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Add transfer function between geophones

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Thomas Dehaeze 2019-04-18 09:20:31 +02:00
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4 changed files with 131 additions and 58 deletions
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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2019-04-17 mer. 18:25 --> <!-- 2019-04-18 jeu. 09:20 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1" />
<title>SpeedGoat</title> <title>SpeedGoat</title>
@ -254,21 +254,22 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orgb04530e">1. Setup</a></li> <li><a href="#org4a1a539">1. Setup</a></li>
<li><a href="#org66e33f8">2. Signal Processing</a> <li><a href="#org474b62b">2. Signal Processing</a>
<ul> <ul>
<li><a href="#org245daf7">2.1. Load data</a></li> <li><a href="#org336ec3e">2.1. Load data</a></li>
<li><a href="#orge44dc4a">2.2. Time Domain Data</a></li> <li><a href="#org2cf9057">2.2. Time Domain Data</a></li>
<li><a href="#org098f046">2.3. Compute PSD</a></li> <li><a href="#orgb221001">2.3. Compute PSD</a></li>
<li><a href="#org761bb7b">2.4. Take into account sensibility of Geophone</a></li> <li><a href="#org655ba9d">2.4. Take into account sensibility of Geophone</a></li>
<li><a href="#orgd36c537">2.5. Transfer function between the two geophones</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-orgb04530e" class="outline-2"> <div id="outline-container-org4a1a539" class="outline-2">
<h2 id="orgb04530e"><span class="section-number-2">1</span> Setup</h2> <h2 id="org4a1a539"><span class="section-number-2">1</span> Setup</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
Two L22 geophones are used. Two L22 geophones are used.
@ -282,14 +283,14 @@ The voltage amplifiers include a low pass filter with a cut-off frequency at 1kH
</p> </p>
<div id="org80f30b9" class="figure"> <div id="orga919daa" class="figure">
<p><img src="./figs/setup.jpg" alt="setup.jpg" width="500px" /> <p><img src="./figs/setup.jpg" alt="setup.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Setup</p> <p><span class="figure-number">Figure 1: </span>Setup</p>
</div> </div>
<div id="org4d7f624" class="figure"> <div id="orgb58846e" class="figure">
<p><img src="./figs/geophones.jpg" alt="geophones.jpg" width="500px" /> <p><img src="./figs/geophones.jpg" alt="geophones.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Geophones</p> <p><span class="figure-number">Figure 2: </span>Geophones</p>
@ -297,38 +298,38 @@ The voltage amplifiers include a low pass filter with a cut-off frequency at 1kH
</div> </div>
</div> </div>
<div id="outline-container-org66e33f8" class="outline-2"> <div id="outline-container-org474b62b" class="outline-2">
<h2 id="org66e33f8"><span class="section-number-2">2</span> Signal Processing</h2> <h2 id="org474b62b"><span class="section-number-2">2</span> Signal Processing</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
</div> </div>
<div id="outline-container-org245daf7" class="outline-3"> <div id="outline-container-org336ec3e" class="outline-3">
<h3 id="org245daf7"><span class="section-number-3">2.1</span> Load data</h3> <h3 id="org336ec3e"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load<span style="color: #458588;">(</span><span style="color: #b8bb26;">'mat/data_001.mat', 't', 'x1', 'x2'</span><span style="color: #458588;">)</span>; <pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_001.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
dt = t<span style="color: #458588;">(</span><span style="color: #d3869b;">2</span><span style="color: #458588;">)</span> <span style="color: #d3869b;">-</span> t<span style="color: #458588;">(</span><span style="color: #d3869b;">1</span><span style="color: #458588;">)</span>; dt = t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orge44dc4a" class="outline-3"> <div id="outline-container-org2cf9057" class="outline-3">
<h3 id="orge44dc4a"><span class="section-number-3">2.2</span> Time Domain Data</h3> <h3 id="org2cf9057"><span class="section-number-3">2.2</span> Time Domain Data</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span style="color: #d3869b;">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span style="color: #458588;">(</span>t, x1<span style="color: #458588;">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>t, x1<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span style="color: #458588;">(</span>t, x2<span style="color: #458588;">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>t, x2<span class="org-rainbow-delimiters-depth-1">)</span>;
