The Apex-Shifted Hyperbolic Radon Transform (ASHRT) is a variant of the Radon Transform. In the field of seismic exploration, it can be applied to simultaneous source separation, diffraction- and reflection-wave separation, seismic data reconstruction, among other purposes. This paper primarily investigates the application of ASHRT in the separation of diffraction and reflection waves. Detailed exploration of complex structures using diffraction wave imaging has become a new trend, thereby necessitating the separation of diffraction wave fields. The conventional ASHRT based on the Stolt operator, due to its weak sparsity, increasingly struggles to meet current separation requirements. Compared to conventional ASHRT, the Stolt-based ASHRT enables fast, efficient computation; however, the Stolt operator exhibits relatively weaker sparseness and fidelity. To address this issue, replacing the Stolt operator with the PS operator for performing ASHRT allows the transform to achieve both high sparseness and high fidelity simultaneously. In this study, synthetic data were used to investigate the advantages of the PS operator over the Stolt operator. Furthermore, both operators were applied to separate diffraction and reflection waves in marine seismic data and land seismic data, respectively. The research demonstrates that, in the separation of diffraction and reflection waves using the ASHRT method, the PS operator provides significant advantages over the Stolt operator in terms of both sparseness and fidelity.
Cao et al. (Fri,) studied this question.