## 4 Results and Discussion
### Relationship between Bearing Estimation Error and Horizontal Peak Displacement  
The results of the bearing estimation of each 1/3 octave frequency band average centered at frequencies 40-1000 Hz for two acoustic sources at site S1 are shown in Figure 5a, where the asterisks indicate the bearing estimation for each frequency band for the first source, the circles indicate the bearing estimation for each frequency band for the second source, the dotted line represents the real bearing angle of \(-5^{\circ}\), and the upper and lower solid lines represent the bearing angle that deviates from the real value by 20\({}^{\circ}\). If the bearing estimation errors exceed 20\({}^{\circ}\), they will fall outside these two lines. Combined with the previous analysis on the relationship between bearing estimation error and peak displacement, the horizontal \(x\)- or \(y\)-direction peak displacements in different frequency bands are extracted. The relationship between the \(x\)-direction peak displacements and 1/3 octave frequencies is shown in Figure 5b, and the relationship between the \(y\)-direction peak displacements and 1/3 octave frequencies is shown in Figure 5c. As shown in Figure 5a, when the frequencies are in the 630-1000 Hz band, the bearing estimation errors significantly increase and are greater than 20\({}^{\circ}\). A threshold line is drawn near the value of the \(x\)- or \(y\)-direction peak displacement at 630 Hz in Figure 5b,c, and the threshold values are \(x\) = 5.3 \(\times\) 10\({}^{-7}\) m and \(y\) = 1.63 \(\times\) 10\({}^{-7}\) m, respectively. The \(x\)- and \(y\)-direction peak displacements in the 630-1000 Hz frequency band are all near or below the threshold. Comparing Figure 5a to Figure 5b,c, it can be found that in the frequency band of 630-1000 Hz, the \(x\)- and \(y\)-direction peak displacements are small and lower than the threshold, while the bearing estimation errors clearly increase and are almost greater than 20\({}^{\circ}\). The results of the bearing estimation for each 1/3 octave frequency band for two acoustic sources at site S2 are shown in Figure 6a, where the dotted line represents the real bearing of \(-5^{\circ}\), and the upper and lower solid lines represent the bearing angle that deviates from the real value by 25\({}^{\circ}\). Because the horizontal distance between the source and the geophone is larger and exceeds 300 m, the bearing estimation error range set in Figure 6a is increased by 5\({}^{\circ}\) compared to that in Figure 5a. Similarly, the relationship between the \(x\)  
Figure 4: Bearing estimation results of each frequency band of the first acoustic source at site S1. (The black line represents the rotational radial power in different directions, and the blue arrow represents the direction of the maximum radial power direction). or \(y\)-direction peak displacements and 1/3 octave frequencies is shown in Figure 6b,c; the threshold value is \(x=2.5\times 10^{-7}\) m in Figure 6b and \(y=1.5\times 10^{-7}\) m in Figure 6c. Figure 5: The bearing estimation and peak displacements for each frequency band at site S1: (**a**) the bearing estimation, (**b**) \(x\)-direction peak displacements and (**c**) \(y\)-direction peak displacements. As shown in Figure 6a, the bearing estimation errors in the two frequency bands, 40-63 Hz and 630-1000 Hz, are mostly greater than 25\({}^{\circ}\). Furthermore, the bearing estimation error at the frequency of 315 Hz is greater than 25\({}^{\circ}\). Similarly, it can be seen in Figure 6b,c that in the same two frequency bands, 40-63 Hz and 630-1000 Hz, the \(x\)- or \(y\)-direction peak displacements are small, mostly near or lower than the threshold, and the \(x\)-direction peak displacement at 315 Hz is near the threshold. The results of the bearing estimation in each frequency band for two acoustic sources at site S3 are shown in Figure 7a, where the dotted line represents the real bearing of 90\({}^{\circ}\), and the upper and lower solid lines represent the bearing that deviates from the true value by 20\({}^{\circ}\).