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Reworked the ground motion page

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This commit is contained in:
Thomas Dehaeze 2019-05-10 17:52:14 +02:00
parent ed61db2f86
commit 5208373cf6
34 changed files with 441 additions and 964 deletions
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2018-01-12 - Marc/index.html
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2018-10-15 - Marc/index.html
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31
Ground Motion/analyze_ground_motion.m
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@ -1,31 +0,0 @@
%%
clear; close all; clc;
%%
id31 = load('ground_motion_psd.mat');
id09 = load('id09_floor_september2018.mat');
cern = load('ground_motion_dist.mat');
%% ID09 Measurements - Time Domain
figure;
hold on;
plot(id09.time3, 1e-6*id09.x_y_z(:, 1), 'DisplayName', 'dx');
plot(id09.time3, 1e-6*id09.x_y_z(:, 2), 'DisplayName', 'dy');
plot(id09.time3, 1e-6*id09.x_y_z(:, 3), 'DisplayName', 'dz');
hold off;
xlabel('Time [s]'); ylabel('Velocity [$m/s$]');
legend();
% Compute PSD of ID09 ground motion
[id09_pxx, id09_f] = pwelch(1e-6*id09.x_y_z(:, 1), hanning(ceil(length(1e-6*id09.x_y_z(:, 1))/10)), 0, [], 1/(id09.time3(end)/(length(id09.time3) - 1)));
%% Compare PSD of Cern, ID09 and ID31
figure;
hold on;
plot(cern.gm.freq, cern.gm.psd, 'DisplayName', 'CERN');
plot(id31.freqs, id31.psd_dx, 'DisplayName', 'ID31');
plot(id09_f, id09_pxx, 'DisplayName', 'ID09');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m^2/Hz$]');
legend('Location', 'northeast');

24
Ground Motion/convert_txt_to_mat.m
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@ -1,24 +0,0 @@
%%
clear; close all; clc;
%%
% 1st column is frequency in Hz
% Then PSD's in (um/s)^2/Hz) for the x,y,z axis respectively.
%%
data = table2array(readtable('id31_camac_floor_PSD_october2014.txt'));
%%
gm.freqs = data(:, 1);
gm.psd_vx = 1e-12*data(:, 2); % [(um/s)^2/Hz] => [(m/s)^2/Hz]
gm.psd_vy = 1e-12*data(:, 3); % [(um/s)^2/Hz] => [(m/s)^2/Hz]
gm.psd_vz = 1e-12*data(:, 4); % [(um/s)^2/Hz] => [(m/s)^2/Hz]
gm.psd_dx = gm.psd_vx./(2*pi*gm.freqs); % velocity to displacement [m^2/Hz]
gm.psd_dy = gm.psd_vy./(2*pi*gm.freqs); % velocity to displacement [m^2/Hz]
gm.psd_dz = gm.psd_vz./(2*pi*gm.freqs); % velocity to displacement [m^2/Hz]
%%
save('../../Matlab/data/signals/gm_esrf.mat', 'gm');

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Ground Motion/data/ground_motion_psd.mat
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800
Ground Motion/data/id31_camac_floor_PSD_october2014.txt
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@ -1,800 +0,0 @@
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9.9749687108886107e+01 1.8443184617283892e-10 3.9040203324277634e-11 6.2439565197587218e-11
9.9874843554443061e+01 1.2868499284992653e-10 4.9309265659747338e-11 1.6915869623320508e-10
1.0000000000000000e+02 2.8246842701623307e-10 9.8111792939866586e-11 8.5125871745196939e-10

