nass-micro-station-measurements/static-measurements/index.org

• Effect of all the control systems on the Sample vibrations
  • Experimental Setup
  • Load data
  • Analysis - Time Domain
  • Analysis - Frequency Domain
    • Vibrations at the sample location
    • Vibrations on the marble
  • Effect of the control system on the transmissibility from ground to sample
  • Conclusion
• Effect of all the control systems on the Sample vibrations - One stage at a time
  • Experimental Setup
  • Load data
  • Analysis - Time Domain
  • Analysis - Frequency Domain
    • Vibrations at the sample location
    • Vibrations on the marble
  • Conclusion
• Effect of the Symetrie Driver
  • Experimental Setup
  • Load data
  • Analysis - Time Domain
  • Analysis - Frequency Domain
    • Vibrations at the sample location
  • Conclusion
• Transfer function from one stage to the other
  • Experimental Setup
    • From Marble to Ty - mat/meas_010.mat
    • From Marble to Ry - mat/meas_011.mat
    • From Ty to Ry - mat/meas_012.mat
  • Load data
  • Analysis - Time Domain
  • Analysis - Frequency Domain
  • Conclusion

#+TITLE:Measurements

For all the measurements shown here:

• geophones used are L22 with a resonance frequency of 1Hz
• the signals are amplified with voltage amplifiers with a gain of 60dB
• the voltage amplifiers include a low pass filter with a cut-off frequency at 1kHz

Effect of all the control systems on the Sample vibrations

<<sec:effect_control_all>>

All the files (data and Matlab scripts) are accessible here.

Experimental Setup

We here measure the signals of two geophones:

• One is located on top of the Sample platform
• One is located on the marble

The signal from the top geophone does not go trought the slip-ring.

First, all the control systems are turned ON, then, they are turned one by one. Each measurement are done during 50s.

Ty	Ry	Slip Ring	Spindle	Hexapod	Meas. file
ON	ON	ON	ON	ON	meas_003.mat
OFF	ON	ON	ON	ON	meas_004.mat
OFF	OFF	ON	ON	ON	meas_005.mat
OFF	OFF	OFF	ON	ON	meas_006.mat
OFF	OFF	OFF	OFF	ON	meas_007.mat
OFF	OFF	OFF	OFF	OFF	meas_008.mat

Summary of the measurements and the states of the control systems

Each of the mat file contains one array data with 3 columns:

Column number	Description
1	Geophone - Marble
2	Geophone - Sample
3	Time

Load data

We load the data of the z axis of two geophones.

  d3 = load('mat/data_003.mat', 'data'); d3 = d3.data;
  d4 = load('mat/data_004.mat', 'data'); d4 = d4.data;
  d5 = load('mat/data_005.mat', 'data'); d5 = d5.data;
  d6 = load('mat/data_006.mat', 'data'); d6 = d6.data;
  d7 = load('mat/data_007.mat', 'data'); d7 = d7.data;
  d8 = load('mat/data_008.mat', 'data'); d8 = d8.data;

Analysis - Time Domain

First, we can look at the time domain data and compare all the measurements:

• comparison for the geophone at the sample location (figure fig:time_domain_sample)
• comparison for the geophone on the granite (figure fig:time_domain_marble)

  figure;
  hold on;
  plot(d3(:, 3), d3(:, 2), 'DisplayName', 'All ON');
  plot(d4(:, 3), d4(:, 2), 'DisplayName', 'Ty OFF');
  plot(d5(:, 3), d5(:, 2), 'DisplayName', 'Ry OFF');
  plot(d6(:, 3), d6(:, 2), 'DisplayName', 'S-R OFF');
  plot(d7(:, 3), d7(:, 2), 'DisplayName', 'Rz OFF');
  plot(d8(:, 3), d8(:, 2), 'DisplayName', 'Hexa OFF');
  hold off;
  xlabel('Time [s]'); ylabel('Voltage [V]');
  xlim([0, 50]);
  legend('Location', 'bestoutside');

