Ground Motion Measurements

1. Preprocessing of id31 ground motion measurement
2. Plots

1 Preprocessing of id31 ground motion measurement

data = table2array(readtable('./data/id31_camac_floor_PSD_october2014.txt'));

The first column is the frequency vector in Hz.

gm.freqs = data(:, 1);

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 \(\frac{(m/s)^2}{Hz}\).

gm.psd_vx = 1e-12*data(:, 2);
gm.psd_vy = 1e-12*data(:, 3);
gm.psd_vz = 1e-12*data(:, 4);

Finally, we integrate the signal to obtain the power spectral density of the ground displacement.

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);

The pre-processed data are saved.

save('./data/gm_esrf.mat', 'gm');

2 Plots

We load measurements made:

at ID31
at ID09
at CERN

id31 = load('./data/ground_motion_psd.mat');
id09 = load('./data/id09_floor_september2018.mat');
cern = load('./data/ground_motion_dist.mat');

2.1 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();

Figure 1: Time domain data - ID09

2.2 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)));

2.3 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');

Figure 2: Comparison of the PSD of ground motion