1 Setup
+
+
1 Setup
Two L22 geophones are used. @@ -282,14 +283,14 @@ The voltage amplifiers include a low pass filter with a cut-off frequency at 1kH
-
+
-
Figure 1: Setup
+
-
Figure 2: Geophones
@@ -297,38 +298,38 @@ The voltage amplifiers include a low pass filter with a cut-off frequency at 1kH
-
2 Signal Processing
+
+
-
2 Signal Processing
-
2.1 Load data
+
+
-2.1 Load data
-
load('mat/data_001.mat', 't', 'x1', 'x2'); -dt = t(2) - t(1); +load('mat/data_001.mat', 't', 'x1', 'x2'); +dt = t(2) - t(1);
-
2.2 Time Domain Data
+
+
2.2 Time Domain Data
-
-figure; +figure; hold on; -plot(t, x1); -plot(t, x2); +plot(t, x1); +plot(t, x2); hold off; -xlabel('Time [s]'); -ylabel('Voltage [V]'); -xlim([t(1), t(end)]); +xlabel('Time [s]'); +ylabel('Voltage [V]'); +xlim([t(1), t(end)]);
+
Figure 3: Time domain Data
@@ -336,19 +337,19 @@ xlim([
-
-figure; +figure; hold on; -plot(t, x1); -plot(t, x2); +plot(t, x1); +plot(t, x2); hold off; -xlabel('Time [s]'); -ylabel('Voltage [V]'); -xlim([0 1]); +xlabel('Time [s]'); +ylabel('Voltage [V]'); +xlim([0 1]);
+
-
Figure 4: Time domain Data - Zoom
@@ -356,39 +357,39 @@ xlim([
-
2.3 Compute PSD
+
+
-2.3 Compute PSD
-
[pxx1, f1] = pwelch(x1, hanning(ceil(length(t)/100)), 0, [], 1/dt); -[pxx2, f2] = pwelch(x2, hanning(ceil(length(t)/100)), 0, [], 1/dt); +[pxx1, f1] = pwelch(x1, hanning(ceil(1/dt)), 0, [], 1/dt); +[pxx2, f2] = pwelch(x2, hanning(ceil(1/dt)), 0, [], 1/dt);
-
2.4 Take into account sensibility of Geophone
+
+
diff --git a/huddle-test-geophones/index.org b/huddle-test-geophones/index.org
index 90dbf4d..78e2066 100644
--- a/huddle-test-geophones/index.org
+++ b/huddle-test-geophones/index.org
@@ -96,8 +96,8 @@ The voltage amplifiers include a low pass filter with a cut-off frequency at 1kH
** Compute PSD
#+begin_src matlab :results none
- [pxx1, f1] = pwelch(x1, hanning(ceil(length(t)/100)), 0, [], 1/dt);
- [pxx2, f2] = pwelch(x2, hanning(ceil(length(t)/100)), 0, [], 1/dt);
+ [pxx1, f1] = pwelch(x1, hanning(ceil(1/dt)), 0, [], 1/dt);
+ [pxx2, f2] = pwelch(x2, hanning(ceil(1/dt)), 0, [], 1/dt);
#+end_src
** Take into account sensibility of Geophone
@@ -147,6 +147,7 @@ The cut-off frequency is set at 1kHz.
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
+ xlim([2, 500]);
#+end_src
#+NAME: fig:psd_velocity
@@ -159,3 +160,37 @@ The cut-off frequency is set at 1kHz.
#+CAPTION: Spectral density of the velocity
#+RESULTS: fig:psd_velocity
[[file:figs/psd_velocity.png]]
+** Transfer function between the two geophones
+#+begin_src matlab :results none
+ [T12, f12] = tfestimate(x1, x2, hanning(1/dt), 0, [], 1/dt);
+#+end_src
+
+#+begin_src matlab :results none
+ figure;
+ ax1 = subplot(2, 1, 1);
+ plot(f12, abs(T12));
+ set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+ set(gca, 'XTickLabel',[]);
+ ylabel('Magnitude');
+
+ ax2 = subplot(2, 1, 2);
+ plot(f12, mod(180+180/pi*phase(T12), 360)-180);
+ set(gca, 'xscale', 'log');
+ ylim([-180, 180]);
+ yticks([-180, -90, 0, 90, 180]);
+ xlabel('Frequency [Hz]'); ylabel('Phase');
+
+ linkaxes([ax1,ax2],'x');
+ xlim([2, 500]);
+#+end_src
+
+#+NAME: fig:tf_geophones
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/tf_geophones.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+ <>
+#+end_src
+
+#+NAME: fig:tf_geophones
+#+CAPTION: Estimated transfer function between the two geophones
+#+RESULTS: fig:tf_geophones
+[[file:figs/tf_geophones.png]]
2.4 Take into account sensibility of Geophone
The Geophone used are L22.
-
S0 = 88; % Sensitivity [V/(m/s)] -f0 = 2; % Cut-off frequnecy [Hz] -S = (s/2/pi/f0)/(1+s/2/pi/f0); +S0 = 88; % Sensitivity [V/(m/s)] +f0 = 2; % Cut-off frequnecy [Hz] +S = (s/2/pi/f0)/(1+s/2/pi/f0);
-
-figure; -bodeFig({S}); -ylabel('Amplitude [V/(m/s)]') +figure; +bodeFig({S}); +ylabel('Amplitude [V/(m/s)]')
+
+
Figure 5: Sensibility of the Geophone
@@ -406,37 +407,74 @@ The cut-off frequency is set at 1kHz.
-
G0 = 60; % [dB] +G0 = 60; % [dB] -G = G0/(1+s/2/pi/1000); +G = G0/(1+s/2/pi/1000);
-
-figure; +figure; hold on; -plot(f1, sqrt(pxx1)./squeeze(abs(freqresp(G, f1, 'Hz')))./squeeze(abs(freqresp(S, f1, 'Hz')))); -plot(f2, sqrt(pxx2)./squeeze(abs(freqresp(G, f2, 'Hz')))./squeeze(abs(freqresp(S, f2, 'Hz')))); +plot(f1, sqrt(pxx1)./squeeze(abs(freqresp(G, f1, 'Hz')))./squeeze(abs(freqresp(S, f1, 'Hz')))); +plot(f2, sqrt(pxx2)./squeeze(abs(freqresp(G, f2, 'Hz')))./squeeze(abs(freqresp(S, f2, 'Hz')))); hold off; -set(gca, 'xscale', 'log'); -set(gca, 'yscale', 'log'); -xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]') +set(gca, 'xscale', 'log'); +set(gca, 'yscale', 'log'); +xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]') +xlim([2, 500]);
+
Figure 6: Spectral density of the velocity
+
2.5 Transfer function between the two geophones
+
+
+
+
+
+[T12, f12] = tfestimate(x1, x2, hanning(1/dt), 0, [], 1/dt); ++
+
+
+
+figure; +ax1 = subplot(2, 1, 1); +plot(f12, abs(T12)); +set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); +set(gca, 'XTickLabel',[]); +ylabel('Magnitude'); + +ax2 = subplot(2, 1, 2); +plot(f12, mod(180+180/pi*phase(T12), 360)-180); +set(gca, 'xscale', 'log'); +ylim([-180, 180]); +yticks([-180, -90, 0, 90, 180]); +xlabel('Frequency [Hz]'); ylabel('Phase'); + +linkaxes([ax1,ax2],'x'); +xlim([2, 500]); ++
+
+
+
Figure 7: Estimated transfer function between the two geophones
+