hold off; hold off;
xlabel<span style="color: #458588;">(</span><span style="color: #b8bb26;">'Time </span><span style="color: #b16286;">[</span><span style="color: #b8bb26;">s</span><span style="color: #b16286;">]</span><span style="color: #b8bb26;">'</span><span style="color: #458588;">)</span>; 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-rainbow-delimiters-depth-1">)</span>;
ylabel<span style="color: #458588;">(</span><span style="color: #b8bb26;">'Voltage </span><span style="color: #b16286;">[</span><span style="color: #b8bb26;">V</span><span style="color: #b16286;">]</span><span style="color: #b8bb26;">'</span><span style="color: #458588;">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</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>;
xlim<span style="color: #458588;">(</span><span style="color: #b16286;">[</span>t<span style="color: #8ec07c;">(</span><span style="color: #d3869b;">1</span><span style="color: #8ec07c;">)</span>, t<span style="color: #8ec07c;">(</span>end<span style="color: #8ec07c;">)</span><span style="color: #b16286;">]</span><span style="color: #458588;">)</span>; xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, t<span class="org-rainbow-delimiters-depth-3">(</span>end<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> </pre>
</div> </div>
<div id="org79270e7" class="figure"> <div id="orgc7e063b" class="figure">
<p><img src="figs/data_time_domain.png" alt="data_time_domain.png" /> <p><img src="figs/data_time_domain.png" alt="data_time_domain.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Time domain Data</p> <p><span class="figure-number">Figure 3: </span>Time domain Data</p>
@ -336,19 +337,19 @@ xlim<span style="color: #458588;">(</span><span style="color: #b16286;">[</span>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span style="color: #d3869b;">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span style="color: #458588;">(</span>t, x1<span style="color: #458588;">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>t, x1<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span style="color: #458588;">(</span>t, x2<span style="color: #458588;">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>t, x2<span class="org-rainbow-delimiters-depth-1">)</span>;
hold off; hold off;
xlabel<span style="color: #458588;">(</span><span style="color: #b8bb26;">'Time </span><span style="color: #b16286;">[</span><span style="color: #b8bb26;">s</span><span style="color: #b16286;">]</span><span style="color: #b8bb26;">'</span><span style="color: #458588;">)</span>; 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-rainbow-delimiters-depth-1">)</span>;
ylabel<span style="color: #458588;">(</span><span style="color: #b8bb26;">'Voltage </span><span style="color: #b16286;">[</span><span style="color: #b8bb26;">V</span><span style="color: #b16286;">]</span><span style="color: #b8bb26;">'</span><span style="color: #458588;">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</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>;
xlim<span style="color: #458588;">(</span><span style="color: #b16286;">[</span><span style="color: #d3869b;">0</span> <span style="color: #d3869b;">1</span><span style="color: #b16286;">]</span><span style="color: #458588;">)</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-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
<div id="org8d2af88" class="figure"> <div id="orgf38ff94" class="figure">
<p><img src="figs/data_time_domain_zoom.png" alt="data_time_domain_zoom.png" /> <p><img src="figs/data_time_domain_zoom.png" alt="data_time_domain_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Time domain Data - Zoom</p> <p><span class="figure-number">Figure 4: </span>Time domain Data - Zoom</p>
@ -356,39 +357,39 @@ xlim<span style="color: #458588;">(</span><span style="color: #b16286;">[</span>
</div> </div>
</div> </div>
<div id="outline-container-org098f046" class="outline-3"> <div id="outline-container-orgb221001" class="outline-3">
