SUMMARY
Low-frequency noise is one of the most common types of noise in seismic and microseismic data. Conventional approaches, such as the high-pass filtering method, utilize the low-frequency nature and distinguish between signal and noise based on their different frequency contents. However, conventional approaches are limited or even invalid when the signal and noise shares the same frequency band. Moreover, high-pass filtering method will suppress not only low-frequency noise but also low-frequency signal when they overlap in a same frequency band, which is extremely important in the inversion process for building the subsurface velocity model. To overcome the drawbacks of conventional high-pass filtering approach, we developed a novel method based on the mathematical morphology theorem to separate signal and noise using their differences in morphological scale. We extracted empirical relation between morphological scale and frequency band so that the mathematical morphology based approach can be conveniently used in low-frequency noise attenuation. The proposed method is termed as the mathematical morphological filtering (MMF) method. We compare the MMF approach with high-pass filtering and empirical mode decomposition (EMD) approaches using synthetic, reflection seismic and microseismic examples. The various examples demonstrate that the proposed MMF method can preserve more low-frequency signal than the high-pass filtering approach, and is more efficient and causes fewer artefacts than the EMD approach.
Color Image Enhancement by an Integral Mask-filtering Approach Employing Nonlinear Transfer Function