## 2 Single-Mode Fiber (SMF)
### Limitations of SMF  
Although SMF DAS technology has found applications in diverse fields in subsurface imaging, including reservoir monitoring, microseismic event detection, and oil exploration, and boasts attributes like distributed detection, superior spatial resolution, and heightened sensitivity, it still grapples with limitations arising from interference fading and inadequate signal consistency. When a seismic wave strikes the optical fiber, axial strain is produced by the fiber [9]. This results in a phase difference of the Rayleigh backscattering; Equation (1) shows the relation between axial strain and the SMF optical-phase difference, referring to the photoelastic effect.  
\[\Delta\varphi=\beta\bigg{[}1-\frac{n^{2}}{2}(p_{12}\ +2p_{11})\bigg{]}\Delta X \tag{1}\]  
where \(p_{12}\) and \(p_{11}\) are fiber tensor coefficients, \(n\) is the fiber refraction index, and \(\beta\) is light propagation. The phase difference between points C and D can be measured, and the quantitative parameter of the acoustic seismic signal can be identified. Specifically, when the pulse-width value is short enough upon measuring the arrival time of the backscattered light, the Rayleigh backscattering signals originating from points C and D (Figure 3) can be identified. An emitted laser travels through the SMF core glass with minimum scattering in a single, simple path and is highly sensitive to axial strain changes in response to the seismic wave signal. The probe pulse defines a pulse width, and because the probe lights increased coherence, the Rayleigh scattering signals from scattering points within this pulse width often interfere with one another [9; 37]. The interference outcome of Rayleigh scattering merely portrays a segment of the fiber in proximity to points C and D.  
The presence of inhomogeneous doping during the optical fiber's fabrication introduces randomness to the Rayleigh scattering interference pattern, thereby exerting an inevitable influence on the efficacy of phase demodulation. To precisely characterize the Rayleigh scattering phenomenon within SMF, researchers formulated a dedicated scattering model for SMF [38]. In cases where interference signals undergo interference cancellation, the signal's intensity weakens, leading decreased optical SNR. This cancellation in light  
Figure 3: The sensing principle of SMF cable in DAS.  
intensity eventually brings it to the level of acquisition noise, effectively submerging the demodulated phase information within the noise domain. This phenomenon gives rise to a region of blind detection termed interference fading. Furthermore, owing to the stochastic nature of the reflectivity amplitude associated with the corresponding scattering point, the positions corresponding to the signals received at different time instances show variance [9]. In essence, the unpredictability inherent in the intensity and positioning of Rayleigh scattering within conventional SMF engenders challenges like interference fading and insufficient temporal consistency of the signal in DAS. These issues hinder the seamless execution of exact sound wave tracing, particularly when scrutinizing the inherent attributes of the medium's interior [32].