Update Ty scans analysis

disturbance-ty/index.org

@@ -131,6 +131,10 @@ We convert the measured voltage to velocity using the function =voltageToVelocit
 #+end_src
 
 ** Time domain plots
+We plot the measured velocity of the marble and sample in the vertical direction (figure [[fig:ty_z_time]]) and in the X direction (figure [[fig:ty_e_time]]).
+
+We also integrate the relative velocity to obtain the relative displacement (figure [[fig:x_relative_disp]] in the X direction and figure [[fig:z_relative_disp]] in the Z direction).
+
 #+begin_src matlab
   figure;
   hold on;
@@ -138,7 +142,7 @@ We convert the measured voltage to velocity using the function =voltageToVelocit
   plot(z_ty(:, 3), z_ty(:, 2), 'DisplayName', 'Sample - Z');
   hold off;
   xlabel('Time [s]'); ylabel('Velocity [m/s]');
-  xlim([0, 100]);
+  xlim([0, 2]);
   legend('Location', 'northeast');
 #+end_src
 
@@ -153,22 +157,6 @@ We convert the measured voltage to velocity using the function =voltageToVelocit
 #+RESULTS: fig:ty_z_time
 [[file:figs/ty_z_time.png]]
 
-#+begin_src matlab :exports none
-  xlim([0, 1]);
-#+end_src
-
-#+NAME: fig:ty_z_time_zoom
-#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
-#+begin_src matlab :var filepath="figs/ty_z_time_zoom.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
-  <<plt-matlab>>
-#+end_src
-
-#+NAME: fig:ty_z_time_zoom
-#+CAPTION: Z velocity of the sample and marble when scanning with the translation stage - Zoom
-#+RESULTS: fig:ty_z_time_zoom
-[[file:figs/ty_z_time_zoom.png]]
-
-
 #+begin_src matlab
   figure;
   hold on;
@@ -176,7 +164,7 @@ We convert the measured voltage to velocity using the function =voltageToVelocit
   plot(e_ty(:, 3), e_ty(:, 2), 'DisplayName', 'Sample - X');
   hold off;
   xlabel('Time [s]'); ylabel('Velocity [m/s]');
-  xlim([0, 100]);
+  xlim([0, 2]);
   legend('Location', 'northeast');
 #+end_src
 
@@ -191,20 +179,41 @@ We convert the measured voltage to velocity using the function =voltageToVelocit
 #+RESULTS: fig:ty_e_time
 [[file:figs/ty_e_time.png]]
 
-#+begin_src matlab :exports none
+#+begin_src matlab
-  xlim([0, 1]);
+  figure;
+  plot(e_ty(:, 3), 1e6*lsim(1/s, e_ty(:, 2)-e_ty(:, 1), e_ty(:, 3)));
+  xlabel('Time [s]'); ylabel('X Relative Displacement [$\mu m$]');
+  xlim([0, 2]);
 #+end_src
 
-#+NAME: fig:ty_e_time_zoom
+#+NAME: fig:x_relative_disp
 #+HEADER: :tangle no :exports results :results value raw replace :noweb yes
-#+begin_src matlab :var filepath="figs/ty_e_time_zoom.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+#+begin_src matlab :var filepath="figs/x_relative_disp.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
   <<plt-matlab>>
 #+end_src
 
-#+NAME: fig:ty_e_time_zoom
+#+NAME: fig:x_relative_disp
-#+CAPTION: Velocity of the sample and marble in the east direction when scanning with the translation stage - Zoom
+#+CAPTION: X relative displacement of the sample with respect to the marble
-#+RESULTS: fig:ty_e_time_zoom
+#+RESULTS: fig:x_relative_disp
-[[file:figs/ty_e_time_zoom.png]]
+[[file:figs/x_relative_disp.png]]
+
+#+begin_src matlab
+  figure;
+  plot(z_ty(:, 3), 1e6*lsim(1/s, z_ty(:, 2)-z_ty(:, 1), z_ty(:, 3)));
+  xlabel('Time [s]'); ylabel('Z Relative Displacement [$\mu m$]');
+  xlim([0, 2]);
+#+end_src
+
+#+NAME: fig:z_relative_disp
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/z_relative_disp.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:z_relative_disp
+#+CAPTION: Z relative disp of the sample with respect to the marble
+#+RESULTS: fig:z_relative_disp
+[[file:figs/z_relative_disp.png]]
 
