Radon Transform for Seismic Data Processing

The Radon transform is a fundamental technique in seismic data processing, primarily employed to separate different wave types in seismic signals, such as direct waves, refracted waves, and reflected waves. These wave types typically appear in seismic data with distinct propagation paths and arrival times. The Radon transform utilizes specific mathematical conversions to isolate them, providing a clearer data foundation for subsequent seismic analysis and interpretation.

In seismic data, direct waves are the first-arriving signals traveling along the shortest path, commonly used to determine the distance from the source to the receiver. Refracted waves arrive after undergoing refraction at subsurface boundaries, carrying velocity information about underground media. Reflected waves return to the surface after reflecting from geological interfaces, containing detailed information about stratum structures and boundaries. Due to their differing propagation paths and arrival times, these wave types often interfere with each other in seismic records, complicating signal interpretation.

The Radon transform converts time-domain seismic data into another parameter domain (e.g., slowness-intercept time domain), where different wave characteristics manifest as linear or nonlinear distributions. This transformation effectively separates direct, refracted, and reflected waves, thereby reducing multipath interference and enhancing the signal-to-noise ratio of seismic data. The inverse Radon transform can reconstruct denoised seismic records, further improving the quality of seismic imaging. Implementation typically involves discrete Radon transform algorithms using summation along hyperbolic or linear trajectories, with key parameters including slowness sampling intervals and curvature limits.

In practical applications, the Radon transform is often combined with other seismic processing techniques such as filtering, stacking, and migration to improve resolution and accuracy in seismic exploration. By optimizing transformation parameters like slowness ranges and intercept time increments, different wave types can be separated more precisely, providing more reliable data support for geological modeling and resource exploration. Code implementations generally involve matrix operations for forward and inverse transforms, with computational efficiency enhanced through Fourier-based methods or sparse matrix solvers.