# Method of Suppressing Rayleigh Waves Based on the Technology of Time-Domain Differential Detection
## 4 Engineering Validation of the Differential Detection Method
### Thickness Detection of Marble Sculptures  
The differential detection method was applied to assess the thickness detection of a marble sculpture. Figure 10 shows that the marble sculpture is approximately 780 cm in length with an average thickness of about 70 cm. The sculpture's front features a wavy surface, whereas the back remains flat. Seismic waves were generated by striking the back of the sculpture with a hand hammer to obtain equal-offset profiles, positioning the two sensors at shot distances of 50 and 60 cm, respectively, with an inter-trace spacing of 10 cm. The variation in the sculpture's thickness along the survey line, determined by laser ranging, is illustrated by the red line in Figure 11. The black dashed line in Figure 11 represents the time-depth conversion curve, achieved after differential suppression of the Rayleigh waves from the dual-trace seismic profile, indicating a strong correlation between the two measurements. The average longitudinal wave speed measured in the marble was 3560 m/s, and the transverse wave speed was 1680 m/s.  
Figure 10: Experimental marble sculpture and location and orientation of measuring lines.  
Figure 9: Seismic profile before and after Rayleigh wave suppression. (**a**) Single-channel isotropic seismic section. (**b**) Equally offset seismic profiles after time-domain differential detector waveforms.  
The seismic record for this thickness testing experiment is shown in Figure 12. In the initial seismic record profile before Rayleigh wave suppression (Figure 12a), the energy of the direct transverse waves (or Rayleigh waves) is extremely intense, and the reflected transverse waves from both ends of the marble slab are significant, creating interference throughout the entire equal-offset profile. This interference completely masks the reflected wave signals from the sculpture's back, challenging technicians' ability to accurately assess the structural signals and ascertain the marble's thickness. Figure 12b displays the seismic profile following time-domain differential processing and compares the thickness trends, with the black dashed line indicating thickness variation. The results demonstrate that the differential suppression technique effectively minimized interference signals, including Rayleigh waves, transverse waves, and reflected transverse waves emanating from the left boundary of the marble, resulting in an enhanced seismic profile.  
Similar to the profile comparisons in Figure 9a,b, before and after Rayleigh wave suppression, the dominant frequency of the seismic waves after differential processing significantly increases.  
Although hammer-induced seismic waves can exhibit effective frequencies approaching 1 kHz, the actual wavelength of longitudinal waves can extend several meters, signifi  
Figure 11: Thickness of marble sculpture vs. time–depth line.  
Figure 12: Seismic profile before and after Rayleigh wave suppression. (**a**) Original iso-offset record. (**b**) Equal-offset record after differential detection.  
cantly exceeding the thickness of the marble sculpture. Along with the interference from the long tail wave effect of direct transverse or Rayleigh waves during hammer excitation, obtaining ideal results using reflection wave methods remains challenging. However, this experiment illustrates that differential detection can suppress Rayleigh or direct transverse waves while indirectly retaining reflected wave energy signals, thus aiding in interpreting the sculpture's thickness using reflection wave methods.  
A vertical fracture intersecting the sculpture is present, and its interface reflection transverse waves are apparent in both the original and differential profiles. These reflections directly influence signal differentiation, consistent with the analysis in Section 2.2, which discusses the impact of boundaries on differential detection, indicating that the interference waves from the end boundary of the survey line are unsuitable for differential suppression.