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#+TITLE: Ground Motion Measurements
#+SETUPFILE: ../config.org
* Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
* Preprocessing of id31 ground motion measurement
#+begin_src matlab :exports code :results silent
data = table2array(readtable('./data/id31_camac_floor_PSD_october2014.txt'));
#+end_src
The first column is the frequency vector in Hz.
#+begin_src matlab :exports code :results silent
gm.freqs = data(:, 1);
#+end_src
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 $\frac{(m/s)^2}{Hz}$.
#+begin_src matlab :exports code :results silent
gm.psd_vx = 1e-12*data(:, 2);
gm.psd_vy = 1e-12*data(:, 3);
gm.psd_vz = 1e-12*data(:, 4);
#+end_src
Finally, we integrate the signal to obtain the power spectral density of the ground displacement.
#+begin_src matlab :results silent
gm.psd_dx = gm.psd_vx./(2*pi*gm.freqs);
gm.psd_dy = gm.psd_vy./(2*pi*gm.freqs);
gm.psd_dz = gm.psd_vz./(2*pi*gm.freqs);
#+end_src
The pre-processed data are saved.
#+begin_src matlab :results silent
save('./data/gm_esrf.mat', 'gm');
#+end_src
* Plots
We load measurements made:
- at ID31
- at ID09
- at CERN
#+begin_src matlab :results silent
id31 = load('./data/ground_motion_psd.mat');
id09 = load('./data/id09_floor_september2018.mat');
cern = load('./data/ground_motion_dist.mat');
#+end_src
** ID09 Measurements - Time Domain
#+begin_src matlab :results silent
figure;
hold on;
plot(id09.time3, 1e-6*id09.x_y_z(:, 1), 'DisplayName', 'dx');
plot(id09.time3, 1e-6*id09.x_y_z(:, 2), 'DisplayName', 'dy');
plot(id09.time3, 1e-6*id09.x_y_z(:, 3), 'DisplayName', 'dz');
hold off;
xlabel('Time [s]'); ylabel('Velocity [$m/s$]');
legend();
#+end_src
#+NAME: fig:id09_time_domain
#+HEADER: :tangle no :exports results :results raw :noweb yes
#+begin_src matlab :var filepath="figs/id09_time_domain.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:id09_time_domain
#+CAPTION: Time domain data - ID09
#+RESULTS: fig:id09_time_domain
[[file:figs/id09_time_domain.png]]
** Compute PSD of ID09 ground motion
#+begin_src matlab :results silent
[id09_pxx, id09_f] = pwelch(1e-6*id09.x_y_z(:, 1), hanning(ceil(length(1e-6*id09.x_y_z(:, 1))/10)), 0, [], 1/(id09.time3(end)/(length(id09.time3) - 1)));
#+end_src
** Compare PSD of Cern, ID09 and ID31
#+begin_src matlab :results silent
figure;
hold on;
plot(cern.gm.freq, cern.gm.psd, 'DisplayName', 'CERN');
plot(id31.freqs, id31.psd_dx, 'DisplayName', 'ID31');
plot(id09_f, id09_pxx, 'DisplayName', 'ID09');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m^2/Hz$]');
legend('Location', 'northeast');
#+end_src
#+NAME: fig:psd_comparison
#+HEADER: :tangle no :exports results :results raw :noweb yes
#+begin_src matlab :var filepath="figs/psd_comparison.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:psd_comparison
#+CAPTION: Comparison of the PSD of ground motion
#+RESULTS: fig:psd_comparison
[[file:figs/psd_comparison.png]]

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@ -114,7 +114,7 @@ We also take into account the gain of the electronics which is here set to be $6
#+begin_src matlab :results none
G0_db = 60; % [dB]
G0 = 10^(60/G0_db); % [abs]
G0 = 10^(G0_db/20); % [abs]
#+end_src
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.

