Mathematical morphological filtering for linear noise attenuation of seismic data

Abstract

Linear coherent noise attenuation is a troublesome problem in a variety of seismic exploration areas. Traditional methods often use the differences in frequency, wavenumber, or amplitude to separate the useful signal and coherent noise. However, the application of traditional methods is limited or even invalid when the aforementioned differences between useful signal and coherent noise are too small to be distinguished. For this reason, we have managed to develop a new algorithm from the differences in the shape of seismic waves, and thus, introduce mathematical morphological filtering (MMF) into coherent noise attenuation. The morphological operation is calculated in the trace direction of a rotating coordinate system. This rotating coordinate system is along the direction of the trajectory of coherent noise to make the energy of the coherent noise distributed along the horizontal direction. The MMF approach is more effective than mean and median filters in rejecting abnormal values and causes fewer artifacts compared with [Formula: see text]-[Formula: see text] filtering. Our technique requires that coherent noise can be picked successfully. Application of our technique on synthetic and field seismic data demonstrates its successful performance.

Deep Convolutional Denoising Autoencoders with Network Structure Optimization for the High-Fidelity Attenuation of Random GPR Noise

“…Finally, the proposed method was applied to field microseismic data, and the results are encouraging in [24]. The authors of [25] developed a novel algorithm based on the difference in seismic wave shapes and introduced mathematical morphological filtering (MMF) into the attenuation of coherent noise. The morphological operation is calculated in the trajectory direction of the rotating coordinate system, and the rotating coordinate system is established along the coherent noise trajectory to distribute the energy of the coherent noise in the horizontal direction.…”

Coherent noise suppression via a self-supervised blind-trace deep learning scheme

“…These methods include the Fourier transform [40], the radial trace (RT) transform [12,19,20] and the wavelet transform (WT) [13,16], among others. Similarly, mathematical morphological filtering and median filtering attenuate linear noise based on the difference in the shape of seismic waves in the transformed coordinate system [21] and the energy difference between noise pixels and the median value of the neighborhood [39,14,10], respectively. In some cases, differences between useful signals and noise in a transformed domain or a coordinate system are too small to be distinguished.…”

Shadow Separation of Pavement Images Based on Morphological Component Analysis

“…is method assumes that, for each source signal in the mixed signal, there is a corresponding dictionary which can sparsely represent the source signal and considers that the dictionary can only sparsely represent the source signal and cannot sparsely represent other source signals; then, using the tracking algorithm to search the most sparse representation will produce an ideal separation effect. MCA is used to realize signal separation in several fields such as firstorder and second-order cyclostationary signal separation [3], to enhance textural differences based on wavelet texture features to improve the image segmentation preprocessing method [4], to decompose oscillation plus the transient signal [5], to decompose the interference hyperspectral image [6], double-layer adaptive shape morphological analysis for retinal image evaluation [7], and to separate different types of noise in seismic image processing [8][9][10][11]. All these show that MCA is effective in signal separation.…”