###### Abstract  
Effective vertical seismic profiling (VSP) of upgoing and downgoing wave separation is essential for high-quality imaging. However, VSP wavefield separation is particularly challenging under complex geological conditions. Existing solutions encompass one derived from the mathematical characteristics of upgoing and downgoing waves, employing signal decomposition methodologies, and another that utilizes data-driven machine learning techniques, achieving wavefield separation by training sample data to identify the distinct characteristics of upgoing and downgoing waves. This study introduces a VSP wave-separation method using signal knowledge representation, primarily by constructing knowledge representations of upgoing and downgoing waves. Physics-informed recurrent neural network FWI and Poynting vector physical knowledge representation yielded accurate velocity models. Axial gradient information was utilized to construct morphological knowledge representations of upgoing and downgoing waves. Directional differentiation knowledge representations were established based on kinematic characteristic disparities between upgoing and downgoing waves in the time-depth domain. These wave knowledge representations (KRs) built a dual convolutional autoencoder. Its distinct branches extracted up/down wave information, while the KRs, transformed into loss functions, enabled knowledge-driven unsupervised VSP wave separation. The proposed methodology was validated using a homogeneous layer and Marmousi models, demonstrating the effective separation of upgoing and downgoing waves from the VSP seismic records. 2025  
wavefield and the upgoing wavefield. The direct measurement of the downgoing wavefield provides invaluable information for determining the seismic source wavelet, accurate interval velocities, and formation attenuation characteristics, while the upgoing wavefield carries detailed information about reflectors and structural features around the wellbore. Consequently, compared to surface seismic exploration, VSP generally offers superior signal-to-noise ratios and higher vertical resolutions. The VSP thus enables more precise measurements of formation velocity parameters, P- and S-wave properties, anisotropy, amplitude information, and lithological characteristics, thereby significantly enhancing seismic data-interpretation capabilities in structural, stratigraphic, and lithological analysis [1]. In VSP-based data processing, the separation of upward and downward wavefields is a prerequisite for seismic migration imaging [2]. Upgoing waves typically contain valuable information from subsurface reflectors. A clean upgoing wavefield forms the basis for performing Amplitude Versus Angle (AVA) or Off-set (AVO) analysis to identify fluid properties, calculating formation absorption attenuation (Q-value) parameters to evaluate reservoir characteristics and achieving accurate well-seismic time-depth calibration. Downgoing waves, on the other hand, mainly consist of direct waves and multiples [3]. Among these, clear direct waves provide precise seismic wave travel time information, serving as crucial input for calculating accurate interval velocities and establishing reliable velocity models. This is vital for subsequent migration imaging and depth-domain interpretation [4; 5]. Furthermore, analyzing the downgoing waves and the multiples they generate aids in understanding the mechanisms of multiple generation within seismic data, subsequently guiding the suppression of multiples in surface seismic data processing. Downgoing waves can also be utilized for extracting the seismic wavelet, performing deconvolution to enhance resolution, and similarly, for estimating the attenuation characteristics of the formation media. In summary, the accuracy of VSP wavefield separation directly dictates the quality of the input data for subsequent processing steps and ultimately determines the reliability and geological significance of the final interpretation results.