psd_gm));
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hold off;
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<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
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xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$'</span>)
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xlim([0.1, 500]);
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</pre>
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</div>
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<div id="org9eb24d7" class="figure">
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<p><img src="figs/ground_motion_id31_asd_displacement.png" alt="ground_motion_id31_asd_displacement.png" />
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</p>
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<p><span class="figure-number">Figure 8: </span>Amplitude Spectral Density of the Displacement</p>
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</div>
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<p>
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And we also plot the PSD of the displacement in \(\frac{{\mu u}^2}{Hz}\) as it is a usual unit used (figure <a href="#org5008310">9</a>).
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One can then compare this curve with the figure <a href="#orgb7f8464">1</a>.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-type">figure</span>;
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hold on;
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plot(f, psd_gm<span class="org-type">.*</span>1e12);
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hold off;
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<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
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<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
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xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'PSD of the measured displacement $\left[\frac{{ \mu m }^2}{Hz}\right]$'</span>)
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xlim([0.1, 500]); ylim([1e<span class="org-type">-</span>13, 1e3]);
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</pre>
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</div>
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<div id="org5008310" class="figure">
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<p><img src="figs/ground_motion_id31_psd_displacement.png" alt="ground_motion_id31_psd_displacement.png" />
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</p>
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<p><span class="figure-number">Figure 9: </span>Power Spectral Density of the measured displacement</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org1e033f3" class="outline-3">
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<h3 id="org1e033f3"><span class="section-number-3">2.7</span> Save</h3>
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<div class="outline-text-3" id="text-2-7">
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<p>
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We save the PSD of the ground motion for further analysis.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">save(<span class="org-string">'./mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gm'</span>, <span class="org-string">'psd_gv'</span>);
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org8d373fd" class="outline-3">
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<h3 id="org8d373fd"><span class="section-number-3">2.8</span> Comparison with other measurements of ground motion</h3>
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<div class="outline-text-3" id="text-2-8">
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<p>
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Now we will compare with other measurements.
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</p>
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</div>
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<div id="outline-container-orgad95d8a" class="outline-4">
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<h4 id="orgad95d8a"><span class="section-number-4">2.8.1</span> Load the measurement data</h4>
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<div class="outline-text-4" id="text-2-8-1">
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<p>
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First we load the measurement data.
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Here we have one measurement of the floor motion made at the ESRF in 2018, and one measurement made at CERN.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">id09 = load(<span class="org-string">'./mat/id09_floor_september2018.mat'</span>);
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cern = load(<span class="org-string">'./mat/ground_motion_dist.mat'</span>);
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-orgd5a5c4f" class="outline-4">
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<h4 id="orgd5a5c4f"><span class="section-number-4">2.8.2</span> Compute PSD of the measurements</h4>
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<div class="outline-text-4" id="text-2-8-2">
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<p>
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We compute the Power Spectral Densities of the measurements.
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</p>
|
|
<div class="org-src-container">
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<pre class="src src-matlab">Fs_id09 = 1<span class="org-type">/</span>(id09.time3(2)<span class="org-type">-</span>id09.time3(1));
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win_id09 = hanning(ceil(10<span class="org-type">*</span>Fs_id09));
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[id09_pxx, id09_f] = pwelch(1e<span class="org-type">-</span>6<span class="org-type">*</span>id09.x_y_z(<span class="org-type">:</span>, 3), win_id09, [], [], Fs_id09);
|
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</pre>
|
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</div>
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|
|
|
<div class="org-src-container">
|
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<pre class="src src-matlab">Fs_cern = 1<span class="org-type">/</span>(cern.gm.time(2)<span class="org-type">-</span>cern.gm.time(1));
|
|
win_cern = hanning(ceil(10<span class="org-type">*</span>Fs_cern));
|
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[cern_pxx, cern_f] = pwelch(cern.gm.signal, win_cern, [], [], Fs_cern);
|
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</pre>
|
|
</div>
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|
</div>
|
|
</div>
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|
|
|
<div id="outline-container-org4688ea2" class="outline-4">
|
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<h4 id="org4688ea2"><span class="section-number-4">2.8.3</span> Compare PSD of Cern, ID09 and ID31</h4>
|
|
<div class="outline-text-4" id="text-2-8-3">
|
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<p>
|
|
And we compare all the measurements (figure <a href="#orgbef99fa">10</a>).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot(id09_f, id09_pxx, <span class="org-string">'DisplayName'</span>, <span class="org-string">'ID09'</span>);
|
|
plot(cern_f, cern_pxx, <span class="org-string">'DisplayName'</span>, <span class="org-string">'CERN'</span>);
|
|
plot(f, psd_gm, <span class="org-string">'k'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'ID31'</span>);
|
|
hold off;
|
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'PSD [$m^2/Hz$]'</span>);
|
|
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
|
|
xlim([0.1, 500]);
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgbef99fa" class="figure">
|
|
<p><img src="figs/ground_motion_compare.png" alt="ground_motion_compare.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </span>Comparison of the PSD of the ground motion measured at different location</p>
|
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</div>
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</div>
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|
</div>
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</div>
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</div>
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</div>
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<div id="postamble" class="status">
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|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2020-11-12 jeu. 10:28</p>
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</div>
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</body>
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</html>
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