1 Experimental Setup
+1 Experimental Setup
Two L22 geophones are used. @@ -319,14 +319,14 @@ The voltage amplifiers include a low pass filter with a cut-off frequency at 1kH
-
Figure 1: Setup
Figure 2: Geophones
@@ -334,8 +334,8 @@ The voltage amplifiers include a low pass filter with a cut-off frequency at 1kH2 Signal Processing
+2 Signal Processing
The Matlab computing file for this part is accessible here.
@@ -343,8 +343,8 @@ The mat file containing the measurement data is accessible
2.1 Load data
+2.1 Load data
We load the data of the z axis of two geophones.
@@ -358,8 +358,8 @@ dt = t(
- Figure 3: Time domain Data Figure 4: Time domain Data - Zoom
We first define the parameters for the frequency domain analysis.
@@ -422,12 +422,12 @@ Fs = 1/
The Geophone used are L22.
-Their sensibility are shown on figure 5.
+Their sensibility are shown on figure 5.
Figure 5: Sensibility of the Geophone
-The ASD of the measured velocity is shown on figure 6.
+The ASD of the measured velocity is shown on figure 6.
Figure 6: Spectral density of the velocity
+We also plot the ASD in displacement (figure 7);
+ Figure 7: Amplitude Spectral Density of the displacement as measured by the geophones
We here compute the transfer function from one geophone to the other.
-The result is shown on figure 7.
+The result is shown on figure 8.
-We also compute the coherence between the two signals (figure 8).
+We also compute the coherence between the two signals (figure 9).
Figure 7: Estimated transfer function between the two geophones Figure 8: Estimated transfer function between the two geophones Figure 8: Cohererence between the signals of the two geophones Figure 9: Cohererence between the signals of the two geophones
The technique to estimate the sensor noise is taken from barzilai98_techn_measur_noise_sensor_presen.
@@ -567,11 +590,11 @@ where:
-The
-Figure 9 illustrate a block diagram model of the system used to determine the sensor noise of the geophone.
+Figure 10 illustrate a block diagram model of the system used to determine the sensor noise of the geophone.
@@ -583,10 +606,10 @@ Each sensor has noise \(N\) and \(M\).
Figure 9: Huddle test block diagram Figure 10: Huddle test block diagram
@@ -598,7 +621,7 @@ We also assume that \(H_1 = H_2 = 1\).
We then obtain:
-From equations \eqref{org65b3ddf} and \eqref{org14038cd}, we finally obtain
+From equations \eqref{orgb78feac} and \eqref{org8419580}, we finally obtain
-The instrumental noise is computed below. The result in V2/Hz is shown on figure 10.
+The instrumental noise is computed below. The result in V2/Hz is shown on figure 11.
Figure 10: Instrumental Noise and Measurement in \(V^2/Hz\) Figure 11: Instrumental Noise and Measurement in \(V^2/Hz\)
-This is then further converted into velocity and compared with the ground velocity measurement. (figure 11)
+This is then further converted into velocity and compared with the ground velocity measurement. (figure 12)
Figure 11: Instrumental Noise and Measurement in \(m/s/\sqrt{Hz}\) Figure 12: Instrumental Noise and Measurement in \(m/s/\sqrt{Hz}\)
The Matlab computing file for this part is accessible here.
@@ -689,8 +712,8 @@ The
We first load the data for the three axis.
@@ -704,8 +727,8 @@ north = load(
-
The PSD for each axis of the two geophones are computed.
@@ -723,23 +746,23 @@ The PSD for each axis of the two geophones are computed.
-We compare them. The result is shown on figure 12.
+We compare them. The result is shown on figure 13.
Figure 12: Compare the measure PSD of the two geophones for the three axis Figure 13: Compare the measure PSD of the two geophones for the three axis
The transfer functions from one geophone to the other are also computed for each axis.
-The result is shown on figure 13.
+The result is shown on figure 14.
Figure 13: Compare the transfer function from one geophone to the other for the 3 axis Figure 14: Compare the transfer function from one geophone to the other for the 3 axis Figure 14: Comparison of Figure 15: Comparison of Created: 2019-04-18 jeu. 17:11 Created: 2019-04-18 jeu. 17:242.2 Time Domain Data
+2.2 Time Domain Data
figure;
@@ -374,7 +374,7 @@ xlim(
+
2.3 Computation of the ASD of the measured voltage
+2.3 Computation of the ASD of the measured voltage
2.4 Scaling to take into account the sensibility of the geophone and the voltage amplifier
+2.4 Scaling to take into account the sensibility of the geophone and the voltage amplifier
G0 = 60; % [dB]
-G = G0/(1+s/2/pi/1000);
+G = 10^(G0/20)/(1+s/2/pi/1000);
scaling = 1./squeeze(abs(freqresp(G, f, 'Hz')))./squeeze(abs(freqresp(S, f, 'Hz')));
+
scaling = 1./squeeze(abs(freqresp(G*S, f, 'Hz')));
2.5 Computation of the ASD of the velocity
+2.5 Computation of the ASD of the velocity
figure;
hold on;
-plot(f, sqrt(pxx1)./scaling);
-plot(f, sqrt(pxx2)./scaling);
+plot(f, sqrt(pxx1).*scaling);
+plot(f, sqrt(pxx2).*scaling);
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
@@ -490,24 +490,47 @@ xlim(
+
figure;
+hold on;
+plot(f, (pxx1.*scaling./f).^2);
+plot(f, (pxx2.*scaling./f).^2);
+hold off;
+set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
+xlim([2, 500]);
+
+
+2.6 Transfer function between the two geophones
+2.6 Transfer function between the two geophones
2.7 Estimation of the sensor noise
+2.7 Estimation of the sensor noise
mscohere function is compared with this formula on Appendix (section 4.1), it is shown that it is identical.
+The mscohere function is compared with this formula on Appendix (section 4.1), it is shown that it is identical.
pxxN = pxx1.*(1 - coh12);
@@ -643,14 +666,14 @@ xlim(
+
figure;
@@ -666,17 +689,17 @@ xlim(
+
3 Compare axis
+3 Compare axis
mat files containing the measurement data are accessible with t
3.1 Load data
+3.1 Load data
3.2 Compare PSD
+3.2 Compare PSD
3.3 Compare TF
+3.3 Compare TF
4 Appendix
+4 Appendix
4.1 Computation of coherence from PSD and CSD
+4.1 Computation of coherence from PSD and CSD
load('mat/data_001.mat', 't', 'x1', 'x2');
@@ -798,10 +821,10 @@ xlim(
+
mscohere and manual computationmscohere and manual computation