  <<plt-matlab>>

Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location

  figure;
  hold on;
  plot(d3(:, 3), d3(:, 1), 'DisplayName', 'All ON');
  plot(d4(:, 3), d4(:, 1), 'DisplayName', 'Ty OFF');
  plot(d5(:, 3), d5(:, 1), 'DisplayName', 'Ry OFF');
  plot(d6(:, 3), d6(:, 1), 'DisplayName', 'S-R OFF');
  plot(d7(:, 3), d7(:, 1), 'DisplayName', 'Rz OFF');
  plot(d8(:, 3), d8(:, 1), 'DisplayName', 'Hexa OFF');
  hold off;
  xlabel('Time [s]'); ylabel('Voltage [V]');
  xlim([0, 50]);
  legend('Location', 'bestoutside');

  <<plt-matlab>>

Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble

Analysis - Frequency Domain

  dt = d3(2, 3) - d3(1, 3);

  Fs = 1/dt;
  win = hanning(ceil(10*Fs));

Vibrations at the sample location

First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.

  [px3, f] = pwelch(d3(:, 2), win, [], [], Fs);
  [px4, ~] = pwelch(d4(:, 2), win, [], [], Fs);
  [px5, ~] = pwelch(d5(:, 2), win, [], [], Fs);
  [px6, ~] = pwelch(d6(:, 2), win, [], [], Fs);
  [px7, ~] = pwelch(d7(:, 2), win, [], [], Fs);
  [px8, ~] = pwelch(d8(:, 2), win, [], [], Fs);

And we compare all the signals (figures fig:psd_sample_comp and fig:psd_sample_comp_high_freq).

  figure;
  hold on;
  plot(f, sqrt(px3), 'DisplayName', 'All ON');
  plot(f, sqrt(px4), 'DisplayName', 'Ty OFF');
  plot(f, sqrt(px5), 'DisplayName', 'Ry OFF');
  plot(f, sqrt(px6), 'DisplayName', 'S-R OFF');
  plot(f, sqrt(px7), 'DisplayName', 'Rz OFF');
  plot(f, sqrt(px8), 'DisplayName', 'Hexa OFF');
  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]);
  legend('Location', 'southwest');

  <<plt-matlab>>

Amplitude Spectral Density of the signal coming from the top geophone

  <<plt-matlab>>

Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)

Vibrations on the marble

Now we plot the same curves for the geophone located on the marble.

  [px3, f] = pwelch(d3(:, 1), win, [], [], Fs);
  [px4, ~] = pwelch(d4(:, 1), win, [], [], Fs);
  [px5, ~] = pwelch(d5(:, 1), win, [], [], Fs);
  [px6, ~] = pwelch(d6(:, 1), win, [], [], Fs);
  [px7, ~] = pwelch(d7(:, 1), win, [], [], Fs);
  [px8, ~] = pwelch(d8(:, 1), win, [], [], Fs);

And we compare the Amplitude Spectral Densities (figures fig:psd_marble_comp and fig:psd_marble_comp_high_freq)

  figure;
  hold on;
  plot(f, sqrt(px3), 'DisplayName', 'All ON');
  plot(f, sqrt(px4), 'DisplayName', 'Ty OFF');
  plot(f, sqrt(px5), 'DisplayName', 'Ry OFF');
  plot(f, sqrt(px6), 'DisplayName', 'S-R OFF');
  plot(f, sqrt(px7), 'DisplayName', 'Rz OFF');
  plot(f, sqrt(px8), 'DisplayName', 'Hexa OFF');
  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]);
  legend('Location', 'northeast');

  <<plt-matlab>>

Amplitude Spectral Density of the signal coming from the top geophone

  <<plt-matlab>>

Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)

Effect of the control system on the transmissibility from ground to sample

As the feedback loops change the dynamics of the system, we should see differences on the transfer function from marble velocity to sample velocity when turning off the control systems (figure fig:trans_comp).

  dt = d3(2, 3) - d3(1, 3);

  Fs = 1/dt;
  win = hanning(ceil(1*Fs));

First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.

