In the lineaments attribute table, the coordinates of the start (X1, Y1) and end (X2, Y2) points were calculated using a script tool in ArcGIS software.

Once the coordinates were obtained, the orientation angle of the lineament was computed by applying the following formula [16] :

Radianangle ( θ ) = Arc   tg [ ( Y 2 − Y 1 ) / ( | X 1 − X 2 | ) ] .

The experimental result corresponds to the value of the angle θ expressed in radian. Then, this value was converted into degrees to indicate the orientations towards to North, as follows: Angle in degrees = (Angle in radian*180)/II.

The direction values α of the faults must be between 0˚ and 180˚ (Figure 6).

The north should be considered as the origin of the measurements and the positive direction is clockwise.

If α < 0, then the value of the direction will be equal to the absolute value of the additional angle, as revealed in (Table 2).

In the quantitative analysis performed to identify the major directions (Figure 6), a table showing the number of lineaments per directions intervals was presented. A direction interval of 15˚ was chosen, as demonstrated in (Table 3).

To highlight the studied directions, a directional rosette was drawn from the quantitative table of lineaments (Figure 7).

A quantitative and spatial analysis based on the coordinates and directions of the lineaments of the tectonic accidents was carried out (Figure 6).

First, a map of the lineaments, indexed by the value of each direction, was constructed. It shows around 810 fractures of variable lengths and is oriented in almost all directions.

The directional rosette, as well as the directional histogram, reveal that the classes of directions ]30, 45], ]45, 60] are the major directions of the lineament lattice considered in our previous works.

The linear density is a very important characteristic that should be further examined [17]. It is determined by the ratio of the total lineament length in meters to the area of the studied zone in square kilometres. Apart from a few places that seem to be significantly less dense, the density map of lineaments of Grombalia shows an almost homogeneous density (Figure 8).

It is worth noting that several rectilinear and curvilinear features emerged from the lineament map.

After transforming all entities into a rectilinear form by applying a script from Arc Toolbox, the length of each lineament was calculated by applying the following formula of Vladimir Levenshtein (1):

Δ X 2 + Δ Y 2 (1)

Using GIS environment, the result of lineaments extraction from geological map allowed the quantitative, the spatial and the statistical analysis (Table 4) necessary to validate the lineaments extraction results obtained from satellite images.

The lineaments lengths range from 62,879 m to 2,666,319 m, with an average of 628,727 m (Table 4).

For geological interpretation purposes, the Principal Component Analysis (PCA) is an effective technique employed to enhance a multi-spectral image [28]. The information in several bands is reduced to a smaller number of components generally representing up to 97% of the total variance of the original data set [29]. Sometimes the information in 5 or 6 bands is minimized by the PCA to only 3 components. This analysis allows the creation of colored compounds of the first three components that constitute an excellent visual interpretation product, which increases the contrast between the various objects on the ground.

In order to obtain the best color composition (Table 5), the optimal index factor technique was used in the experiments.

In addition, the Optimal Index Factor (OIF), (2) is a statistical value that provides the optimal combination of three bands out of all the bands in a satellite image from which a color composite can be obtained (Figure 9). This combination contains the largest amount of information (the maximum value of standard deviations), with the minimum duplication (lowest correlation among the pairs of bands).

To calculate the optimal index factors, a map list containing at least three raster maps was created and a correlation matrix or variance-covariance matrix was calculated for the map list, which provided the standard deviations and correlation coefficients applied to calculate the IFM.

The algorithms used to compute the IFM are generally executed according to the following formula in GRASS GIS manual (https://grass.osgeo.org/):

OIF = ∑ k = 1 3 S k ∑ j = 1 3 | r j | (2)

where:

∑ S k : is the sum of the standard deviations (standard deviations) of the combinations of the 3 bands k1, k2, k3;

∑ | r j | : denotes the sum of the absolute values of the correlation coefficient.

The calculation of the OIF was performed by the (ILWIS) software that integrated the GIS platform with remote sensing for vector and matrix processing the objects used in our study.

In order to improve the Sentinel 2A satellite image of the area under this study, Principal Component Analysis (PCA) was applied.

Filtering aims at eliminating noise in data. In geology, scientists focus on finding discontinuities in the textures present in the images (e.g. the contours of relatively homogeneous zones that can reveal the presence of faults or fractures. Lineaments are enhanced by highlighting strong reflectance transitions in the image and the associated spatial high frequencies. Then, the numerical value of a pixel is modified according to its relationship with the values of neighbouring pixels obtained by spatial convolution filtering. The size of the window in pixels is directly proportional to the order of the magnitude of the spatial changes related to the lineaments to be detected.