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#+TITLE: Ground Motion Measurements
#+SETUPFILE: ../config.org
* Experimental Setup
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.
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.
One L22 geophone is put on the ID31 floor.
The signal is then filtered with a first order low pass filter with a cut-off frequency of $1kHz$.
Then the signal is amplified by a Voltage Amplifier with the following settings:
- AC/DC option set to DC
- Amplification of 60dB (1000)
- Low pass filter at the output with a cut-off frequency of $1kHz$
On figure [[fig:ground_motion_measurements]] is an overview of multiple measurements made at famous location.
#+name: fig:ground_motion_measurements
#+caption: Power spectral density of ground vibration in the vertical direction at multiple locations ([[https://vibration.desy.de/][source]])
#+attr_html: :width 800px
[[file:./img/ground_motion_measurements.png]]
* Measurement Analysis
:PROPERTIES:
:header-args:matlab+: :tangle matlab/ground_meas_id31.m
:header-args:matlab+: :comments org :mkdirp yes
:END:
<<sec:ground_meas_id31>>
#+begin_src bash :exports none :results none
if [ matlab/ground_meas_id31.m -nt data/ground_meas_id31.zip ]; then
cp matlab/ground_meas_id31.m ground_meas_id31.m;
zip data/ground_meas_id31 \
mat/data_028.mat \
mat/id09_floor_september2018.mat \
mat/ground_motion_dist.mat \
ground_meas_id31.m
rm ground_meas_id31.m;
fi
#+end_src
#+begin_note
All the files (data and Matlab scripts) are accessible [[file:data/ground_meas_id31.zip][here]].
#+end_note
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
** Load data
#+begin_src matlab
data = load('mat/data_028.mat', 'data'); data = data.data;
#+end_src
** Time domain plots
#+begin_src matlab
figure;
hold on;
plot(data(:, 3), data(:, 1));
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 100]);
#+end_src
#+NAME: fig:ground_motion_id31_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ground_motion_id31_time.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ground_motion_id31_time
#+CAPTION: Measurement of the ground motion - Time domain
#+RESULTS: fig:ground_motion_id31_time
[[file:figs/ground_motion_id31_time.png]]
** Computation of the ASD of the measured voltage
#+begin_src matlab :results none
dt = data(2, 3) - data(1, 3);
Fs = 1/dt;
win = hanning(ceil(10*Fs));
#+end_src
#+begin_src matlab :results none
[px_dc, f] = pwelch(data(:, 1), win, [], [], Fs);
#+end_src
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(px_dc));
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
#+end_src
#+NAME: fig:ground_motion_id31_asd_volt
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ground_motion_id31_asd_volt.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ground_motion_id31_asd_volt
#+CAPTION: Amplitude Spectral Density of the measured Voltage
#+RESULTS: fig:ground_motion_id31_asd_volt
[[file:figs/ground_motion_id31_asd_volt.png]]
** Scaling to take into account the sensibility of the geophone and the voltage amplifier
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 frequency [Hz]
S = S0*(s/2/pi/f0)/(1+s/2/pi/f0);
#+end_src
#+begin_src matlab :results none :exports none
figure;
bodeFig({S}, logspace(-1, 2, 1000));
ylabel('Amplitude $\left[\frac{V}{m/s}\right]$')
#+end_src
#+NAME: fig:geophone_sensibility
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/geophone_sensibility.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:geophone_sensibility
#+CAPTION: Sensibility of the Geophone
#+RESULTS: fig:geophone_sensibility
[[file:figs/geophone_sensibility.png]]
We also take into account the gain of the electronics which is here set to be $60dB$.
#+begin_src matlab :results none
G0_db = 60; % [dB]
G0 = 10^(G0_db/20); % [abs]
#+end_src