  [T3, f] = tfestimate(d3(:, 1), d3(:, 2), win, [], [], Fs);
  [T4, ~] = tfestimate(d4(:, 1), d4(:, 2), win, [], [], Fs);
  [T5, ~] = tfestimate(d5(:, 1), d5(:, 2), win, [], [], Fs);
  [T6, ~] = tfestimate(d6(:, 1), d6(:, 2), win, [], [], Fs);
  [T7, ~] = tfestimate(d7(:, 1), d7(:, 2), win, [], [], Fs);
  [T8, ~] = tfestimate(d8(:, 1), d8(:, 2), win, [], [], Fs);

  figure;
  ax1 = subplot(2, 1, 1);
  hold on;
  plot(f, abs(T3), 'DisplayName', 'All ON');
  plot(f, abs(T4), 'DisplayName', 'Ty OFF');
  plot(f, abs(T5), 'DisplayName', 'Ry OFF');
  plot(f, abs(T6), 'DisplayName', 'S-R OFF');
  plot(f, abs(T7), 'DisplayName', 'Rz OFF');
  plot(f, abs(T8), 'DisplayName', 'Hexa OFF');
  hold off;
  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
  set(gca, 'XTickLabel',[]);
  ylabel('Magnitude');
  legend('Location', 'northwest');

  ax2 = subplot(2, 1, 2);
  hold on;
  plot(f, mod(180+180/pi*phase(T3), 360)-180);
  plot(f, mod(180+180/pi*phase(T4), 360)-180);
  plot(f, mod(180+180/pi*phase(T5), 360)-180);
  plot(f, mod(180+180/pi*phase(T6), 360)-180);
  plot(f, mod(180+180/pi*phase(T7), 360)-180);
  plot(f, mod(180+180/pi*phase(T8), 360)-180);
  hold off;
  set(gca, 'xscale', 'log');
  ylim([-180, 180]);
  yticks([-180, -90, 0, 90, 180]);
  xlabel('Frequency [Hz]'); ylabel('Phase');

  linkaxes([ax1,ax2],'x');
  xlim([1, 500]);

  <<plt-matlab>>

Comparison of the transfer function from the geophone on the marble to the geophone at the sample location

Conclusion

• The control system of the Ty stage induces a lot of vibrations of the marble

• Why it seems that the measurement noise at high frequency is the limiting factor when the slip ring is ON but not when it is OFF?

Effect of all the control systems on the Sample vibrations - One stage at a time

<<sec:effect_control_one>>

All the files (data and Matlab scripts) are accessible here.

Experimental Setup

We here measure the signals of two geophones:

• One is located on top of the Sample platform
• One is located on the marble

The signal from the top geophone does go trought the slip-ring.

All the control systems are turned OFF, then, they are turned on one at a time.

Each measurement are done during 100s.

The settings of the voltage amplifier are shown on figure fig:amplifier_settings. A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.

Ty	Ry	Slip Ring	Spindle	Hexapod	Meas. file
OFF	OFF	OFF	OFF	OFF	meas_013.mat
ON	OFF	OFF	OFF	OFF	meas_014.mat
OFF	ON	OFF	OFF	OFF	meas_015.mat
OFF	OFF	ON	OFF	OFF	meas_016.mat
OFF	OFF	OFF	ON	OFF	meas_017.mat
OFF	OFF	OFF	OFF	ON	meas_018.mat

Summary of the measurements and the states of the control systems

Each of the mat file contains one array data with 3 columns:

Column number	Description
1	Geophone - Marble
2	Geophone - Sample
3	Time

Voltage amplifier settings for the measurement

Load data

We load the data of the z axis of two geophones.

  d_of = load('mat/data_013.mat', 'data'); d_of = d_of.data;
  d_ty = load('mat/data_014.mat', 'data'); d_ty = d_ty.data;
  d_ry = load('mat/data_015.mat', 'data'); d_ry = d_ry.data;
  d_sr = load('mat/data_016.mat', 'data'); d_sr = d_sr.data;
  d_rz = load('mat/data_017.mat', 'data'); d_rz = d_rz.data;
  d_he = load('mat/data_018.mat', 'data'); d_he = d_he.data;

Analysis - Time Domain

First, we can look at the time domain data and compare all the measurements:

