## 2 Vibration Control Methods
The average propagation velocity c of vibration waves can be obtained in the same method for different geological conditions. Therefore, Equation (1) can be rewritten in the form of Equation (2). \[t(i)=t_{1}(i)+\|\mathbf{H}(i)\mathbf{M}\|/\left(\Delta R/\Delta t_{\rm T}\right) \tag{2}\]  
where \(t(i)\) represents the time at which the vibration wave from the \(i\)-th hole reaches the monitoring point; \(t_{1}(i)\) is the detonation time of the \(i\)-th hole; \(H(i)\) denotes the positional coordinates of the \(i\)-th hole; \(M\) is the positional coordinates of the monitoring point; \(\mid\mathbf{H}(i)\mathbf{M}\mid\mid\) represents the distance between the \(i\)-th hole and monitoring point M; \(\Delta R\) is the difference in propagation distance; and \(\Delta t_{\rm T}\) is the difference in propagation time. Problems That Can Be Solved by Analyzing to Wave Arrial Time Sequence and Their Positive Implications  
In open pit mine-blasting operations, vibration levels exceeding safety thresholds may induce vibration hazards. Specifically: (1) slope rock masses may experience progressive displacement accumulation, increasing risks of slippage or localized collapse; (2) surrounding structures may sustain structural impacts including micro-crack initiation and reduced fatigue life of components. These vibration hazards exhibit positive correlation with vibration intensity, necessitating the implementation of scientific monitoring and control measures for effective mitigation. Based on the above principle, the time series of vibration waves (generated by different blast holes) arriving at the same monitoring point can be calculated under the precise detonation conditions of electronic detonators. By analyzing and comparing this sequence, the blasting delay parameters can be adjusted. Specifically, the half-period interference vibration reduction technique is employed to separate overlapping vibration waves through localized delay adjustments, thereby reducing the number of waves arriving simultaneously at the monitoring point and achieving vibration mitigation. Furthermore, such delay time adjustments address two critical challenges in open pit bench-blasting vibration control. _Problem 1: Vibration hazard caused by simultaneous arrival waves from multiple blast-holes at the same monitoring points._  
Due to the spatial distribution of blast holes, the propagation distances and times of vibration waves through the medium vary, which may result in vibration waves from two or more blast holes initiated at different times arriving simultaneously at the same monitoring point. It is noteworthy that single-hole vibration curves arriving simultaneously at a monitoring point may exhibit phase differences, leading to partial cancellation of wave peaks and troughs upon arrival. However, given the complexity of blasting sites, it is impractical to monitor the vibration curves of each hole at every location. Therefore, it is assumed that variations in blast-induced vibrations are caused by differences in charge, distance, site factors, and other parameters. The measured single-hole vibration curve is used as a baseline to reconstruct the single-hole vibration curves at the monitoring point for holes at different locations. Under this premise, when a large number of vibration waves arrive at the monitoring point within the same time window, the superposition of wave peaks is likely to occur, leading to potential vibration hazard. The monitoring duration is divided into several continuous time intervals of fixed length. The number of arrival waves within each time interval is then counted based on Equation (3). Figure 1 illustrates the vibration waves arriving at the monitoring point within the same time window, where \(T\) represents the vibration wave period. Time segments with a high number of concurrent wave arrivals are defined as clustering arrival periods.