A fast amplitude preserving three-parameter 3D parabolic Radon transform and its application on multiple attenuation

Abstract

Seismic wavefields propagate through three-dimensional (3D) space, and their precise characterization is crucial for understanding subsurface structures. Traditional 2D algorithms, due to their limitations, are insufficient to fully represent three-dimensional wavefields. The classic 3D Radon transform algorithm assumes that the wavefield's propagation characteristics are consistent in all directions, which often does not hold true in complex underground media. To address this issue, we present an improved 3D three-parameter Radon algorithm that considers the wavefield variation with azimuth and provides a more accurate wavefield description. However, introducing new parameters to describe the azimuthal variation also poses computational challenges. The new Radon transform operator involves five variables and cannot be simply decomposed into small matrices for efficient computation; instead, it requires large matrix multiplication and inversion operations, significantly increasing the computational load. To overcome this challenge, we have integrated the curvature and frequency parameters, simplifying all frequency operators to the same, thereby significantly improving computation efficiency. Furthermore, existing transform algorithms neglect the lateral variation of seismic amplitudes, leading to discrepancies between the estimated multiples and those in the data. To enhance the amplitude preservation of the algorithm, we employ orthogonal polynomial fitting to capture the amplitude spatial variation in 3D seismic data. Combining these improvements, we propose a fast, amplitude-preserving, 3D three-parameter Radon transform algorithm. This algorithm not only enhances computational efficiency while maintaining the original wavefield characteristics, but also improves the representation of seismic data by increasing amplitude fidelity. We validated the algorithm in multiple attenuation using both synthetic and real seismic data. The results demonstrate that the new algorithm significantly improves both accuracy and computational efficiency, providing an effective tool for analyzing seismic wavefields in complex subsurface structures.