## 3 Results and Discussion
This value is 36.1 \(\upmu\)T less than the maximum field of the defect S1, which represents a reduction of 20.8%. This decrease is related to the less depth (2.0 mm) of the defect S2 in comparison to the depth (3.65 mm) of defect S1. The width of  
Figure 5: Tangential MMM signal of the rectangular defect S1 of the ASTM A-36 steel pipe. Figure 6: Normal MMM signal of the rectangular defect S1 of the ASTM A-36 steel pipe. the tangential MMM signal is related to the defect width (3.80 mm). The measured tangential MMM response has a magnetic flux offset close to 35 \(\upmu\)T at the right edge of the defect S2. The measured tangential MMM signal has a behaviour similar to that obtained by the analytical model. On the other hand, the measured normal MMM signal (see Figure 8) of the defect S2 has maximum and minimum values (25.8 \(\upmu\)T and \(-\)27.2 \(\upmu\)T) around both defect edges. The polarity of this MMM signal is altered at the defect center S2 (\(y\) = 0 mm). In addition, the normal MMM signal obtained through the analytical model agree well with the experimental data in the positions between \(-\)2.0 and 2.0 mm. However, the analytical response of the tangential MMM signal has a high absolute difference (18.67 \(\upmu\)T and 20.17 \(\upmu\)T) with respect to the measured MMM signal in the positions from \(-\)5.0 m to 5.0 mm. The offset of both tangential and normal MMM signals is due to the magnetic flux along the pipe surface close to the defects. In addition, the results of both MMM signals determined with the 2D magnetic dipole method have a discrepancy with respect to measured MMM responses. This is due to the fact that the analytical model considers a constant magnetic permeability of the ferromagnetic material. In addition, the defect S2 has edges with small inclinations that can affect the measured response of both MMM signals. For the third rectangular defect (S3), the measured tangential MMM signal has a maximum value (53.6 \(\upmu\)T) at the defect center (see Figure 9). This value is 119.6 \(\upmu\)T less than that obtained of the defect S1, which represents a reduction of 69.1%. This largest variation is related to the smallest depth (0.50 mm) of the defect S3. In addition, the width of this tangential MMM response decreases in comparison to the MMM signal of the defects S1 and S2, respectively. For the defect S3, both tangential MMM signals  
Figure 8: Normal MMM signal of the rectangular defect S2 of the ASTM A-36 steel pipe. Figure 7: Tangential MMM signal of the rectangular defect S2 of the ASTM A-36 steel pipe. have a similar behaviour between the positions from \(-\)1.4 mm to 1.4 mm. The distance between these positions corresponds to the width of the defect S3. Nevertheless, the absolute difference between both MMM signals increases for positions out of this width. For \(y=\pm\)5.0 mm, the absolute difference between both tangential MMM signals are 8.12 \(\upmu\)T and 20.68 \(\upmu\)T, respectively. On the other hand, the normal MMM response of the defect S3 has two peaks values (48.3 \(\upmu\)T and \(-\)59.5 \(\upmu\)T) close to their edges, achieving a polarity shift at the defect center (see Figure 10). The defect S3 has less width (2.80 mm) in comparison to the defects S2 (3.80 mm) and S3 (4.36 mm), respectively, which causes a reduction in the width of the tangential MMM signal. In addition, the maximum and minimum magnitudes (48.3 \(\upmu\)T and \(-\)59.5 \(\upmu\)T) of the measured normal MMM signal reach close to the edges of the defect S3. For the positions between \(-\)1.4 mm and 1.4 mm, the analytical normal MMM signal has a good approximation with respect to the measured MMM signal. However, the absolute difference between these signals increases for positions out of the range \(y=\pm\) 1.4 mm. For the positions \(y=\pm\) 5.0 mm, the absolute difference between both normal MMM signals are 40.69 \(\upmu\)T and 8.12 \(\upmu\)T, respectively.