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<div id="content">
<h1 class="title">Ground Motion Measurements</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org51a66d9">1. Preprocessing of id31 ground motion measurement</a></li>
<li><a href="#orga36c9a4">2. Plots</a>
<ul>
<li><a href="#orgd4b4350">2.1. ID09 Measurements - Time Domain</a></li>
<li><a href="#org13c38c6">2.2. Compute PSD of ID09 ground motion</a></li>
<li><a href="#org8526d27">2.3. Compare PSD of Cern, ID09 and ID31</a></li>
</ul>
</li>
</ul>
</div>
</div>
<p>
<a href="../index.html">Back to main page</a>.
</p>
<div id="outline-container-org51a66d9" class="outline-2">
<h2 id="org51a66d9"><span class="section-number-2">1</span> Preprocessing of id31 ground motion measurement</h2>
<div class="outline-text-2" id="text-1">
<div class="org-src-container">
<pre class="src src-matlab">data = table2array<span style="color: #DCDCCC;">(</span>readtable<span style="color: #BFEBBF;">(</span><span style="color: #CC9393;">'./data/id31_camac_floor_PSD_october2014.txt'</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<p>
The first column is the frequency vector in Hz.
</p>
<div class="org-src-container">
<pre class="src src-matlab">gm.freqs = data<span style="color: #DCDCCC;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<p>
The other colmns are the PSD of the ground velocity in \(\frac{(\mu m/s)^2}{Hz}\) for the x,y,z axis.
It is converted to \(\frac{(m/s)^2}{Hz}\).
</p>
<div class="org-src-container">
<pre class="src src-matlab">gm.psd_vx = <span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">12</span><span style="color: #7CB8BB;">*</span>data<span style="color: #DCDCCC;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">)</span>;
gm.psd_vy = <span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">12</span><span style="color: #7CB8BB;">*</span>data<span style="color: #DCDCCC;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span>;
gm.psd_vz = <span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">12</span><span style="color: #7CB8BB;">*</span>data<span style="color: #DCDCCC;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">4</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<p>
Finally, we integrate the signal to obtain the power spectral density of the ground displacement.
</p>
<div class="org-src-container">
<pre class="src src-matlab">gm.psd_dx = gm.psd_vx<span style="color: #7CB8BB;">./</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">*</span>gm.freqs<span style="color: #DCDCCC;">)</span>;
gm.psd_dy = gm.psd_vy<span style="color: #7CB8BB;">./</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">*</span>gm.freqs<span style="color: #DCDCCC;">)</span>;
gm.psd_dz = gm.psd_vz<span style="color: #7CB8BB;">./</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">*</span>gm.freqs<span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<p>
The pre-processed data are saved.
</p>
<div class="org-src-container">
<pre class="src src-matlab">save<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./data/gm_esrf.mat', 'gm'</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-orga36c9a4" class="outline-2">
<h2 id="orga36c9a4"><span class="section-number-2">2</span> Plots</h2>
<div class="outline-text-2" id="text-2">
<p>
We load measurements made:
</p>
<ul class="org-ul">
<li>at ID31</li>
<li>at ID09</li>
<li>at CERN</li>
</ul>
<div class="org-src-container">
<pre class="src src-matlab">id31 = load<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./data/ground_motion_psd.mat'</span><span style="color: #DCDCCC;">)</span>;
id09 = load<span style="color: #DCDCCC;">(</span>'<span style="color: #7CB8BB;">./</span>data<span style="color: #7CB8BB;">/</span>id09_floor_september2018.mat'<span style="color: #DCDCCC;">)</span>;
cern = load<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./data/ground_motion_dist.mat'</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
</div>
<div id="outline-container-orgd4b4350" class="outline-3">
<h3 id="orgd4b4350"><span class="section-number-3">2.1</span> ID09 Measurements - Time Domain</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
plot<span style="color: #DCDCCC;">(</span>id09.time3, <span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span><span style="color: #7CB8BB;">*</span>id09.x_y_z<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span>, <span style="color: #CC9393;">'DisplayName', 'dx'</span><span style="color: #DCDCCC;">)</span>;
plot<span style="color: #DCDCCC;">(</span>id09.time3, <span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span><span style="color: #7CB8BB;">*</span>id09.x_y_z<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span>, <span style="color: #CC9393;">'DisplayName', 'dy'</span><span style="color: #DCDCCC;">)</span>;