<h3 id="org098f046"><span class="section-number-3">2.3</span> Compute PSD</h3> <h3 id="orgb221001"><span class="section-number-3">2.3</span> Compute PSD</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span style="color: #458588;">[</span>pxx1, f1<span style="color: #458588;">]</span> = pwelch<span style="color: #458588;">(</span>x1, hanning<span style="color: #b16286;">(</span>ceil<span style="color: #8ec07c;">(</span>length<span style="color: #d65d0e;">(</span>t<span style="color: #d65d0e;">)</span><span style="color: #d3869b;">/</span><span style="color: #d3869b;">100</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>, <span style="color: #d3869b;">0</span>, <span style="color: #b16286;">[]</span>, <span style="color: #d3869b;">1</span><span style="color: #d3869b;">/</span>dt<span style="color: #458588;">)</span>; <pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx1, f1<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>x1, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-1">)</span>;
<span style="color: #458588;">[</span>pxx2, f2<span style="color: #458588;">]</span> = pwelch<span style="color: #458588;">(</span>x2, hanning<span style="color: #b16286;">(</span>ceil<span style="color: #8ec07c;">(</span>length<span style="color: #d65d0e;">(</span>t<span style="color: #d65d0e;">)</span><span style="color: #d3869b;">/</span><span style="color: #d3869b;">100</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>, <span style="color: #d3869b;">0</span>, <span style="color: #b16286;">[]</span>, <span style="color: #d3869b;">1</span><span style="color: #d3869b;">/</span>dt<span style="color: #458588;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx2, f2<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>x2, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org761bb7b" class="outline-3"> <div id="outline-container-org655ba9d" class="outline-3">
<h3 id="org761bb7b"><span class="section-number-3">2.4</span> Take into account sensibility of Geophone</h3> <h3 id="org655ba9d"><span class="section-number-3">2.4</span> Take into account sensibility of Geophone</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
The Geophone used are L22. The Geophone used are L22.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">S0 = <span style="color: #d3869b;">88</span>; <span style="color: #7c6f64;">% Sensitivity [V/(m/s)]</span> <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 style="color: #d3869b;">2</span>; <span style="color: #7c6f64;">% Cut-off frequnecy [Hz]</span> f0 = <span class="org-highlight-numbers-number">2</span>; <span class="org-comment">% Cut-off frequnecy [Hz]</span>
S = <span style="color: #458588;">(</span>s<span style="color: #d3869b;">/</span><span style="color: #d3869b;">2</span><span style="color: #d3869b;">/</span><span style="color: #d3869b;">pi</span><span style="color: #d3869b;">/</span>f0<span style="color: #458588;">)</span><span style="color: #d3869b;">/</span><span style="color: #458588;">(</span><span style="color: #d3869b;">1</span><span style="color: #d3869b;">+</span>s<span style="color: #d3869b;">/</span><span style="color: #d3869b;">2</span><span style="color: #d3869b;">/</span><span style="color: #d3869b;">pi</span><span style="color: #d3869b;">/</span>f0<span style="color: #458588;">)</span>; S = <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> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span style="color: #d3869b;">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
bodeFig<span style="color: #458588;">(</span><span style="color: #b16286;">{</span>S<span style="color: #b16286;">}</span><span style="color: #458588;">)</span>; bodeFig<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span>S<span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>;
ylabel<span style="color: #458588;">(</span><span style="color: #b8bb26;">'Amplitude </span><span style="color: #b16286;">[</span><span style="color: #b8bb26;">V/</span><span style="color: #8ec07c;">(</span><span style="color: #b8bb26;">m/s</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">]</span><span style="color: #b8bb26;">'</span><span style="color: #458588;">)</span> ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Amplitude </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-3">(</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></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>
</pre> </pre>
</div> </div>
<div id="org2161300" class="figure"> <div id="org8d58394" class="figure">
<p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" /> <p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Sensibility of the Geophone</p> <p><span class="figure-number">Figure 5: </span>Sensibility of the Geophone</p>
@ -406,37 +407,74 @@ The cut-off frequency is set at 1kHz.