• comparison for the geophone at the sample location (figure fig:time_domain_sample_lpf)
• comparison for the geophone on the granite (figure fig:time_domain_marble_lpf)

  figure;
  hold on;
  plot(d_of(:, 3), d_of(:, 2), 'DisplayName', 'All OFF';
  plot(d_ty(:, 3), d_ty(:, 2), 'DisplayName', 'Ty ON');
  plot(d_ry(:, 3), d_ry(:, 2), 'DisplayName', 'Ry ON');
  plot(d_sr(:, 3), d_sr(:, 2), 'DisplayName', 'S-R ON');
  plot(d_rz(:, 3), d_rz(:, 2), 'DisplayName', 'Rz ON');
  plot(d_he(:, 3), d_he(:, 2), 'DisplayName', 'Hexa ON');
  hold off;
  xlabel('Time [s]'); ylabel('Voltage [V]');
  xlim([0, 50]);
  legend('Location', 'bestoutside');

  <<plt-matlab>>

Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location

  figure;
  hold on;
  plot(d_of(:, 3), d_of(:, 1), 'DisplayName', 'All OFF');
  plot(d_ty(:, 3), d_ty(:, 1), 'DisplayName', 'Ty ON');
  plot(d_ry(:, 3), d_ry(:, 1), 'DisplayName', 'Ry ON');
  plot(d_sr(:, 3), d_sr(:, 1), 'DisplayName', 'S-R ON');
  plot(d_rz(:, 3), d_rz(:, 1), 'DisplayName', 'Rz ON');
  plot(d_he(:, 3), d_he(:, 1), 'DisplayName', 'Hexa ON');
  hold off;
  xlabel('Time [s]'); ylabel('Voltage [V]');
  xlim([0, 50]);
  legend('Location', 'bestoutside');

  <<plt-matlab>>

Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble

Analysis - Frequency Domain

  dt = d_of(2, 3) - d_of(1, 3);

  Fs = 1/dt;
  win = hanning(ceil(10*Fs));

Vibrations at the sample location

First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.

  [px_of, f] = pwelch(d_of(:, 2), win, [], [], Fs);
  [px_ty, ~] = pwelch(d_ty(:, 2), win, [], [], Fs);
  [px_ry, ~] = pwelch(d_ry(:, 2), win, [], [], Fs);
  [px_sr, ~] = pwelch(d_sr(:, 2), win, [], [], Fs);
  [px_rz, ~] = pwelch(d_rz(:, 2), win, [], [], Fs);
  [px_he, ~] = pwelch(d_he(:, 2), win, [], [], Fs);

And we compare all the signals (figures fig:psd_sample_comp_lpf and fig:psd_sample_comp_high_freq_lpf).

  figure;
  hold on;
  plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
  plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
  plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
  plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
  plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
  plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
  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]);
  legend('Location', 'southwest');

  <<plt-matlab>>

Amplitude Spectral Density of the signal coming from the top geophone

  <<plt-matlab>>

Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)

Vibrations on the marble

Now we plot the same curves for the geophone located on the marble.

  [px_of, f] = pwelch(d_of(:, 1), win, [], [], Fs);
  [px_ty, ~] = pwelch(d_ty(:, 1), win, [], [], Fs);
  [px_ry, ~] = pwelch(d_ry(:, 1), win, [], [], Fs);
  [px_sr, ~] = pwelch(d_sr(:, 1), win, [], [], Fs);
  [px_rz, ~] = pwelch(d_rz(:, 1), win, [], [], Fs);
  [px_he, ~] = pwelch(d_he(:, 1), win, [], [], Fs);

And we compare the Amplitude Spectral Densities (figures fig:psd_marble_comp_lpf and fig:psd_marble_comp_lpf_high_freq)

  figure;
  hold on;
  plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
  plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
  plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
  plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
  plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
  plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
  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]);
  legend('Location', 'northeast');

  <<plt-matlab>>

Amplitude Spectral Density of the signal coming from geophone located on the marble

  <<plt-matlab>>

Amplitude Spectral Density of the signal coming from the geophone located on the marble (zoom at high frequencies)

Conclusion

• The Ty stage induces vibrations of the marble and at the sample location above 100Hz
• The hexapod stage induces vibrations at the sample position above 220Hz

Effect of the Symetrie Driver

<<sec:effect_symetrie_driver>>

All the files (data and Matlab scripts) are accessible here.