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(G0*S, f, 'Hz')));
#+end_src
** Computation of the ASD of the velocity and displacement
The ASD of the measured velocity is shown on figure [[fig:ground_motion_id31_asd_velocity]].
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(px_dc).*scaling);
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
#+end_src
#+NAME: fig:ground_motion_id31_asd_velocity
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ground_motion_id31_asd_velocity.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ground_motion_id31_asd_velocity
#+CAPTION: Amplitude Spectral Density of the Velocity
#+RESULTS: fig:ground_motion_id31_asd_velocity
[[file:figs/ground_motion_id31_asd_velocity.png]]
We also plot the ASD in displacement (figure [[fig:ground_motion_id31_asd_displacement]]);
#+begin_src matlab :results none
figure;
hold on;
plot(f, (sqrt(px_dc).*scaling)./(2*pi*f));
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
#+end_src
#+NAME: fig:ground_motion_id31_asd_displacement
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ground_motion_id31_asd_displacement.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ground_motion_id31_asd_displacement
#+CAPTION: Amplitude Spectral Density of the Displacement
#+RESULTS: fig:ground_motion_id31_asd_displacement
[[file:figs/ground_motion_id31_asd_displacement.png]]
And we also plot the PSD of the displacement in $\frac{{\mu u}^2}{Hz}$ as it is a usual unit used (figure [[fig:ground_motion_id31_psd_displacement]]).
One can then compare this curve with the figure [[fig:ground_motion_measurements]].
#+begin_src matlab :results none
figure;
hold on;
plot(f, ((sqrt(px_dc).*scaling)./(2*pi*f).*1e6).^2);
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD of the measured displacement $\left[\frac{{ \mu m }^2}{Hz}\right]$')
xlim([0.1, 500]);
#+end_src
#+NAME: fig:ground_motion_id31_psd_displacement
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ground_motion_id31_psd_displacement.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ground_motion_id31_psd_displacement
#+CAPTION: Power Spectral Density of the measured displacement
#+RESULTS: fig:ground_motion_id31_psd_displacement
[[file:figs/ground_motion_id31_psd_displacement.png]]
** Comparison with other measurements of ground motion
Now we will compare with other measurements.
*** Load the measurement data
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.
#+begin_src matlab
id09 = load('./mat/id09_floor_september2018.mat');
cern = load('./mat/ground_motion_dist.mat');
#+end_src
*** Compute PSD of the measurements
We compute the Power Spectral Densities of the measurements.
#+begin_src matlab
Fs_id09 = 1/(id09.time3(2)-id09.time3(1));
win_id09 = hanning(ceil(10*Fs_id09));
[id09_pxx, id09_f] = pwelch(1e-6*id09.x_y_z(:, 3), win_id09, [], [], Fs_id09);
#+end_src
#+begin_src matlab
Fs_cern = 1/(cern.gm.time(2)-cern.gm.time(1));
win_cern = hanning(ceil(10*Fs_cern));
[cern_pxx, cern_f] = pwelch(cern.gm.signal, win_cern, [], [], Fs_cern);
#+end_src
*** Compare PSD of Cern, ID09 and ID31
And we compare all the measurements (figure [[fig:ground_motion_compare]]).
#+begin_src matlab :results silent
figure;
hold on;
plot(id09_f, id09_pxx, 'DisplayName', 'ID09');
plot(cern_f, cern_pxx, 'DisplayName', 'CERN');
plot(f, ((sqrt(px_dc).*scaling)./(2*pi*f)).^2, 'k', 'DisplayName', 'ID31');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m^2/Hz$]');
legend('Location', 'northeast');
xlim([0.1, 500]);
#+end_src
#+NAME: fig:ground_motion_compare
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ground_motion_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ground_motion_compare
#+CAPTION: Comparison of the PSD of the ground motion measured at different location
#+RESULTS: fig:ground_motion_compare
[[file:figs/ground_motion_compare.png]]

