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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="#orgddb7761">1. Experimental Setup</a></li>
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<li><a href="#org828fff9">2. Measurement Analysis</a>
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<ul>
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<li><a href="#orgadf99c0">2.1. Load data</a></li>
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<li><a href="#org93551bb">2.2. Time domain plots</a></li>
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<li><a href="#orgfd0b3a8">2.3. Computation of the ASD of the measured voltage</a></li>
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<li><a href="#org4d7ad21">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="#org1b04be0">2.5. Computation of the ASD of the velocity and displacement</a></li>
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<li><a href="#orge570bf0">2.6. Comparison with other measurements of ground motion</a>
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<ul>
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<li><a href="#org9008f38">2.6.1. Load the measurement data</a></li>
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<li><a href="#org906cad8">2.6.2. Compute PSD of the measurements</a></li>
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<li><a href="#orgab58013">2.6.3. 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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<div id="outline-container-orgddb7761" class="outline-2">
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<h2 id="orgddb7761"><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="#org3e1d768">1</a> is an overview of multiple measurements made at famous location.
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</p>
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<div id="org3e1d768" 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-org828fff9" class="outline-2">
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<h2 id="org828fff9"><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="org1ffac8a"></a>
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</p>
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<div class="note">
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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-orgadf99c0" class="outline-3">
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<h3 id="orgadf99c0"><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-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_028.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</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-org93551bb" class="outline-3">
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<h3 id="org93551bb"><span class="section-number-3">2.2</span> Time domain plots</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<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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hold off;
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xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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</pre>
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</div>
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<div id="orga85fb0d" 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 id="outline-container-orgfd0b3a8" class="outline-3">
|
|
<h3 id="orgfd0b3a8"><span class="section-number-3">2.3</span> Computation of the ASD of the measured voltage</h3>
|
|
<div class="outline-text-3" id="text-2-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">dt = data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
|
|
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt;
|
|
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px_dc, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_dc<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org6f3989c" class="figure">
|
|
<p><img src="figs/ground_motion_id31_asd_volt.png" alt="ground_motion_id31_asd_volt.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>Amplitude Spectral Density of the measured Voltage</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4d7ad21" class="outline-3">
|
|
<h3 id="org4d7ad21"><span class="section-number-3">2.4</span> Scaling to take into account the sensibility of the geophone and the voltage amplifier</h3>
|
|
<div class="outline-text-3" id="text-2-4">
|
|
<p>
|
|
The Geophone used are L22. Their sensibility is shown on figure <a href="#org137d089">4</a>.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">S0 = <span class="org-highlight-numbers-number">88</span>; <span class="org-comment">% Sensitivity [V/(m/s)]</span>
|
|
f0 = <span class="org-highlight-numbers-number">2</span>; <span class="org-comment">% Cut-off frequency [Hz]</span>
|
|
|
|
S = S0<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>f0<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>f0<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org137d089" class="figure">
|
|
<p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>Sensibility of the Geophone</p>
|
|
</div>
|
|
|
|
<p>
|
|
We also take into account the gain of the electronics which is here set to be \(60dB\).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">G0_db = <span class="org-highlight-numbers-number">60</span>; <span class="org-comment">% [dB]</span>
|
|
|
|
G0 = <span class="org-highlight-numbers-number">10</span><span class="org-type">^</span><span class="org-rainbow-delimiters-depth-1">(</span>G0_db<span class="org-type">/</span><span class="org-highlight-numbers-number">20</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% [abs]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We divide the ASD measured (in \(\text{V}/\sqrt{\text{Hz}}\)) by the gain of the voltage amplifier to obtain the ASD of the voltage across the geophone.
|
|
We further divide the result by the sensibility of the Geophone to obtain the ASD of the velocity in \(m/s/\sqrt{Hz}\).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">scaling = <span class="org-highlight-numbers-number">1</span><span class="org-type">./</span>squeeze<span class="org-rainbow-delimiters-depth-1">(</span>abs<span class="org-rainbow-delimiters-depth-2">(</span>freqresp<span class="org-rainbow-delimiters-depth-3">(</span>G0<span class="org-type">*</span>S, f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1b04be0" class="outline-3">
|
|
<h3 id="org1b04be0"><span class="section-number-3">2.5</span> Computation of the ASD of the velocity and displacement</h3>
|
|
<div class="outline-text-3" id="text-2-5">
|
|
<p>
|
|
The ASD of the measured velocity is shown on figure <a href="#orgcf7bd1e">5</a>.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_dc<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">.*</span>scaling<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgcf7bd1e" class="figure">
|
|
<p><img src="figs/ground_motion_id31_asd_velocity.png" alt="ground_motion_id31_asd_velocity.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the Velocity</p>
|
|
</div>
|
|
|
|
<p>
|
|
We also plot the ASD in displacement (figure <a href="#orge1d92c4">6</a>);
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, <span class="org-rainbow-delimiters-depth-2">(</span>sqrt<span class="org-rainbow-delimiters-depth-3">(</span>px_dc<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">.*</span>scaling<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span><span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the displacement $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orge1d92c4" class="figure">
|
|
<p><img src="figs/ground_motion_id31_asd_displacement.png" alt="ground_motion_id31_asd_displacement.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the Displacement</p>
|
|
</div>
|
|
|
|
<p>
|
|
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="#org149605d">7</a>).
