## 2 Approach
### Averaging and Moving Differential  
The authors of [47] present a relatively simple algorithm having an acceptable efficiency under the research conditions. The algorithm operation was tested by processing data obtained with the DAS system using two different sources of radiation and two different sources of acoustic events: a shaker located at a distance of 3500 m from the sensitive element input facet and a piezoelectric transducer located at a distance of 1800 m, at frequencies exposure to 350, 500, 1200, 3700, and 5600 Hz. The sensitive element of the sensor consisted of 4 km of SMF-28 telecommunications optical fiber (Figure 2). Figure 1: One of the cost-effective DAS prototypes used to obtain experimental data. PC—personal computer, DAC—digital-to-analog converter, EDFA—erbium-doped fiber amplifier, ADC—analog-to-digital converter. As a rule, any DAS technology works as follows: a light pulse is injected into the fiber optic sensing element through an optical circulator or coupler. As it propagates along the fiber, a part of its energy is scattered in all directions every moment on intrinsic refractive index inhomogeneities of subwavelength scale. Sometimes the inhomogeneities in the fiber could be specially induced (like fiber Bragg gratings, FBGs). A part of the scattered radiation guided by the optical fiber core begins to propagate in the direction opposite to the probing. The optical circulator or splitter at the input end of the fiber transmits this signal to the photodetector. The arrival time of backscattered signal from a specific point in the optical fiber unveils the information about the distance to this point, and its intensity, can, for example, give evidence of an acoustic impact presence or absence. This is possible due to the fact that acoustic waves are able to exert the pressure to an optical fiber and thus modulate its core refractive index and the positions of the inhomogeneities causing Rayleigh backscattering (and, therefore, its intensity in this location), with the frequency they have themselves. Thus, DAS raw data is a sequence of \(\varphi\)-OTDR traces recorded continuously for some time, that is, the dependences of the backscattering intensity on time. They can be arranged in the form of a matrix, the rows of which contain the backscattering intensity distribution along the length of the fiber, and the columns, respectively, the backscattering intensity distribution at a specific point of the fiber over time. The data acquired by the sensor from [47] had exactly the same form. An \(N\times M\)\(\{s_{nm}\}\) matrix consisted of \(M=8000\) rows, corresponding to the distribution along the fiber (trace) and \(N=932\) columns, corresponding to the time distribution (932 traces sequentially obtained by the sensor). The noise suppression algorithm consisted of two parts. First, each element was averaged over the 20 nearest elements of the row--in the spatial domain:  
\[\widetilde{s}_{nm}=\left[\sum_{a}^{b}s_{nk}\right]\left[w^{-1}\right] \tag{1}\]  
where \(w=21\) and \(k\) increases from \(a=m-0.5(w-1)\) to \(b=m+0.5(w-1)\). This allows one to reduce noise outside the spatial spectrum and make the resulting traces smoother. However, it reduces the spatial resolution in proportion to the number of neighboring elements selected to average the given one. In the second part, the moving differential algorithm [48] was applied to the time domain-matrix columns. This also made it possible to reduce the noise background and to obtain, after performing fast Fourier transform (FFT) over the matrix columns, frequency spectra with pronounced peaks at the frequencies of the vibrations applied to the sensor (Figure 3). Figure 2: Experimental setup and data samples (\(\varphi\)-DAS traces) acquired using a semiconductor (**a**) and a commercial fiber laser (**b**). The peaks denote the acoustic events that took place along the fiber. DFB—distributed feedback, AOM—acousto-optic modulator, BPF—bandpass filter, PM—polarization-maintaining.