# Method of Suppressing Rayleigh Waves Based on the Technology of Time-Domain Differential Detection
## 2 Differential Detection Method for Suppressing Rayleigh Waves at Common Shot Points
### Analysis of the Impact of Operating Boundaries on Time-Domain Differential Technology
#### 2.2.1 Shear Wave Reflections from Lateral Interfaces Parallel to the Survey Line  
As shown in Figure 2, shear wave reflections from lateral interfaces parallel to the survey line are common in seismic exploration. Analyzing their impact on the effectiveness of differential detection can provide further insights for implementing this method. This section assumes that the shear wave speed near the free interface approximates the Rayleigh wave speed and that the effects and suppression processes for seismic reflection wave exploration are comparable. The distance between the survey line and the lateral interface is denoted as d, the distance between the two detectors as \(\Delta\)S, the offset as S\({}_{1}\), and the shear wave speed in the cover layer as Vs. The Rayleigh wave speed, V\({}_{\text{R}}\), is approximately equal to the direct shear wave speed. The expression for the time difference of the reflected shear wave from the lateral interface is expressed as follows:  
\[\Delta t_{\text{c}}=\left(\sqrt{\left(\left(\text{x}+\Delta\text{S}\right)^{2 }+4\text{d}^{2}\right)}-\sqrt{\left(\text{x}^{2}+4\text{d}^{2}\right)}\right) /\text{Vs} \tag{3}\]  
For a constant d, the reflection time \(\Delta t_{\text{c}}\) is a hyperbolic function of the shot-to-detector distance x. As d increases from the minimal value of d = 0, \(\Delta t_{\text{c}}\) gradually decreases from its initial value \(\Delta T\). If \(\Delta T\) is used for time-domain differential processing to eliminate Rayleigh waves, given the proximity of the shear wave speed to the Rayleigh wave speed, unless the distance from the reflection interface to the survey line is minimal, the interface shear wave reflection is also effectively suppressed. Otherwise, this reflected shear wave remains after differential processing, forming interference waves on the shot gather and typical offset profile. In practice, lateral interfaces are detrimental. Specific technical methods should be intentionally employed to circumvent them to mitigate the interference of lateral interface shear wave reflections. A strategic design of the operational method, such as positioning the survey line along a vertical boundary, as mentioned earlier, can be implemented, followed by differential signal processing at later stages. Figure 2: Schematic top view of the impact boundaries of time-domain differential technology. 2.2 Reflections of Shear Waves from End and End-Boundary Interfaces Perpendicular to the Survey Line  
Figure 2 indicates that shear wave reflections perpendicular to the survey line can originate from the end and tail boundaries, each exhibiting distinct propagation patterns. For the shear wave reflection from the end boundary, the time difference in arrival at the two detectors is precisely \(\Delta T\), which is equivalent to the direct Rayleigh wave differential time. Thus, direct Rayleigh waves can be eliminated in practical differential operations, and reflections from the end boundary can also be suppressed. The time difference for shear wave reflections from the tail boundary is \(-\Delta T\). If \(\Delta T\) is still utilized for differential processing, the shear wave reflections from the tail interface arriving at the two detectors cannot be subtracted or eliminated. Instead, they remain as complex interference shear waves in the new time profile. Furthermore, the intense energy and prolonged tail waves associated with boundary shear wave reflections significantly impair the effectiveness of differential processing. Considering the differential effects of reflections from both the end and tail boundaries, the end boundary acts as a beneficial interface, while the tail boundary is the least favorable. In practice, when a lateral shear wave reflection interface is encountered on the ground, it is advisable to position this interface as close to the source as possible to prevent it from becoming a tail boundary reference point.