</ul> </ul>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">G0 = <span style="color: #d3869b;">60</span>; <span style="color: #7c6f64;">% [dB]</span> <pre class="src src-matlab">G0 = <span class="org-highlight-numbers-number">60</span>; <span class="org-comment">% [dB]</span>
G = G0<span style="color: #d3869b;">/</span><span style="color: #458588;">(</span><span style="color: #d3869b;">1</span><span style="color: #d3869b;">+</span>s<span style="color: #d3869b;">/</span><span style="color: #d3869b;">2</span><span style="color: #d3869b;">/</span><span style="color: #d3869b;">pi</span><span style="color: #d3869b;">/</span><span style="color: #d3869b;">1000</span><span style="color: #458588;">)</span>; G = G0<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><span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span style="color: #d3869b;">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span style="color: #458588;">(</span>f1, sqrt<span style="color: #b16286;">(</span>pxx1<span style="color: #b16286;">)</span><span style="color: #d3869b;">./</span>squeeze<span style="color: #b16286;">(</span>abs<span style="color: #8ec07c;">(</span>freqresp<span style="color: #d65d0e;">(</span>G, f1, <span style="color: #b8bb26;">'Hz'</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #b8bb26;">./squeeze</span><span style="color: #b16286;">(</span><span style="color: #b8bb26;">abs</span><span style="color: #8ec07c;">(</span><span style="color: #b8bb26;">freqresp</span><span style="color: #d65d0e;">(</span><span style="color: #b8bb26;">S, f1, 'Hz'</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f1, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx1<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>squeeze<span class="org-rainbow-delimiters-depth-2">(</span>abs<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G, f1, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">./squeeze</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">(</span></span><span class="org-string">abs</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">(</span></span><span class="org-string">freqresp</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">(</span></span><span class="org-string">S, f1, 'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</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>;
plot<span style="color: #458588;">(</span>f2, sqrt<span style="color: #b16286;">(</span>pxx2<span style="color: #b16286;">)</span><span style="color: #d3869b;">./</span>squeeze<span style="color: #b16286;">(</span>abs<span style="color: #8ec07c;">(</span>freqresp<span style="color: #d65d0e;">(</span>G, f2, <span style="color: #b8bb26;">'Hz'</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #b8bb26;">./squeeze</span><span style="color: #b16286;">(</span><span style="color: #b8bb26;">abs</span><span style="color: #8ec07c;">(</span><span style="color: #b8bb26;">freqresp</span><span style="color: #d65d0e;">(</span><span style="color: #b8bb26;">S, f2, 'Hz'</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f2, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx2<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>squeeze<span class="org-rainbow-delimiters-depth-2">(</span>abs<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G, f2, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">./squeeze</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">(</span></span><span class="org-string">abs</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">(</span></span><span class="org-string">freqresp</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">(</span></span><span class="org-string">S, f2, 'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</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>;
hold off; hold off;
<span style="color: #d3869b;">set</span><span style="color: #458588;">(</span><span style="color: #83a598;">gca</span>, <span style="color: #b8bb26;">'xscale', 'log'</span><span style="color: #458588;">)</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">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span style="color: #d3869b;">set</span><span style="color: #458588;">(</span><span style="color: #83a598;">gca</span>, <span style="color: #b8bb26;">'yscale', 'log'</span><span style="color: #458588;">)</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 style="color: #458588;">(</span><span style="color: #b8bb26;">'Frequency </span><span style="color: #b16286;">[</span><span style="color: #b8bb26;">Hz</span><span style="color: #b16286;">]</span><span style="color: #b8bb26;">'</span><span style="color: #458588;">)</span><span style="color: #b8bb26;">; ylabel</span><span style="color: #458588;">(</span><span style="color: #b8bb26;">'PSD </span><span style="color: #b16286;">[</span><span style="color: #b8bb26;">m/s/sqrt</span><span style="color: #8ec07c;">(</span><span style="color: #b8bb26;">Hz</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">]</span><span style="color: #b8bb26;">'</span><span style="color: #458588;">)</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">'PSD </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s/sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">(</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></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>