 ** Frequency Domain analysis
 We get the typical ground velocity to compare with the velocities measured.
@@ -232,15 +241,23 @@ First for the geophone located on the marble
 
 And for the geophone located at the sample position.
 #+begin_src matlab
-  [pxz_ty_s, f] = pwelch(z_ty(:, 2), win, [], [], Fs);
+  [pxz_ty_s, ~] = pwelch(z_ty(:, 2), win, [], [], Fs);
   [pxe_ty_s, ~] = pwelch(e_ty(:, 2), win, [], [], Fs);
   [pxe_of_s, ~] = pwelch(e_of(:, 2), win, [], [], Fs);
 #+end_src
 
+And finally for the relative velocity between the sample and the marble.
+#+begin_src matlab
+  [pxz_ty_r, ~] = pwelch(z_ty(:, 2)-z_ty(:, 1), win, [], [], Fs);
+  [pxe_ty_r, ~] = pwelch(e_ty(:, 2)-e_ty(:, 1), win, [], [], Fs);
+  [pxe_of_r, ~] = pwelch(e_of(:, 2)-e_of(:, 1), win, [], [], Fs);
+#+end_src
+
 And we plot the ASD of the measured velocities:
 - figure [[fig:asd_east_marble]] compares the marble velocity in the east direction when scanning and when Ty is OFF
 - figure [[fig:asd_east_sample]] compares the sample velocity in the east direction when scanning and when Ty is OFF
 - figure [[fig:asd_z_direction]] shows the marble and sample velocities in the Z direction when scanning with the translation stage
+- figure [[fig:asd_e_relative]] shows the relative velocity of the sample with respect to the granite in the X direction when the translation stage is OFF and when it is scanning at 1Hz
 
 #+begin_src matlab
   figure;
@@ -319,6 +336,31 @@ And we plot the ASD of the measured velocities:
 #+RESULTS: fig:asd_z_direction
 [[file:figs/asd_z_direction.png]]
 
+
+#+begin_src matlab
+  figure;
+  hold on;
+  plot(f, sqrt(pxe_of_r), 'DisplayName', 'Ty OFF - Relative - E');
+  plot(f, sqrt(pxe_ty_r), 'DisplayName', 'Ty 1Hz - Relative - E');
+  hold off;
+  set(gca, 'xscale', 'log');
+  set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
+  legend('Location', 'northwest');
+  xlim([0.1, 500]);
+#+end_src
+
+#+NAME: fig:asd_e_relative
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/asd_e_relative.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:asd_e_relative
+#+CAPTION: Amplitude spectral density of the measured relative velocity in the X direction
+#+RESULTS: fig:asd_e_relative
+[[file:figs/asd_e_relative.png]]
+
 ** Transfer function from marble motion in the East direction to sample motion in the East direction
 Let's compute the transfer function for the marble velocity in the east direction to the sample velocity in the east direction.
 

disturbance-ty/matlab/disturbance_ty.m

@@ -23,6 +23,10 @@ e_ty(:, 2) = voltageToVelocityL22(e_ty(:, 2), e_ty(:, 3), 40);
 e_of(:, 2) = voltageToVelocityL22(e_of(:, 2), e_of(:, 3), 40);
 
 % Time domain plots
+% We plot the measured velocity of the marble and sample in the vertical direction (figure [[fig:ty_z_time]]) and in the X direction (figure [[fig:ty_e_time]]).
+
+% We also integrate the relative velocity to obtain the relative displacement (figure [[fig:x_relative_disp]] in the X direction and figure [[fig:z_relative_disp]] in the Z direction).
+
 
 figure;
 hold on;
@@ -30,7 +34,7 @@ plot(z_ty(:, 3), z_ty(:, 1), 'DisplayName', 'Marble - Z');
 plot(z_ty(:, 3), z_ty(:, 2), 'DisplayName', 'Sample - Z');
 hold off;
 xlabel('Time [s]'); ylabel('Velocity [m/s]');
-xlim([0, 100]);
+xlim([0, 2]);
 legend('Location', 'northeast');
 
 
@@ -41,24 +45,13 @@ legend('Location', 'northeast');
 % [[file:figs/ty_z_time.png]]
 
