## 3 Results
### Temporal Statistics of the Principal Strain-Rates
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Element (d)** & \(\overline{\lambda_{1}}\)**(year\({}^{-1}\))** & \(\overline{\lambda_{3}}\)**(year\({}^{-1}\))** & \(\overline{\lambda_{3}}\)**(year\({}^{-1}\))** & \(\overline{n_{1}^{\prime}}\)**\(\Longrightarrow\)**\(\overline{\lambda_{4}}\)** & \(n_{2}^{\prime}\)**\(\Longrightarrow\)**\(\overline{\lambda_{2}}\)** & \(n_{3}^{\prime}\)**\(\Longrightarrow\)**\(\overline{\lambda_{3}}\)** \\ \hline
1 & 0.1157 & \(-\)0.0086 & \(-\)0.0687 & \([-\)0.0414 \(-\)0.4365 \(\pm\)0.7519] & \([1.0770\pm 0.1339\) & \(-\)0.9751] & \([1.0628\pm 0.8900\) & 0.5175] \\
2 & 0.5087 & \(-\)0.0085 & \(-\)0.0859 & \([-\)0.5777 \(\pm 0.5570\) \(\pm 0.5964)] & \([-\)0.4299 \(-\)0.1592 \(-\)0.8907] & \([-\)0.0636 \(-\)0.5909 \(\pm\)0.3956] \\
3 & 0.3919 & \(-\)0.0440 & \(-\)0.1662 & \([-\)0.3746 \(-\)0.7054 \(\pm 0.6017)] & \([-\)0.9968 \(\pm 0.3035\) \(\pm 0.0789]\) & \([0.3127\pm 0.7926\) & \(<\)0.5234] \\
4 & 0.0868 & 0.0041 & \(-\)0.0193 & \([-\)0.4684 \(\pm 0.8217\) \(\pm 0.3247]\) & \([-\)0.0619 \(\pm 0.3756\) \(\pm 0.9247]\) & \([-\)0.0733 \(-\)0.4414 \(-\)0.5246] \\
5 & 0.0435 & \(-\)0.0236 & \([-\)0.0659 \(-\)0.2139 \(\pm 0.8999\) \(\pm 0.4148]\) & \([-\)0.0091 \(\pm 0.7280\) \(\pm 0.8906]\) & \([0.2229\pm 0.2816\) \(-\)0.9333] \\
6 & 0.1834 & 0.0096 & \(-\)0.0536 & \([-\)0.2271 \(\pm 0.8400\) \(\pm 0.4859]\) & \([-\)0.6281 \(\pm 0.27046]\) & \([-\)0.4426 \(\pm 0.8540\) \(\pm 0.3083]\) \\
7 & 0.0647 & \(-\)0.0059 & \(-\)0.0485 & \([-\)0.5357 \(\pm 0.64016\) \(\pm 0.5678]\) & \([0.0741 \(-\)0.9392 \(\pm 0.0938)]\) & \([0.2985\pm 0.4328\) \(-\)0.8504] \\
8 & 0.1436 & \(-\)0.0198 & \(-\)0.0174 & \([-\)0.3994 \(\pm 0.4101894]\) & \([-\)0.1094 \(\pm 0.9614\) \(-\)0.2525] & \([0.3964\pm 0.6844\) \(-\)0.2952] \\
9 & 0.6311 & 0.0178 & \(-\)0.1144 & \([-\)0.0242 \(-\)0.0619 \(\pm 0.6785]\) & \([0.1227\pm 0.2958\) \(\pm 0.9278]\) & \([1.0717\pm 0.8523\) \(\pm 0.6211]\) \\
10 & 0.0355 & 0.0098 & \(-\)0.0745 & \([-\)0.4275 \(\pm 0.8293\) \(-\)0.1449] & \([0.8656\pm 0.3153\) \(-\)0.0551] & \([-\)0.5198 \(\pm 0.2220\) \(-\)0.8249] \\
11 & 0.0452 & \(-\)0.0239 & \(-\)0.1039 & \([-\)0.4724 \(\pm 0.9088\) \(\pm 0.8753]\) & \([-\)0.7018 \(-\)0.0693 \(\pm 0.1650]\) & \([-\)0.3132 \(-\)0.0495 \(-\)0.1693] \\
12 & 0.2054 & 0.0326 & \(-\)0.0703 & \(-\)0.5086 \(-\)0.8585 & \(-\)0.1954 & \([0.1867\pm 0.6567\) \(\pm 0.7707]\) & \([0.0406\pm 0.476\) \(-\)0.8801] \\
13 & 1.1642 & \(-\)0.0118 & \(-\)0.3192 & \([-\)0.4800 \(\pm 0.6926\) \(\pm 0.6609\) \(\pm 0.6909]\) & \([-\)0.9632 \(\pm 0.2605\) \(\pm 0.0654]\) & \([-\)0.5135 \(\pm 0.5798\) \(-\)0.6285] \\
14 & 0.1923 & \(-\)0.0415 & \(-\)0.2640 & \([-\)0.4758 \(\pm 0.8168\) \(\pm 0.35624]\) & \([0.9507\pm 0.2698\) \(-\)0.1076] & \([0.4038\pm 0.2751]\) & \([0.4038\pm 0.2751]\) \\
15 & 0.0552 & 0.00085 & \(-\)0.0363 & \([-\)0.2364 \(\pm 0.60610\) \(\pm 0.7514]\) & \([0.7513\pm 0.2789\) \(\pm 0.5978]\) & \([0.6817\pm 0.6544]\) & \([-\)0.3270] \\
16 & 0.0438 & 0.0175 & \(-\)0.0059 & \([0.2794\pm 0.9257\) \(-\)0.2549] & \([0.8449\pm 0.2441\) \(\pm 0.4760]\) & \([-\)0.5430 \(-\)0.2902 \(-\)0.7883] \\
17 & 0.2113 & \(-\)0.0196 & \(-\)0.3129 & \([-\)0.0062 \(\pm 0.9666\) \(\pm 0.2599)\) & \([0.0760\pm 0.2441\) \(\pm 0.9668]\) & \([0.0666\pm 0.9959\) \(-\)0.0609] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Time-averaged eigenspace components. Figure 6: The trajectory patterns of the time-averaged principal strain-rates: averaged first principal strain-rate (**top**); averaged second principal strain-rate (**middle**); and averaged third principal strain-rate (**bottom**). In these graphs, the red color is used to represent extension, while the blue color depicts contraction. Example and decreases near Sants. In the case of the contraction-rate in the PC3 dimension, it is mostly present between Nou Barris and Horta, and in smaller magnitude between Horta and Sant Andreu. The contraction-rate between the remaining districts is negligible in all dimensions.