Seismic random noise attenuation method based on empirical mode decomposition of Hausdorff dimension

Introduction Empirical mode decomposition (EMD) is a noise suppression algorithm by using wave field separation, which is based on the scale differences between effective signal and noise. However, since the complexity of the real seismic wave field results in serious aliasing modes, it is not ideal and effective to denoise with this method alone. Based on the multi-scale decomposition characteristics of the signal EMD algorithm, combining with Hausdorff dimension constraints, we propose a new method for seismic random noise attenuation. First of all, We apply EMD algorithm adaptive decomposition of seismic data and obtain a series of intrinsic mode function (IMF)with different scales. Based on the difference of Hausdorff dimension between effectively signals and random noise, we identify IMF component mixed with random noise. Then we use threshold correlation filtering process to separate the valid signal and random noise effectively. Compared with traditional EMD method, the results show that the new method of seismic random noise attenuation has a better suppression effect. The implementation process The EMD algorithm is used to decompose seismic signals into IMF sets and analyze its spectrum. Since most of the random noise is high frequency noise, the IMF sets can be divided into three categories: the first category is the effective wave composition of the larger scale; the second category is the noise part of the smaller scale; the third category is the IMF component containing random noise. Then, the third kind of IMF component is processed by the Hausdorff dimension algorithm, and the appropriate time window size, initial step and increment amount are selected to calculate the Hausdorff instantaneous dimension of each component. The dimension of the random noise is between 1.0 and 1.05, while the dimension of the effective wave is between 1.05 and 2.0. On the basis of the previous steps, according to the dimension difference between the random noise and effective signal, we extracted the sample points, whose fractal dimension value is less than or equal to 1.05 for the each IMF components, to separate the residual noise. Using the IMF components after dimension filtering processing and the effective wave IMF components after the first selection for reconstruction, we can obtained the results of de-noising.