Seismic data analysis with dual-tree M-band wavelet transforms

Abstract

SummaryThe complexity of seismic data still challenges signal processing algorithms in several applications. The rediscovery of wavelet transforms by J. Morlet et al. has allowed improvements in addressing several data representation (local analysis, compression) and restoration problems. However, despites their achievements, traditional approaches based on discrete and separable (both for computational purposes) wavelets fail at efficiently representing directional or higher dimensional data features, such as line or plane singularities, especially in severe noise conditions. Subsequent extensions to wavelets (multiscale pyramids, curvelets [YaTrHe04][Do06], contourlets, bandlets) have recently generated tremendous theoretical and practical interests. They feature local and multiscale properties associated with a certain amount of redundancy, which may represent an issue for huge datasets processing.We propose here seismic data processing based on dual-tree M-band wavelet transforms [ChDuPe06]. They combine:• orthogonal M-band filter banks which better separate frequency bands in seismic data than wavelets, due to the increased degrees of freedom in the filter design,• Hilbert transform and complex representation of seismic signals which have been effective, especially for attributes definition, with a relatively low redundancy (a factor of two). These transforms have been successfully applied to random noise removal in traditional and remote sensing imagery.We apply them to seismic data and address their potential for local slope analysis and coherent noise (ground-roll) filtering.