Several authors, such as ( [30] [31] ), used 5 × 5 windows on Landsat-TM images with a ground resolution of 30 m × 30 m for structural study (Table 6).

Other researchers ( [9] [10] [11] [32] ) retained 7 × 7 windows (Table 7).

The two tables presented above show that directional filters improve the perception of lineaments by causing an optical shadow effect on the image.

In this approach, these filters were applied in four main directions: N-S, E-W, NE-SW, SE-NW, in order to improve the perception of lineaments not exposed to the illumination source.

Only lineaments with a length greater than half of the convolution window were detected. Therefore, we can conclude that the choice of filter size depends on the length of the lineament to be extracted. In our study, we chose a convolution window of 3 by 3 to detect lineaments with a few meters length (Table 8).

With an angular range of 45˚ of the directional filters around the main enhancement direction, four drift images were first generated from four Sobel directional filters (NO NW, OW, SO SW and S). Subsequently, the modified 3 × 3 Prewitt filters were retained to detect the lineaments in all possible directions.

Given the size of the study area and the order of magnitude of the structures, a 3 × 3 window was used to detect the major lineaments and generate the finer structures ( [23] [24] [32] ).

In order to enhance the linear characteristics, directional filters were employed, which improved the perception of the lineaments by causing an optical shadow effect on the image.

All previous works used Sobel’s directional filters. However, Prewitt’s filters are often compared to Sobel’s filters to detect contours.

Thus, the Prewitt filters were applied in the four directions (N-S, E-W, NE-SW and NW-SE) knowing that the NE-SW and NW-SE directions are rarely used in this type of filter. Afterwards, the directional Prewitt filters (Table 9) were modified to obtain better results.

PCI Geomatica’s LINE module is generally utilized to extract linear shapes from the image and produce vector files, using 6 parameters to be identified by the user (Table 9 and Table 10). The used parameters are chosen by the photo-interpreter, which results in directed extraction [25].

Indeed, the parameters defining the discontinuities in the filtered images are complex and depend on the length, the angle and the gradient level thresholds of a pixel or a set of pixels considered as a single linear or curvilinear element (Table 10).

The extracted lineaments were processed in vector (.shp) format to conduct the statistical analyses.

The LINE algorithm consists of three steps:

• Edge detection;

• Thresholding;

• Curve extraction.

In the first step, Canny’s edge detection algorithm was applied to produce an edge intensity image. The application of this algorithm can be divided into three sub-steps. First, the input image was filtered with a Gaussian function whose radius was provided by the Filter Radius parameter. Second, the gradient was calculated from the filtered image. Finally, pixels whose gradient does not correspond to the local maximum were removed by setting the edge intensity to 0.

In the second step, the edge intensity image was thresholded to obtain a binary image. Each activated pixel of the binary image represents an edge element. The threshold value was finally defined by the GTHR (Edge Gradient Threshold) parameter.

In the third step, the curves were extracted from the binary edge image. This step can be divided into several sub-stages. First, a thinning algorithm was applied to the binary edge image to produce the pixel skeleton curves. Subsequently, a sequence of pixels for each curve was extracted from the image. Further processing ignored curves containing a number of pixels less than the value of the LTHR (curve length threshold) parameter. After that, an extracted pixel curve was converted into vector form by fitting line segments to it. The resulting polyline approximates the original pixel curve where the maximum fitting error

(distance between the two) is specified by the FTHR (Line Fitting Threshold) parameter. Finally, the algorithm linked pairs of poly-lines that meet the following criteria:

• The two end segments of the two poly-lines are apposite to each other and have similar orientation (the angle between the two segments is less than the value specified by ATHR);

• The two end segments are close to each other (the distance between the end points is less than the value of DTHR);

The final polylines were stored in a vector segment.

Several values of Line PCI module calibration parameters have been used and we notice that the best result has been obtained by applying the following parameters (Table 11).

Four images were produced for each filter related to the 4 directions N-S, E-W, NE-SW and NW-SE. This set of resulting images is used as input for the automatic lineament extraction methods.

By superimposing the four lineament maps obtained in the four directions, a synthesis map of the lineaments was created (Figure 10).

Automatic methods often generate a lot of insignificant lineaments as well as other types of lineaments, such as roads, tracks, outcrops, river systems, etc., these shapes have been identified and eliminated.