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< / head >
< body >
< div id = "content" >
< h1 class = "title" > SpeedGoat< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#org0d60e7b" > 1. Setup< / a > < / li >
< li > < a href = "#org7eef25c" > 2. Signal Processing< / a >
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< ul >
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< li > < a href = "#orgca77dc3" > 2.1. Load data< / a > < / li >
< li > < a href = "#org679612f" > 2.2. Time Domain Data< / a > < / li >
< li > < a href = "#org03c3a8f" > 2.3. Compute PSD< / a > < / li >
< li > < a href = "#org63e55c2" > 2.4. Take into account sensibility of Geophone< / a > < / li >
< li > < a href = "#orgbf05153" > 2.5. Transfer function between the two geophones< / a > < / li >
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< / ul >
< / li >
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< / ul >
< / div >
< / div >
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< div id = "outline-container-org0d60e7b" class = "outline-2" >
< h2 id = "org0d60e7b" > < span class = "section-number-2" > 1< / span > Setup< / h2 >
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< div class = "outline-text-2" id = "text-1" >
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< p >
Two L22 geophones are used.
They are placed on the ID31 granite.
They are leveled.
< / p >
< p >
The signals are amplified using voltage amplifier with a gain of 60dB.
The voltage amplifiers include a low pass filter with a cut-off frequency at 1kHz.
< / p >
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< div id = "org6a1fa99" class = "figure" >
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< p > < img src = "./figs/setup.jpg" alt = "setup.jpg" width = "500px" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Setup< / p >
< / div >
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< div id = "org30e0467" class = "figure" >
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< p > < img src = "./figs/geophones.jpg" alt = "geophones.jpg" width = "500px" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > Geophones< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org7eef25c" class = "outline-2" >
< h2 id = "org7eef25c" > < span class = "section-number-2" > 2< / span > Signal Processing< / h2 >
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< div class = "outline-text-2" id = "text-2" >
< / div >
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< div id = "outline-container-orgca77dc3" class = "outline-3" >
< h3 id = "orgca77dc3" > < span class = "section-number-3" > 2.1< / span > Load data< / h3 >
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< 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 > ;
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org679612f" class = "outline-3" >
< h3 id = "org679612f" > < span class = "section-number-3" > 2.2< / span > Time Domain Data< / h3 >
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< / pre >
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< div id = "org53abd46" class = "figure" >
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< p > < img src = "figs/data_time_domain.png" alt = "data_time_domain.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 3: < / span > Time domain Data< / p >
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< / div >
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< / div >
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< div id = "org2c53eef" class = "figure" >
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< / p >
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< p > < span class = "figure-number" > Figure 4: < / span > Time domain Data - Zoom< / p >
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< / div >
< / div >
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< h3 id = "org63e55c2" > < span class = "section-number-3" > 2.4< / span > Take into account sensibility of Geophone< / h3 >
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< div class = "outline-text-3" id = "text-2-4" >
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< p >
The Geophone used are L22.
< / p >
< div class = "org-src-container" >
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< 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 frequnecy [Hz]< / 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 > ;
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< / pre >
< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-type" > figure< / 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 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 >
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< / pre >
< / div >
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< div id = "orgf3fae86" class = "figure" >
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< p > < img src = "figs/geophone_sensibility.png" alt = "geophone_sensibility.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 5: < / span > Sensibility of the Geophone< / p >
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< / div >
< p >
We take into account the gain of the electronics.
The cut-off frequency is set at 1kHz.
< / p >
< ul class = "org-ul" >
< li class = "off" > < code > [  ]< / code > Check what is the order of the filter< / li >
< li class = "off" > < code > [  ]< / code > Maybe I should not use this filter as there is no high frequencies anyway?< / li >
< / ul >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > G0 = < span class = "org-highlight-numbers-number" > 60< / span > ; < span class = "org-comment" > % [dB]< / span >
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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 > ;
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< / pre >
< / div >
< 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 > 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 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 > ;
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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-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" > '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 > ;
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< / pre >
< / div >
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< div id = "orga831714" class = "figure" >
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< p > < img src = "figs/psd_velocity.png" alt = "psd_velocity.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 6: < / span > Spectral density of the velocity< / p >
< / div >
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< / div >
< / div >
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< div id = "outline-container-orgbf05153" class = "outline-3" >
< h3 id = "orgbf05153" > < span class = "section-number-3" > 2.5< / span > Transfer function between the two geophones< / h3 >
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< div class = "outline-text-3" id = "text-2-5" >
< div class = "org-src-container" >
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< 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 > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > length< span class = "org-rainbow-delimiters-depth-4" > (< / span > x1< span class = "org-rainbow-delimiters-depth-4" > )< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 100< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / 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 > ;
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< / 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 > ;
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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" > 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 >
< / div >
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< div id = "org4ff60a3" class = "figure" >
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< 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 >
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< / div >
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: Thomas Dehaeze< / p >
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< p class = "date" > Created: 2019-04-18 jeu. 09:47< / p >
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< p class = "validation" > < a href = "http://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
< / div >
< / body >
< / html >