Experimental Setup

We here measure the signals of two geophones:

• One is located on top of the Sample platform
• One is located on the marble

The signal from the top geophone does go trought the slip-ring.

All the control systems are turned OFF except the Hexapod one.

Each measurement are done during 100s.

The settings of the voltage amplifier are:

• DC
• 60dB
• 1kHz

A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.

The measurements are:

• meas_018.mat: Hexapod's driver on the granite
• meas_019.mat: Hexapod's driver on the ground

Each of the mat file contains one array data with 3 columns:

Column number	Description
1	Geophone - Marble
2	Geophone - Sample
3	Time

Load data

We load the data of the z axis of two geophones.

  d_18 = load('mat/data_018.mat', 'data'); d_18 = d_18.data;
  d_19 = load('mat/data_019.mat', 'data'); d_19 = d_19.data;

Analysis - Time Domain

  figure;
  hold on;
  plot(d_19(:, 3), d_19(:, 1), 'DisplayName', 'Driver - Ground');
  plot(d_18(:, 3), d_18(:, 1), 'DisplayName', 'Driver - Granite');
  hold off;
  xlabel('Time [s]'); ylabel('Voltage [V]');
  xlim([0, 50]);
  legend('Location', 'bestoutside');

  <<plt-matlab>>

Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location

Analysis - Frequency Domain

  dt = d_18(2, 3) - d_18(1, 3);

  Fs = 1/dt;
  win = hanning(ceil(10*Fs));

Vibrations at the sample location

First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.

  [px_18, f] = pwelch(d_18(:, 1), win, [], [], Fs);
  [px_19, ~] = pwelch(d_19(:, 1), win, [], [], Fs);

  figure;
  hold on;
  plot(f, sqrt(px_19), 'DisplayName', 'Driver - Ground');
  plot(f, sqrt(px_18), 'DisplayName', 'Driver - Granite');
  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]);
  legend('Location', 'southwest');

  <<plt-matlab>>

Amplitude Spectral Density of the signal coming from the top geophone

  <<plt-matlab>>

Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)

Conclusion

Even tough the Hexapod's driver vibrates quite a lot, it does not generate significant vibrations of the granite when either placed on the granite or on the ground.

Transfer function from one stage to the other

<<sec:tf_stages_geophone>>

All the files (data and Matlab scripts) are accessible here.

Experimental Setup

For all the measurements in this section:

• all the control stages are OFF.
• the measurements are on the $z$ direction

From Marble to Ty - mat/meas_010.mat

One geophone is on the marble, one is on the Ty stage (see figures fig:setup_m_ty, fig:setup_m_ty_zoom and fig:setup_m_ty_top).

The data array contains the following columns:

Column	Description
1	Ground
2	Ty
3	Time

Setup with one geophone on the marble and one on top of the translation stage

Setup with one geophone on the marble and one on top of the translation stage - Close up view

Setup with one geophone on the marble and one on top of the translation stage - Top view

From Marble to Ry - mat/meas_011.mat

One geophone is on the marble, one is on the Ry stage (see figure fig:setup_m_ry)

The data array contains the following columns:

Column	Description
1	Ground
2	Ry
3	Time

Setup with one geophone on the marble and one on top of the Tilt Stage

From Ty to Ry - mat/meas_012.mat

One geophone is on the Ty stage, one is on the Ry stage (see figures fig:setup_ty_ry, fig:setup_ty_ry_top and fig:setup_ty_ry_zoom) One geophone on the Ty stage, one geophone on the Ry stage.