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</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> </pre>
</div> </div>
<div id="org6ace9e8" class="figure"> <div id="org9606210" class="figure">
<p><img src="figs/psd_velocity.png" alt="psd_velocity.png" /> <p><img src="figs/psd_velocity.png" alt="psd_velocity.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Spectral density of the velocity</p> <p><span class="figure-number">Figure 6: </span>Spectral density of the velocity</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgd36c537" class="outline-3">
<h3 id="orgd36c537"><span class="section-number-3">2.5</span> Transfer function between the two geophones</h3>
<div class="outline-text-3" id="text-2-5">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>T12, f12<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>x1, x2, hanning<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt<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>;
ax1 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f12, abs<span class="org-rainbow-delimiters-depth-2">(</span>T12<span class="org-rainbow-delimiters-depth-2">)</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">'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>;
<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">'XTickLabel'</span>,<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><span class="org-string">'Magnitude'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
ax2 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f12, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T12<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</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">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
yticks<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</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">'Phase'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
linkaxes<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>ax1,ax2<span class="org-rainbow-delimiters-depth-2">]</span>,<span class="org-string">'x'</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">2</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="org9571503" class="figure">
<p><img src="figs/tf_geophones.png" alt="tf_geophones.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Estimated transfer function between the two geophones</p>
</div>
</div>
</div>
</div> </div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p> <p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-04-17 mer. 18:25</p> <p class="date">Created: 2019-04-18 jeu. 09:20</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>

39
huddle-test-geophones/index.org
View File

@ -96,8 +96,8 @@ The voltage amplifiers include a low pass filter with a cut-off frequency at 1kH
** Compute PSD ** Compute PSD
#+begin_src matlab :results none #+begin_src matlab :results none
[pxx1, f1] = pwelch(x1, hanning(ceil(length(t)/100)), 0, [], 1/dt); [pxx1, f1] = pwelch(x1, hanning(ceil(1/dt)), 0, [], 1/dt);
[pxx2, f2] = pwelch(x2, hanning(ceil(length(t)/100)), 0, [], 1/dt); [pxx2, f2] = pwelch(x2, hanning(ceil(1/dt)), 0, [], 1/dt);
#+end_src #+end_src
** Take into account sensibility of Geophone ** Take into account sensibility of Geophone
@ -147,6 +147,7 @@ The cut-off frequency is set at 1kHz.
set(gca, 'xscale', 'log'); set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]') xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
xlim([2, 500]);
#+end_src #+end_src
#+NAME: fig:psd_velocity #+NAME: fig:psd_velocity
@ -159,3 +160,37 @@ The cut-off frequency is set at 1kHz.
#+CAPTION: Spectral density of the velocity #+CAPTION: Spectral density of the velocity
#+RESULTS: fig:psd_velocity #+RESULTS: fig:psd_velocity
[[file:figs/psd_velocity.png]] [[file:figs/psd_velocity.png]]
** Transfer function between the two geophones
#+begin_src matlab :results none
[T12, f12] = tfestimate(x1, x2, hanning(1/dt), 0, [], 1/dt);
#+end_src
#+begin_src matlab :results none
figure;
ax1 = subplot(2, 1, 1);
plot(f12, abs(T12));
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
set(gca, 'XTickLabel',[]);
ylabel('Magnitude');
ax2 = subplot(2, 1, 2);
plot(f12, mod(180+180/pi*phase(T12), 360)-180);
set(gca, 'xscale', 'log');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
xlabel('Frequency [Hz]'); ylabel('Phase');
linkaxes([ax1,ax2],'x');
xlim([2, 500]);
#+end_src
#+NAME: fig:tf_geophones
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/tf_geophones.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:tf_geophones
#+CAPTION: Estimated transfer function between the two geophones
#+RESULTS: fig:tf_geophones
[[file:figs/tf_geophones.png]]