## 1 Introduction  
Seismic imaging is an effective method for exploring subsurface structures with the aim of obtaining accurate images of the true reflectivity of underground formations. It is widely regarded as one of the most effective techniques for mapping subsurface structures using seismic data [1]. Among seismic imaging methods, reverse time migration (RTM) is particularly notable because of the use of the two-way wave equation, which is not constrained by the dip angle of subsurface structures. Consequently, this method can be used to image various complex geological formations with high accuracy [2, 3, 4]. Considerable research has been conducted to enhance the quality of seismic imaging results. [PERSON] et al. reduced low-frequency noise in imaging results by separating up-going and down-going wavefields [5]. [PERSON] and [PERSON] improved imaging quality by incorporating the Poynting vector into the imaging condition [6]. [PERSON] et al. achieved longitudinal and transverse wave separation in elastic wave reverse-time migration [7]. Moreover, the quality of seismic data significantly influences the results of seismic imaging methods. Low-quality seismic data can result in numerous artifacts in the imaging results, compromising both the reliability and accuracy of seismic imaging outcomes. Therefore, in conventional RTM methods, primary waves are typically used as effective data to ensure seismic data quality, whereas multiple waves are treated as noise and are suppressed [8; 9; 10]. However, multiple waves can also provide useful information. Compared with primary reflections, multiple waves exhibit smaller reflection angles and longer propagation paths, offering a broader illumination coverage and richer subsurface structural information [11; 12]. Therefore, with the advancement in seismic exploration technology, an increasing number of researchers have attempted to utilize multiple waves as effective signals [10]. [PERSON] applied the one-way wave equation, using seismic data to replace the seismic wavelet and propagated multiple waves instead of traditional seismic data to obtain multiple-wave imaging results [13]. [PERSON] and [PERSON] converted multiple waves into primary waves and employed conventional seismic imaging methods [14]. [PERSON] et al. integrated multiple-wave imaging with RTM based on the two-way wave equation and proposed an RTM method for multiple waves [15]. However, incorrect cross-correlations between multiple waves can substantially degrade imaging quality. To address this issue, [PERSON] et al. combined least-squares migration with multiple-wave imaging to reduce artifacts in imaging results [16]. [PERSON] et al. proposed a least-squares migration for water-bottom-related multiples, which further eliminated crosstalk in multiple-wave imaging and improved the spatial resolution of the imaging results [12]. Vertical seismic profiling (VSP) refers to a seismic observation method in which the source is located at the surface, while seismic receivers are deployed in observation wells that are vertical to the ground [17]. Compared with surface seismic methods, VSP provides stronger seismic signals because the receivers are closer to the target structures and can better mitigate the effects of low-velocity layers on seismic data. Consequently, VSP offers higher-quality imaging in areas near observation wells [18]. Addressing the improvement of VSP RTM, [PERSON] et al. combined wavefield decomposition imaging conditions with the Poynting vector, thereby enhancing imaging quality [19]. [PERSON] et al. significantly reduced the impact of migration noise on imaging quality by constructing dip angle gathers and estimating coverage redundancy in the dip domain [20]. [PERSON] et al. employed Hilbert transform to separate up-going and down-going waves, reducing the influence of low-frequency noise and artifacts on the imaging results [21].