|
|
One can then compare this curve with the figure <a href="#org3e1d768">1</a>.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, <span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">(</span>sqrt<span class="org-rainbow-delimiters-depth-4">(</span>px_dc<span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">.*</span>scaling<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">./</span><span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">.*</span><span class="org-highlight-numbers-number">1e6</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>PSD of the measured displacement $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-rainbow-delimiters-depth-4">{</span> <span class="org-type">\</span>mu m <span class="org-rainbow-delimiters-depth-4">}</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">}{</span>Hz<span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org149605d" class="figure">
|
|
<p><img src="figs/ground_motion_id31_psd_displacement.png" alt="ground_motion_id31_psd_displacement.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>Power Spectral Density of the measured displacement</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge570bf0" class="outline-3">
|
|
<h3 id="orge570bf0"><span class="section-number-3">2.6</span> Comparison with other measurements of ground motion</h3>
|
|
<div class="outline-text-3" id="text-2-6">
|
|
<p>
|
|
Now we will compare with other measurements.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org9008f38" class="outline-4">
|
|
<h4 id="org9008f38"><span class="section-number-4">2.6.1</span> Load the measurement data</h4>
|
|
<div class="outline-text-4" id="text-2-6-1">
|
|
<p>
|
|
First we load the measurement data.
|
|
Here we have one measurement of the floor motion made at the ESRF in 2018, and one measurement made at CERN.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">id09 = load<span class="org-rainbow-delimiters-depth-1">(</span>'<span class="org-type">./</span>mat<span class="org-type">/</span>id09_floor_september2018.mat'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
cern = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/ground_motion_dist.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org906cad8" class="outline-4">
|
|
<h4 id="org906cad8"><span class="section-number-4">2.6.2</span> Compute PSD of the measurements</h4>
|
|
<div class="outline-text-4" id="text-2-6-2">
|
|
<p>
|
|
We compute the Power Spectral Densities of the measurements.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Fs_id09 = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span>id09.time3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>id09.time3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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win_id09 = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs_id09<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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<span class="org-rainbow-delimiters-depth-1">[</span>id09_pxx, id09_f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">6</span><span class="org-type">*</span>id09.x_y_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, win_id09, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs_id09<span class="org-rainbow-delimiters-depth-1">)</span>;
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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 = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span>cern.gm.time<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>cern.gm.time<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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win_cern = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs_cern<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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|
<span class="org-rainbow-delimiters-depth-1">[</span>cern_pxx, cern_f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>cern.gm.signal, win_cern, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs_cern<span class="org-rainbow-delimiters-depth-1">)</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-orgab58013" class="outline-4">
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<h4 id="orgab58013"><span class="section-number-4">2.6.3</span> Compare PSD of Cern, ID09 and ID31</h4>
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<div class="outline-text-4" id="text-2-6-3">
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<p>
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And we compare all the measurements (figure <a href="#org2a2b94e">8</a>).
|
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</p>
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|
|
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<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
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|
plot<span class="org-rainbow-delimiters-depth-1">(</span>id09_f, id09_pxx, <span class="org-string">'DisplayName', '</span>ID09'<span class="org-rainbow-delimiters-depth-1">)</span>;
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|
plot<span class="org-rainbow-delimiters-depth-1">(</span>cern_f, cern_pxx, <span class="org-string">'DisplayName', 'CERN'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, <span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">(</span>sqrt<span class="org-rainbow-delimiters-depth-4">(</span>px_dc<span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">.*</span>scaling<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">./</span><span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span>, <span class="org-string">'k', 'DisplayName', 'ID31'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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|
hold off;
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|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XScale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'YScale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span>'Frequency <span class="org-rainbow-delimiters-depth-2">[</span>Hz<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span>'PSD <span class="org-rainbow-delimiters-depth-2">[</span>$m<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span>Hz$<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
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|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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|
</pre>
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|
</div>
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|
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<div id="org2a2b94e" class="figure">
|
|
<p><img src="figs/ground_motion_compare.png" alt="ground_motion_compare.png" />
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|
</p>
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|
<p><span class="figure-number">Figure 8: </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>
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|
<p class="date">Created: 2019-05-10 ven. 17:51</p>
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|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</body>
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</html>
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