The data array contains the following columns:

Column	Description
1	Ty
2	Ry
3	Time

Setup with one geophone on the translation stage and one on top of the Tilt Stage

Setup with one geophone on the translation stage and one on top of the Tilt Stage - Top view

Setup with one geophone on the translation stage and one on top of the Tilt Stage - Close up view

Load data

We load the data of the z axis of two geophones.

  m_ty  = load('mat/data_010.mat', 'data'); m_ty  = m_ty.data;
  m_ry  = load('mat/data_011.mat', 'data'); m_ry  = m_ry.data;
  ty_ry = load('mat/data_012.mat', 'data'); ty_ry = ty_ry.data;

Analysis - Time Domain

First, we can look at the time domain data.

  figure;
  hold on;
  plot(m_ty(:, 3), m_ty(:, 1), 'DisplayName', 'Marble');
  plot(m_ty(:, 3), m_ty(:, 2), 'DisplayName', 'Ty');
  hold off;
  xlabel('Time [s]'); ylabel('Voltage [V]');
  legend('Location', 'northeast');
  xlim([0, 500]);

  <<plt-matlab>>

Time domain - Marble and translation stage

  figure;
  hold on;
  plot(m_ry(:, 3), m_ry(:, 1), 'DisplayName', 'Marble');
  plot(m_ry(:, 3), m_ry(:, 2), 'DisplayName', 'Ty');
  hold off;
  xlabel('Time [s]'); ylabel('Voltage [V]');
  legend('Location', 'northeast');
  xlim([0, 500]);

  <<plt-matlab>>

Time domain - Marble and tilt stage

  figure;
  hold on;
  plot(ty_ry(:, 3), ty_ry(:, 1), 'DisplayName', 'Ty');
  plot(ty_ry(:, 3), ty_ry(:, 2), 'DisplayName', 'Ry');
  hold off;
  xlabel('Time [s]'); ylabel('Voltage [V]');
  legend('Location', 'northeast');
  xlim([0, 500]);

  <<plt-matlab>>

Time domain - Translation stage and tilt stage

Analysis - Frequency Domain

  dt = m_ty(2, 3) - m_ty(1, 3);

  Fs = 1/dt;
  win = hanning(ceil(1*Fs));

First, we compute the transfer function estimate between the two geophones for the 3 experiments (figure fig:compare_tf_geophones). We also plot their coherence (figure fig:coherence_two_geophones).

  [T_m_ty,  f] = tfestimate(m_ty(:, 1),  m_ty(:, 2),  win, [], [], Fs);
  [T_m_ry,  ~] = tfestimate(m_ry(:, 1),  m_ry(:, 2),  win, [], [], Fs);
  [T_ty_ry, ~] = tfestimate(ty_ry(:, 1), ty_ry(:, 2), win, [], [], Fs);

  figure;
  ax1 = subplot(2, 1, 1);
  hold on;
  plot(f, abs(T_m_ty),  'DisplayName', 'Marble - Ty');
  plot(f, abs(T_m_ry),  'DisplayName', 'Marble - Ry');
  plot(f, abs(T_ty_ry), 'DisplayName', 'Ty - Ry');
  hold off;
  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
  set(gca, 'XTickLabel',[]);
  ylabel('Magnitude');
  legend('Location', 'northwest');

  ax2 = subplot(2, 1, 2);
  hold on;
  plot(f, mod(180+180/pi*phase(T_m_ty),  360)-180);
  plot(f, mod(180+180/pi*phase(T_m_ry),  360)-180);
  plot(f, mod(180+180/pi*phase(T_ty_ry), 360)-180);
  hold off;
  set(gca, 'xscale', 'log');
  ylim([-180, 180]);
  yticks([-180, -90, 0, 90, 180]);
  xlabel('Frequency [Hz]'); ylabel('Phase');

  linkaxes([ax1,ax2],'x');
  xlim([10, 500]);

  <<plt-matlab>>

Transfer function from the first geophone to the second geophone for the three experiments

  [coh_m_ty,  f] = mscohere(m_ty(:, 1),  m_ty(:, 2),  win, [], [], Fs);
  [coh_m_ry,  ~] = mscohere(m_ry(:, 1),  m_ry(:, 2),  win, [], [], Fs);
  [coh_ty_ry, ~] = mscohere(ty_ry(:, 1), ty_ry(:, 2), win, [], [], Fs);

  <<plt-matlab>>

Coherence between the two geophones for the three experiments

Conclusion

These measurements are not relevant.