## 1 Introduction  
In a vertical seismic profile (VSP) recording, positive-slowness downgoing wavefields and negative-slowness upgoing wavefields interfere with each other [1]. An effective separation of original VSP data (common shot point gather) is essential before imaging, and separation represents one of the fundamental processing steps for VSP data [2]. Many methods exist that can be used successfully to separate wavefields propagating uniformly within a chosen analysis window [3; 4; 5; 6]. The f-k (frequency-wave number) filtering method utilizes the difference of the slowness in the upgoing and downgoing waves for wavefield separation [7]. However, the overlap of the energy spectrum between different f-k quadrants can prevent these wavefields from being separated accurately [8]. Additionally, spatial samples are required to be sufficiently dense, otherwise the spatial alias frequency is generated. [PERSON] et al. [9] pointed out that for an f-k filter, a stable wavefield separation depends on the discrimination of different wavefields in the f-k domain. The Radon transform is a method of wavefield separation in the \(\tau\)-\(p\) (intercept time-slowness) domain that utilizes the slowness of the upgoing and downgoing waves [10], and it can be implemented with either a linear Radon transform (also called the \(\tau\)-\(p\) transform [11]) or a nonlinear Radon transform. [PERSON] et al. [12] proved, through a case study, that the Radon transform wavefield separation technique is effective for separating the upgoing and downgoing waves, and application of a hyperbolic filter further improved the wavefield separation. [PERSON] et al. [13] introduced the sparse constraint and proposed the high-resolution Radon transform method, which can be used to improve the accuracy of wavefield separation. [PERSON] et al. [14] used an iterative double weighted conjugate gradient algorithm to solve nonlinear inversion problems of the high-resolution Radon transform. However, the resolution and AVO (amplitude versus offset) characteristics of common Radon transform methods are hard to retain [15]. The methods for wavefield separation with amplitude preservation include median filtering [16], mean filtering, and various other improved methods [17; 18; 19; 20]. Among these methods, median filtering has been widely used for VSP wavefield separation because of the resulting low amplitude change and the stability in cases of short arrays. In order to effectively separate VSP downgoing and upgoing waves, [PERSON] et al. [21] combined the \(\tau\)-\(p\) domain masking filter, the median filter, and the f-k domain masking filter in a dynamic manner. [PERSON] et al. [8] compared the median filter and other methods commonly used in the industry and showed how the median filter treated coherent and random noise; they also demonstrated that the median filter had a unique ability to preserve discontinuities and avoid smearing. [PERSON] et al. [22] developed a new type of multichannel filter called a \"constrained eigenvector filter\"; this method can obtain better separation results than the median filters and eigenvector filters because it combines the advantages of the two approaches. In the application of these methods, seismic traces should be aligned according to the first arrival of the target wavefield [23]. Therefore, extensive first-break pickup work is inevitable and the events of a target wavefield can be aligned only if the first arrival is parallel to the other events of the target wavefield. However, a different offset of the same wavefield will result in non-parallel events in the non-zero offset VSP [24; 25]. Furthermore, the events of the same wavefield may come from different reflection layers and the reflection coefficients may be different, which will lead to changes in the slowness and the non-parallel events of the same wavefield. Therefore, a static time shift cannot exactly align the events of the target wavefield, thus resulting in a reduction of the wavefield separation accuracy.