## 3 Analysis Method
### Analysis Conditions  
The constructed model was a three-dimensional model, as shown in Figure 7. The material parameters of the base material in the analysis were assumed to be steel with a longitudinal wave velocity of 5900 m/s, transverse wave velocity of 3200 m/s, density of 7900 kg/m\({}^{3}\), and the defective area as a vacuum. This is because the inner space of a blowhole caused by zinc vapor is almost a vacuum containing only a small amount of hydrogen, and zinc is believed to adhere to the inner wall during the cooling process [20]. Even if zinc vapor or other substances remain in the defect due to insufficient cooling, it is safe to treat the defect as a vacuum because the waves are almost completely reflected from the viewpoint of acoustic impedance. The pressure wave generated by laser irradiation is known as a one-cycle waveform [21], and the pressure wave used in the analysis was assumed to be a 5 MHz wave representing a propagating wave. The mesh size was 0.05 mm, which is sufficiently small compared to the wavelength of 0.64 mm calculated from the propagation speed of the slowest transverse wave and the frequency of the given ultrasonic. The base metal existed at both ends of the model in the welding and longitudinal directions, and the propagating waves were not reflected back. Therefore, an absorption zone was established to absorb the propagating waves and minimize reflections from the boundary. The thickness of the absorption band was set to 2.36 mm, twice the thickness of the longest wavelength, with the longitudinal wave of 1.18 mm. Since many of the defects observed in the X-ray CT of the specimens had similar shapes, a three-dimensional defect model was created based on the X-ray CT results as shown in Figure 8a, combining cones and a sphere, whose external forms are shown in Figure 8b,c. Figure 7: The 3D model of lap joint welding involves a blowhole for FEM analysis. In this study, we examined a measurement method that was single-point detection and multi-point generation, but not the simultaneous excitation of ultrasonic waves at multiple points. In other words, the experimental conditions shown in Figure 3 resulted in 61 excitation and detection points per cross-section. On the other hand, the software analyzes a single ultrasonic propagation at once. Thus, analysis of one cross-section requires 61 calculations. To obtain more efficient analytical results, we focused on the wave reciprocal theorem, widely known in ultrasonic testing research. The reciprocal theorem states that switching the generation and detection points can obtain the same waveforms. Applying this to the irradiation conditions in this study means that the same waveform is obtained by one generation point and multiple detection points after exchanging the generation and detection positions. This allows us to obtain the B-scope of one cross-section in one calculation. Therefore, the generating and detecting points are exchanged in the subsequent analysis. However, the notation of generation/detection in the figures indicates the original position. As in the experiment, the generating and detecting points in the \(xz\) plane were set in the range \(x=-8\) mm for the detecting point and \(x=-3\)-\(3\) mm for the generating point in 0.1 mm gaps, as shown in Figure 9.  
On the other hand, since the defect shape is not uniform in the \(y\) direction of the weld line, the detection indicator depends on the irradiation position in the \(y\) direction. The analysis range in the \(y\) direction was set to \(-2.56\)-\(2.56\) mm, which includes the region where the defect exists. However, as shown in Figure 10, when the measurement was made while traveling in the \(y\) direction, the generation point became oblique in the \(xy\) plane, and the obliquity changed, depending on the traveling speed.