## 2 Materials and Methods
### Vibration Detection  
The vibration detection takes as input the raw measurements acquired within one second for all the cable segments along the optical fiber. Given a sampling rate of 2000 Hz and a spatial resolution of 0.68 m with a monitored fiber length of 40 km (corresponding to around 60,000 channels), the raw data consist of 2000 \(\times\) 60,000 samples each second. In the following, we will denote the data matrix containing all the raw measurement data for second \(i\) as \(M_{i}\). The result of the vibration detection for this second in time, \(v_{i}\), is a vector of Boolean values of length 60,000, where each element of this vector indicates whether vibration is present at the second \(i\) or not for that specific cable segment. Therefore, the vibration detection step corresponds to a data reduction from \(M_{i}\) to \(v_{i}\).  
In the following, we will describe the steps we used to perform vibration detection. We use machine learning techniques to decide whether the vector \(M_{i,x}\) containing the sensing samples for a given cable segment \(x\) and a given second in time \(i\) contains vibration or not. The decision is based on the spectral distribution of the raw signal \(M_{i,x}\) and is done based on the following steps detailed  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Laser pulse length & 100 & ns \\ Laser wavelength & 1550 & nm \\ Pulse repetition frequency & 2000 & Hz \\ Signal sampling frequency & 150 & kHz \\ Signal ADC sampling resolution & 16 & bit \\ Fiber light speed & 202,020,208 & m/s \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summarized parameters of measurement, optical fiber, and laser pulses used for this work.  
below. Note that the decision has to be made independently for all the cable segments without any spatial averaging; in the following, therefore, we will describe the procedure for one cable channel.  
1. Computation of the spectral energy in 10 frequency bins.
2. Normalization of the 10 energy values to make them sum up to 1.
3. Using Principal Component Analysis (PCA) to reduce the 10 feature values to two feature values.
4. Employ a pre-trained Support Vector Machine (SVM) to classify the feature vector of length 2 as vibration or background.  
**Computation of spectral energy.** The energy of the frequencies of the signal \(M_{i,x}\) are estimated using the Fast Fourier Transform (FFT). The squared absolute values of the Fourier transformed signal \(|M_{i,x}(\xi)|^{2}\) are then summed up individually for ten bins  
\[b_{k}=\sum_{\xi\in B_{k}}|M_{i,x}(\xi)|^{2}, \tag{1}\]  
where \(B_{k}\) denotes the \(k\)-th bin with \(k\in\{0,\dots,9\}\). The frequency bins are linearly spaced and span the frequencies between 10 Hz and 990 Hz.  
**PCA computation.** We use PCA to reduce the number of features from the frequency binning from 10 to 2. This is done by computing two linear combinations of the 10 original features optimally with respect to the variance of the data they can explain. Computationally, this PCA can be represented as a \(10\times 2\) matrix. The data used for computing the principal components are from the manually annotated test dataset described in Section 2.2.  
**SVM classification.** SVM classification is used for each cable segment to categorize it as vibration or background for each second in time. The SVM classifier is trained on manually annotated data. We use the SVM implementation of openCV 2.4 with an RBFkernel [17].