Application of curvelet denoising to 2D and 3D seismic data — Practical considerations

• Strategy for complex scale- and angle-adaptive thresholding
• Denoising both synthetic and real types of seismic data
• Attenuation of various types of noises
• Application of 2D DCT for 3D seismic data denoising

Contamination of seismic signal with noise of various origins is one of the main challenges encountered during processing and interpretation of seismic data. Several methods exist for eliminating different types of noises like coherent or incoherent noise and multiples, but optimal random noise attenuation remains difficult. Here we investigate relatively new technique based on discrete curvelet transform (DCT). Features like multi-resolution, multi-direction and locality of DCT introduce minimal overlapping between coefficients representing signal and noise in curvelet domain which is the prime advantage of this method. We present practical application of DCT describing its main features and focusing on useful details, especially more complex thresholding based on analyzing 2D Fourier spectrum and the vector of curvelet coefficients. We demonstrate that better understanding of relations between DCT properties and obtained results in pair with additional investigation of curvelet domain provides better localization and, in consequence, separation of noise and signal energy. Introduced scale and angle dependent weighting of curvelet coefficients leads to significant improvements of results with respect to noise attenuation and signal energy preservation. Effectiveness of our approach is demonstrated both on synthetic 2D sections with white and colored noise added, as well as on real 2D and 3D post-stack seismic data. Finally, we demonstrate the use of curvelet denoising as the data-preconditioning tool for frequency-domain full-waveform inversion. Curvelet denoising seems to be much more robust as compared with traditional filtering (e.g. F–X deconvolution), especially when noise and signal spectra overlap.