# Characterization of Shallow Sedimentary Layers in the Oran Region Using Ambient Vibration Data
## 3 Methodology and Data Processing
### Spatial Autocorrelation (SPAC) Technique  
The SPAC method is a highly effective technique for determining shear-wave velocity structures in the subsurface using ambient vibration array measurements. It was proposedby [41] and determines the dispersion curve of the surface wave phase velocity. The method assumes that surface waves dominate the ambient vibration signal. The SPAC method is based on several assumptions: (1) ambient vibration waves are stationary in time and the horizontal plane; (2) ambient vibration sources are uniformly distributed; (3) the subsurface Vs structure of the observation arrays consists of horizontal flat layers. The SPAC method requires a circular array of at least four seismographs [31]. Three sensors are distributed around the circumference of the circle and the fourth is located in the center. However, some authors (e.g., [22]), have used additional circles, all centered with the same station for better coverage. In our case, an array of seven stations, forming two circles centered with one station (see Figure 3a), has been used. By recording between the sensors at regular intervals, the mean azimuthal coherence function (i.e., the SPAC coefficient) can be obtained.  
The SPAC technique has been carried out with Geopsy software. The SPAC toolbox within the software has been used to define the ring parameters as a first step. After inputting the sensor coordinates, the software automatically establishes a series of sensor pairs distributed in space. Typically, this comprises 21 pairs for 7 sensors. Subsequently, these sensor pairs have been assigned to one or more rings based on optimal matches determined by entering the inner and outer radii. Each ring should consist of at least two pairs and it is recommended to use the maximum number of rings to improve resolution [42]. The signals have been segmented into several windows with a duration of 50 s. The selection of the window was carried out using an anti-triggering algorithm. The subsequent analysis has resulted in the calculation of spatial autocorrelation curves for each ring. Spac2 Disp module (from Geopsy package, release 2.10.1 [36]) has been used to visualize the phase velocity histograms derived from the computed spatial autocorrelation values. The final dispersion curve has been derived by selecting the Rayleigh phase velocity values that contributed significantly to the dispersion curve within the Kmin and Kmax ranges. A similar procedure has been applied to the data from the 15 arrays.  
Regarding the estimated dispersion curves, some differences are observed with respect to the f-k method. In the SPAC technique, the dispersion curves are picked manually by visually following the maximum energy. In this way, small errors in picking may lead to different dispersion curves. The same differences have already been observed in a previous work in the Middle-Chelif Basin about 200 km east of our study area [22]. The authors pointed out that the SPAC technique appeared to be more sensitive to soft slopes. Therefore, the dispersion curves obtained with the SPAC technique sometimes differ from those obtained with the f-k method when the recording site is on a slope.