 
-xlim([0, 1]);
-
-
-
-% #+NAME: fig:ty_z_time_zoom
-% #+CAPTION: Z velocity of the sample and marble when scanning with the translation stage - Zoom
-% #+RESULTS: fig:ty_z_time_zoom
-% [[file:figs/ty_z_time_zoom.png]]
-
-
-
 figure;
 hold on;
 plot(e_ty(:, 3), e_ty(:, 1), 'DisplayName', 'Marble - X');
 plot(e_ty(:, 3), e_ty(:, 2), 'DisplayName', 'Sample - X');
 hold off;
 xlabel('Time [s]'); ylabel('Velocity [m/s]');
-xlim([0, 100]);
+xlim([0, 2]);
 legend('Location', 'northeast');
 
 
@@ -69,7 +62,23 @@ legend('Location', 'northeast');
 % [[file:figs/ty_e_time.png]]
 
 
-xlim([0, 1])
+figure;
+plot(e_ty(:, 3), 1e6*lsim(1/s, e_ty(:, 2)-e_ty(:, 1), e_ty(:, 3)));
+xlabel('Time [s]'); ylabel('X Relative Displacement [$\mu m$]');
+xlim([0, 2]);
+
+
+
+% #+NAME: fig:x_relative_disp
+% #+CAPTION: X relative displacement of the sample with respect to the marble
+% #+RESULTS: fig:x_relative_disp
+% [[file:figs/x_relative_disp.png]]
+
+
+figure;
+plot(z_ty(:, 3), 1e6*lsim(1/s, z_ty(:, 2)-z_ty(:, 1), z_ty(:, 3)));
+xlabel('Time [s]'); ylabel('Z Relative Displacement [$\mu m$]');
+xlim([0, 2]);
 
 % Frequency Domain analysis
 % We get the typical ground velocity to compare with the velocities measured.
@@ -100,16 +109,25 @@ win = hanning(ceil(10*Fs));
 
 % And for the geophone located at the sample position.
 
-[pxz_ty_s, f] = pwelch(z_ty(:, 2), win, [], [], Fs);
+[pxz_ty_s, ~] = pwelch(z_ty(:, 2), win, [], [], Fs);
 [pxe_ty_s, ~] = pwelch(e_ty(:, 2), win, [], [], Fs);
 [pxe_of_s, ~] = pwelch(e_of(:, 2), win, [], [], Fs);
 
 
 
+% And finally for the relative velocity between the sample and the marble.
+
+[pxz_ty_r, ~] = pwelch(z_ty(:, 2)-z_ty(:, 1), win, [], [], Fs);
+[pxe_ty_r, ~] = pwelch(e_ty(:, 2)-e_ty(:, 1), win, [], [], Fs);
+[pxe_of_r, ~] = pwelch(e_of(:, 2)-e_of(:, 1), win, [], [], Fs);
+
+
+
 % And we plot the ASD of the measured velocities:
 % - figure [[fig:asd_east_marble]] compares the marble velocity in the east direction when scanning and when Ty is OFF
 % - figure [[fig:asd_east_sample]] compares the sample velocity in the east direction when scanning and when Ty is OFF
 % - figure [[fig:asd_z_direction]] shows the marble and sample velocities in the Z direction when scanning with the translation stage
+% - figure [[fig:asd_e_relative]] shows the relative velocity of the sample with respect to the granite in the X direction when the translation stage is OFF and when it is scanning at 1Hz
 
 
 figure;
@@ -162,7 +180,27 @@ plot(f_gm, sqrt(pxx_gm), 'k--', 'DisplayName', 'Ground Motion');
 hold off;
 set(gca, 'xscale', 'log');
 set(gca, 'yscale', 'log');
-xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
+xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
+legend('Location', 'northwest');
+xlim([0.1, 500]);
+
+
+
+% #+NAME: fig:asd_z_direction
+% #+CAPTION: Amplitude spectral density of the measure velocity corresponding to the geophone in the vertical direction located on the granite and at the sample location when the translation stage is scanning at 1Hz
+% #+RESULTS: fig:asd_z_direction
+% [[file:figs/asd_z_direction.png]]
+
+
+
+figure;
+hold on;
+plot(f, sqrt(pxe_of_r), 'DisplayName', 'Ty OFF - Relative - E');
+plot(f, sqrt(pxe_ty_r), 'DisplayName', 'Ty 1Hz - Relative - E');
+hold off;
+set(gca, 'xscale', 'log');
+set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
 legend('Location', 'northwest');
 xlim([0.1, 500]);