Multicomponent Seismic Data Denoising and Reconstruction with Fast Quaternion Curvelet Transform

Abstract In the field of multicomponent (MC) seismic data, vector processing has become an important research trend. Unlike conventional scalar approaches that handle each component individually, vector approaches can exploit the inner relationship among different components to achieve better performance. The quaternion algebra is used to jointly represent MC data because of its inner orthogonal structure. Subsequently, we introduce the quaternion curvelet transform (QCT) to achieve a multi-scale and multi-angle vector decomposition for MC data. To improve the computational efficiency, we develop a fast quaternion curvelet transform (FQCT) algorithm. Based on the proposed FQCT, a vector threshold denoising algorithm and a vector projection onto convex sets (VPOCS) reconstruction algorithm are used to evaluate the denoising and reconstruction performance of QCT. Experiments on both 3C synthetic and field seismic data demonstrate that the proposed QCT outperforms the traditional scalar curvelet transform (CT) in denoising and reconstruction.