The transform base function method is one of the most commonly used techniques for seismic denoising, which achieves the purpose of removing noise by utilizing the sparseness and separateness of seismic data in the transform base function domain. However, the effect is not satisfactory because it needs to pre-select a set of fixed transform-base functions and process the corresponding transform. In order to find a new approach, we introduce learning-type overcomplete dictionaries, i.e., optimally sparse data representation is achieved through learning and training driven by seismic modeling data, instead of using a single set of fixed transform bases. In this paper, we combine dictionary learning with total variation （TV） minimization to suppress pseudo-Gibbs artifacts and describe the effects of non-uniform dictionary sub-block scale on removing noises. Taking the discrete cosine transform and random noise as an example, we made comparisons between a single transform base, non-learning-type, overcomplete dictionary and a learning-type overcomplete dictionary and also compare the results with uniform and nonuniform size dictionary atoms. The results show that, when seismic data is represented sparsely using the learning-type overcomplete dictionary, noise is also removed and visibility and signal to noise ratio is markedly increased. We also compare the results with uniform and nonuniform size dictionary atoms, which demonstrate that a nonuniform dictionary atom is more suitable for seismic denoising.
Wavefields in porous media saturated by two immiscible fluids are simulated in this paper.Based on the sealed system theory,the medium model considers both the relative motion between the fluids and the solid skeleton and the relaxation mechanisms of porosity and saturation（capillary pressure）.So it accurately simulates the numerical attenuation property of the wavefields and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium model on the basis of open system theory.The velocity and attenuation for different wave modes in this medium have been discussed in previous literature but studies of the complete wave-field have not been reported.In our work,wave equations with the relaxation mechanisms of capillary pressure and the porosity are derived.Furthermore,the wavefield and its characteristics are studied using the numerical finite element method.The results show that the slow P3-wave in the non-wetting phase can be observed clearly in the seismic band.The relaxation of capillary pressure and the porosity greatly affect the displacement of the non-wetting phase.More specifically,the displacement decreases with increasing relaxation coefficient.
