Vertical seismic profiling （VSP） benefits imaging by recording along borehole depth, but reliable imaging requires separating upgoing and downgoing energy. We compare three classical approaches—f−κ filtering, median filtering, and Radon transform—on synthetic VSP data from the Marmousi model, with and without added noise. Radon achieves the cleanest separation in complex media and shows the best noise robustness, at the expense of higher computational cost. f−κ filtering is efficient and effective for simple stratification, but suffers from aliasing and edge artifacts when sampling is marginal or dips are complicated. Median filtering is practical and good for impulsive noise, yet depends strongly on first-arrival picking and window selection, which degrades performance under low SNR or wavefield overlap. We summarize trade-offs, provide quantitative metrics, and outline parameter choices to guide method selection under varying structural complexity and noise levels.

In the VSP data processing workflow, wavefield separation is a crucial step. Since seismic waves generate multiple wave types during underground propagation, including upgoing waves and downgoing waves, the mixing of these wavefields seriously affects the final imaging quality. To further optimize the utilization efficiency of seismic data and improve imaging quality, accurately separating upgoing waves and downgoing waves has become a key technical link. Effective wavefield separation not only improves the signal-to-noise ratio of seismic data but also provides high-quality input data for subsequent processing steps such as velocity analysis and migration imaging.

This article focuses on the comparative study of three classic wavefield separation methods: f−κ filtering, median filtering, and Radon transform. These three methods each have their theoretical foundations and applicable ranges, showing different advantages and limitations under different geological conditions and data quality.

The core idea of the f−κ filter is to utilize the different apparent velocity characteristics of upgoing waves and downgoing waves in the f−κ domain, separating wavefields propagating in different directions by designing appropriate filters. f−κ filters have the advantages of high computational efficiency and simple implementation. The median filter method mainly relies on accurate picking of first arrivals, achieving separation of upgoing and downgoing waves by analyzing the arrival time characteristics of wavefields. Median filtering has significant advantages in processing impulse noise and can effectively suppress anomalous values in data. The Radon transform method is based on the sparse representation characteristics of wavefields in the Radon domain, achieving wavefield separation by transforming seismic data to the τ-p domain （time-ray parameter domain）. This method can better handle complex wavefields, especially in the presence of multiples and noise interference, where the Radon transform shows strong robustness. However, its computational process is relatively complex and requires more computational resources.

To evaluate the application effects of these methods under complex geological conditions, we used the Marmousi velocity model for finite-difference forward modeling to generate seismic data containing complex structural features. The Marmousi model is a widely recognized standard test model in the geophysical community, whose complex geological structures and velocity distributions can well simulate various complex situations in actual geological environments.

Through systematic comparative analysis, we found that the three wavefield separation methods each have their characteristics and applicable ranges: The Radon transform shows higher separation accuracy when dealing with complex wavefields, especially in the presence of strong noise and multiple interference; its robustness is significantly superior to the other two methods. This benefit is mainly attributed to the Radon transform's ability to better distinguish wavefield components with different propagation directions and apparent velocities in the τ-p domain. The f−κ filter has significant advantages in computational efficiency, capable of quickly completing wavefield separation tasks and is suitable for large-scale data processing. However, in complex wavefields, f−κ filters are prone to wavefield aliasing phenomena, which affect separation effectiveness. This aliasing mainly occurs when wavefield components are complex and frequency content is rich, limiting its application effectiveness in complex geological environments. Median filtering largely depends on accurate picking of first arrivals, which requires data to have a high signal-to-noise ratio and clear first arrival characteristics. When noise is strong or first arrivals are not obvious, the performance of median filters will significantly decline. Additionally, this method also has wavefield aliasing problems, resulting in generally poor overall separation performance. However, median filters perform excellently in processing impulse noise and can effectively suppress anomalous interference in data.

For complex structures and strong noise environments, the Radon transform method shows stronger robustness, capable of maintaining high separation accuracy under complex conditions. The median filter method has significant effects in processing impulse noise and is suitable for situations where VSP data has serious noise interference. In such application scenarios, median filters can effectively suppress anomalous values and improve data quality.

This study not only provides a comprehensive discussion and empirical analysis of wavefield separation methods in VSP technology but also provides important reference for selecting optimal separation strategies in complex geological environments in the future. Through systematic comparative research, we have developed a thorough understanding of the advantages and limitations of various methods, providing a scientific basis for practical applications.