# Efficient Method for Enhancing Reverse-Time Migration Images Using Vertical Seismic Profiling Data
## 1 Introduction
The cross-correlation imaging condition, first proposed by [PERSON], provides stable structural images [24; 25]. To address the lack of a clear physical relationship between the cross-correlation imaging results and reflection coefficients, the normalization of the imaging results using the source or receiver wavefields can be employed to obtain results that correlate with the true reflection coefficients [26]. Building on these ICs, [PERSON] et al. proposed the deconvolution imaging condition [27], [PERSON] et al. introduced a time-space shift imaging condition [28], and [PERSON] et al. developed an improved backscattering imaging condition to separate the effects of impedance and velocity perturbations on reflectivity [29]. The primary objective of vertical seismic profiling (VSP) is to image small-scale structures effectively and provide high-quality imaging results in the vicinity of an observation well [30]. In VSP observation systems, the seismic source is typically positioned horizontally on the surface, while geophones are placed vertically within the observation well. This configuration allows the geophones to be closer to the target layers, thereby reducing the influence of low-velocity layers on seismic data. Consequently, VSP seismic data generally exhibit a higher quality compared to conventional surface seismic data. However, the unique characteristics of the VSP system lead to good coverage only in the vicinity of the observation well, with significantly uneven coverage across the complete subsurface structure. This uneven coverage can introduce substantial noise when traditional surface seismic imaging methods are directly applied. Noise suppression in migration imaging has been a longstanding challenge. Moreover, existing research has not provided effective methods for suppressing noise generated during the migration imaging process under asymmetric observation systems. To address this issue and achieve effective noise suppression in migration imaging within VSP systems, this study proposes a common-receiver RTM (CRRTM) imaging method. By shifting the observation signals to their source locations, this method suppresses the noise caused by the uneven coverage characteristics of the VSP observation system. In addition, we propose an excitation time-constrained cross-correlation imaging condition (ETC-IC). By controlling the effective time range within the cross-correlation imaging condition, this method suppresses the imaging noise caused by multiple reflections. The analysis of theoretical models and simulation experiments demonstrates that the method proposed in this paper can effectively suppress noise generated during VSP migration imaging. Comparative experiments show that the common-receiver point imaging method offers an approximately 12% improvement in image quality compared to traditional methods. The subsequent chapters of this paper are organized as follows:  
Section 2 analyzes the theoretical causes of migration noise in the RTM imaging process and demonstrates the rationale and effectiveness of the CRRTM and the ETC-IC through theoretical proofs. Section 3 starts with a simple model and employs simulation experiments to illustrate how noise affects imaging quality in traditional VSP migration imaging methods and how the proposed method suppresses noise. Section 4 presents specific experimental results to compare the imaging outcomes of the traditional VSP RTM method with those of the CRRTM method. Section 5 contains the discussion. Section 6 provides the conclusion.