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%% Clear Workspace and Close figures
clear; close all; clc;
%% Intialize Laplace variable
s = zpk('s');
% Load data
data = load('mat/data_028.mat', 'data'); data = data.data;
% Time domain plots
figure;
hold on;
plot(data(:, 3), data(:, 1));
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 100]);
% Computation of the ASD of the measured voltage
dt = data(2, 3) - data(1, 3);
Fs = 1/dt;
win = hanning(ceil(10*Fs));
[px_dc, f] = pwelch(data(:, 1), win, [], [], Fs);
figure;
hold on;
plot(f, sqrt(px_dc));
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
% Scaling to take into account the sensibility of the geophone and the voltage amplifier
% The Geophone used are L22. Their sensibility is shown on figure [[fig:geophone_sensibility]].
S0 = 88; % Sensitivity [V/(m/s)]
f0 = 2; % Cut-off frequency [Hz]
S = S0*(s/2/pi/f0)/(1+s/2/pi/f0);
figure;
bodeFig({S}, logspace(-1, 2, 1000));
ylabel('Amplitude $\left[\frac{V}{m/s}\right]$')
% #+NAME: fig:geophone_sensibility
% #+CAPTION: Sensibility of the Geophone
% #+RESULTS: fig:geophone_sensibility
% [[file:figs/geophone_sensibility.png]]
% We also take into account the gain of the electronics which is here set to be $60dB$.
G0_db = 60; % [dB]
G0 = 10^(G0_db/20); % [abs]
% 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 $m/s/\sqrt{Hz}$.
scaling = 1./squeeze(abs(freqresp(G0*S, f, 'Hz')));
% Computation of the ASD of the velocity
% The ASD of the measured velocity is shown on figure [[fig:ground_motion_id31_asd_velocity]].
figure;
hold on;
plot(f, sqrt(px_dc).*scaling);
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
% #+NAME: fig:ground_motion_id31_asd_velocity
% #+CAPTION: Amplitude Spectral Density of the Velocity
% #+RESULTS: fig:ground_motion_id31_asd_velocity
% [[file:figs/ground_motion_id31_asd_velocity.png]]
% We also plot the ASD in displacement (figure [[fig:ground_motion_id31_asd_displacement]]);
figure;
hold on;
plot(f, (sqrt(px_dc).*scaling)./(2*pi*f));
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
% #+NAME: fig:ground_motion_id31_asd_displacement
% #+CAPTION: Amplitude Spectral Density of the Displacement
% #+RESULTS: fig:ground_motion_id31_asd_displacement
% [[file:figs/ground_motion_id31_asd_displacement.png]]
% And also in $\frac{{\mu u}^2}{Hz}$ (figure [[fig:ground_motion_id31_psd_displacement]]).
figure;
hold on;
plot(f, ((sqrt(px_dc).*scaling)./(2*pi*f).*1e6).^2);
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD of the measured displacement $\left[\frac{{ \mu m }^2}{Hz}\right]$')
xlim([0.1, 500]);
% Load the measurement data
% 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.
id09 = load('./mat/id09_floor_september2018.mat');
cern = load('./mat/ground_motion_dist.mat');
% Compute PSD of the measurements
% We compute the Power Spectral Densities of the measurements.
Fs_id09 = 1/(id09.time3(2)-id09.time3(1));
win_id09 = hanning(ceil(10*Fs_id09));
[id09_pxx, id09_f] = pwelch(1e-6*id09.x_y_z(:, 3), win_id09, [], [], Fs_id09);
Fs_cern = 1/(cern.gm.time(2)-cern.gm.time(1));
win_cern = hanning(ceil(10*Fs_cern));
[cern_pxx, cern_f] = pwelch(cern.gm.signal, win_cern, [], [], Fs_cern);
% Compare PSD of Cern, ID09 and ID31
% And we compare all the measurements (figure [[fig:ground_motion_compare]]).
figure;
hold on;
plot(id09_f, id09_pxx, 'DisplayName', 'ID09');
plot(cern_f, cern_pxx, 'DisplayName', 'CERN');
plot(f, ((sqrt(px_dc).*scaling)./(2*pi*f)).^2, 'k', 'DisplayName', 'ID31');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m^2/Hz$]');
legend('Location', 'northeast');
xlim([0.1, 500]);

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Ground Motion/readme.org → ground-motion/readme.org
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huddle-test-geophones/index.html
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huddle-test-geophones/index.org
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@ -177,7 +177,7 @@ We also take into account the gain of the electronics which is here set to be $6
#+begin_src matlab :results none
G0_db = 60; % [dB]
G0 = 10^(60/G0_db); % [abs]
G0 = 10^(G0_db/20); % [abs]
#+end_src
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.

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huddle-test-geophones/matlab/huddle_test_signal_processing.m
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@ -104,7 +104,7 @@ ylabel('Amplitude $\left[\frac{V}{m/s}\right]$')
G0_db = 60; % [dB]
G0 = 10^(60/G0_db); % [abs]
G0 = 10^(G0_db/20); % [abs]