plot<span style="color: #DCDCCC;">(</span>id09.time3, <span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span><span style="color: #7CB8BB;">*</span>id09.x_y_z<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span>, <span style="color: #CC9393;">'DisplayName', 'dz'</span><span style="color: #DCDCCC;">)</span>;
hold off;
xlabel<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'Time </span><span style="color: #BFEBBF;">[</span><span style="color: #CC9393;">s</span><span style="color: #BFEBBF;">]</span><span style="color: #CC9393;">'</span><span style="color: #DCDCCC;">)</span><span style="color: #CC9393;">; ylabel</span><span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'Velocity </span><span style="color: #BFEBBF;">[</span><span style="color: #CC9393;">$m/s$</span><span style="color: #BFEBBF;">]</span><span style="color: #CC9393;">'</span><span style="color: #DCDCCC;">)</span>;
legend<span style="color: #DCDCCC;">()</span>;
</pre>
</div>
<div id="orgce3682d" class="figure">
<p><img src="figs/id09_time_domain.png" alt="id09_time_domain.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Time domain data - ID09</p>
</div>
</div>
</div>
<div id="outline-container-org13c38c6" class="outline-3">
<h3 id="org13c38c6"><span class="section-number-3">2.2</span> Compute PSD of ID09 ground motion</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #DCDCCC;">[</span>id09_pxx, id09_f<span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span><span style="color: #7CB8BB;">*</span>id09.x_y_z<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span>, hanning<span style="color: #BFEBBF;">(</span>ceil<span style="color: #D0BF8F;">(</span>length<span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span><span style="color: #7CB8BB;">*</span>id09.x_y_z<span style="color: #9FC59F;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #9FC59F;">)</span><span style="color: #93E0E3;">)</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">10</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span>, <span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">(</span>id09.time3<span style="color: #D0BF8F;">(</span>end<span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">/</span><span style="color: #D0BF8F;">(</span>length<span style="color: #93E0E3;">(</span>id09.time3<span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">-</span> <span style="color: #BFEBBF;">1</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org8526d27" class="outline-3">
<h3 id="org8526d27"><span class="section-number-3">2.3</span> Compare PSD of Cern, ID09 and ID31</h3>
<div class="outline-text-3" id="text-2-3">
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
plot<span style="color: #DCDCCC;">(</span>cern.gm.freq, cern.gm.psd, <span style="color: #CC9393;">'DisplayName', 'CERN'</span><span style="color: #DCDCCC;">)</span>;
plot<span style="color: #DCDCCC;">(</span>id31.freqs, id31.psd_dx, <span style="color: #CC9393;">'DisplayName', 'ID31'</span><span style="color: #DCDCCC;">)</span>;
plot<span style="color: #DCDCCC;">(</span>id09_f, id09_pxx, <span style="color: #CC9393;">'DisplayName', '</span>ID09'<span style="color: #DCDCCC;">)</span>;
hold off;
<span style="color: #7CB8BB;">set</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">gca</span>, <span style="color: #CC9393;">'XScale', 'log'</span><span style="color: #DCDCCC;">)</span><span style="color: #CC9393;">; set</span><span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">gca, 'YScale', 'log'</span><span style="color: #DCDCCC;">)</span>;
xlabel<span style="color: #DCDCCC;">(</span>'Frequency <span style="color: #BFEBBF;">[</span>Hz<span style="color: #BFEBBF;">]</span>'<span style="color: #DCDCCC;">)</span>; ylabel<span style="color: #DCDCCC;">(</span>'PSD <span style="color: #BFEBBF;">[</span>$m<span style="color: #7CB8BB;">^</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">/</span>Hz$<span style="color: #BFEBBF;">]</span>'<span style="color: #DCDCCC;">)</span>;
legend<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'Location', 'northeast'</span><span style="color: #DCDCCC;">)</span>;
</pre>
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<div id="orgd6dc880" class="figure">
<p><img src="figs/psd_comparison.png" alt="psd_comparison.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Comparison of the PSD of ground motion</p>
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<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-03-15 ven. 11:42</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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