From f7b4a29c9673d2e16a1738605be50b5941ba1ae3 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Fri, 3 May 2019 11:32:54 +0200 Subject: [PATCH] Correct unit of curves and scalling --- .../figs/asd_displacement.png | Bin 118159 -> 145329 bytes huddle-test-geophones/figs/asd_voltage.png | Bin 0 -> 137622 bytes huddle-test-geophones/figs/coh_geophones.png | Bin 55586 -> 56146 bytes .../figs/data_time_domain.png | Bin 42664 -> 42823 bytes .../figs/data_time_domain_zoom.png | Bin 47905 -> 47982 bytes .../figs/geophone_sensibility.png | Bin 63774 -> 56623 bytes .../figs/intrumental_noise_V.png | Bin 181041 -> 173121 bytes .../figs/intrumental_noise_velocity.png | Bin 160778 -> 156666 bytes huddle-test-geophones/figs/psd_velocity.png | Bin 142661 -> 139017 bytes huddle-test-geophones/figs/tf_geophones.png | Bin 102208 -> 101426 bytes huddle-test-geophones/index.html | Bin 59963 -> 64118 bytes huddle-test-geophones/index.org | 66 ++++++++++++------ 12 files changed, 46 insertions(+), 20 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#+end_src +Then we compute the Power Spectral Density using =pwelch= function. #+begin_src matlab :results none [pxx1, f] = pwelch(x1, win, [], [], Fs); [pxx2, ~] = pwelch(x2, win, [], [], Fs); #+end_src +And we plot the result on figure [[fig:asd_voltage]]. + +#+begin_src matlab :results none + figure; + hold on; + plot(f, sqrt(pxx1)); + plot(f, sqrt(pxx2)); + hold off; + set(gca, 'xscale', 'log'); + set(gca, 'yscale', 'log'); + xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$') + xlim([0.1, 500]); +#+end_src + +#+NAME: fig:asd_voltage +#+HEADER: :tangle no :exports results :results value raw replace :noweb yes +#+begin_src matlab :var filepath="figs/asd_voltage.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:asd_voltage +#+CAPTION: Amplitude Spectral Density of the measured voltage +#+RESULTS: fig:asd_voltage +[[file:figs/asd_voltage.png]] + ** Scaling to take into account the sensibility of the geophone and the voltage amplifier -The Geophone used are L22. -Their sensibility are shown on figure [[fig:geophone_sensibility]]. +The Geophone used are L22. Their sensibility is shown on figure [[fig:geophone_sensibility]]. #+begin_src matlab :results none S0 = 88; % Sensitivity [V/(m/s)] f0 = 2; % Cut-off frequnecy [Hz] - S = (s/2/pi/f0)/(1+s/2/pi/f0); + + S = S0*(s/2/pi/f0)/(1+s/2/pi/f0); #+end_src #+begin_src matlab :results none :exports none figure; - bodeFig({S}); - ylabel('Amplitude [V/(m/s)]') + bodeFig({S}, logspace(-1, 2, 1000)); + ylabel('Amplitude $\left[\frac{V}{m/s}\right]$') #+end_src #+NAME: fig:geophone_sensibility @@ -144,19 +171,18 @@ Their sensibility are shown on figure [[fig:geophone_sensibility]]. We also take into account the gain of the electronics which is here set to be $60dB$. -The amplifiers also include a low pass filter with a cut-off frequency set at 1kHz. #+begin_src matlab :results none - G0 = 60; % [dB] + G0_db = 60; % [dB] - G = 10^(G0/20)/(1+s/2/pi/1000); + G0 = 10^(60/G0_db); % [abs] #+end_src -We divide the ASD measured (in $\text{V}/\sqrt{\text{Hz}}$) by the transfer function of the voltage amplifier to obtain the ASD of the voltage across the geophone. +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 $m/s/\sqrt{Hz}$. #+begin_src matlab :results none - scaling = 1./squeeze(abs(freqresp(G*S, f, 'Hz'))); + scaling = 1./squeeze(abs(freqresp(G0*S, f, 'Hz'))); #+end_src ** Computation of the ASD of the velocity @@ -170,7 +196,7 @@ The ASD of the measured velocity is shown on figure [[fig:psd_velocity]]. hold off; set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); - xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]') + xlabel('Frequency [Hz]'); ylabel('ASD of the measured Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$') xlim([0.1, 500]); #+end_src @@ -181,7 +207,7 @@ The ASD of the measured velocity is shown on figure [[fig:psd_velocity]]. #+end_src #+NAME: fig:psd_velocity -#+CAPTION: Spectral density of the velocity +#+CAPTION: Amplitude Spectral Density of the Velocity #+RESULTS: fig:psd_velocity [[file:figs/psd_velocity.png]] @@ -190,11 +216,11 @@ We also plot the ASD in displacement (figure [[fig:asd_displacement]]); #+begin_src matlab :results none figure; hold on; - plot(f, (pxx1.*scaling./f).^2); - plot(f, (pxx2.*scaling./f).^2); + plot(f, (sqrt(pxx1).*scaling)./(2*pi*f)); + plot(f, (sqrt(pxx2).*scaling)./(2*pi*f)); hold off; set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); - xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]') + xlabel('Frequency [Hz]'); ylabel('ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$') xlim([0.1, 500]); #+end_src @@ -205,7 +231,7 @@ We also plot the ASD in displacement (figure [[fig:asd_displacement]]); #+end_src #+NAME: fig:asd_displacement -#+CAPTION: Amplitude Spectral Density of the displacement as measured by the geophones +#+CAPTION: Amplitude Spectral Density of the Displacement #+RESULTS: fig:asd_displacement [[file:figs/asd_displacement.png]] @@ -232,7 +258,7 @@ We also compute the coherence between the two signals (figure [[fig:coh_geophone set(gca, 'xscale', 'log'); ylim([-180, 180]); yticks([-180, -90, 0, 90, 180]); - xlabel('Frequency [Hz]'); ylabel('Phase'); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); linkaxes([ax1,ax2],'x'); xlim([0.1, 500]); @@ -338,7 +364,7 @@ The instrumental noise is computed below. The result in V^2/Hz is shown on figur plot(f, pxxN, 'k--'); hold off; set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); - xlabel('Frequency [Hz]'); ylabel('PSD [$V^2/Hz$]'); + xlabel('Frequency [Hz]'); ylabel('PSD of the measured Voltage $\left[\frac{V^2}{Hz}\right]$'); xlim([0.1, 500]); #+end_src @@ -362,7 +388,7 @@ This is then further converted into velocity and compared with the ground veloci plot(f, sqrt(pxxN).*scaling, 'k--'); hold off; set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); - xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]'); + xlabel('Frequency [Hz]'); ylabel('ASD of the Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'); xlim([0.1, 500]); #+end_src

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