De-noising Methods Of Adaptive Filtering Based On The Fractal Dimension

Content: De-noising is an inevitable problem in all kinds of seismic data processingmethods. Over the years, many scholars have developed a variety of methods:frequency-based filtering and radon transform, the FK filtering, the FX filtering, theCMP-weighted superposition, vector decomposition method and so on. This thesisstudies the two different methods compared with the above: one is based on fractaldimension; the other is based on adaptive noise canceling technology. In this thesis,two methods have been analyzed to find out if they can avoid the inadequacies of theconventional methods.Filtering method based on fractal dimension is an unconventional filteringmethod, the main principle is base on the difference of the characteristics betweenthe seismic wave and the random noise, and its fractal dimension is very different.We collected seismic data, including the useful signal and noise. According to fractaltheory, we can know the useful signal and noise in the seismic records has a differentfractal dimension, so we can separate them. But because of the limitations in thefractal dimension filtering, when the effective signal and noise overlap, we use thefractal dimension can not be distinguished them, so we have introduced adaptivefiltering.In this thesis, we studied the adaptive noise canceling technology, which mustobtain an initial noise model by some way from the seismic data, and the model anddata must be relevant. After the adaptive training to the model, a noise model data,which is consistent with the noise data in the seismic data, can be obtained.Subtracting seismic data and the trained noise model, we can filter out the noise. Butthe adaptive filter requires a certain degree of convergence time, so there will besome oscillation in the initial position of the signal sequence and the rear position ofthe effective signal, resulting in deterioration of the filtering effect. So the fractaldimension has been introduced to remove the irrelevant part in the seismic data, andthe corresponding irrelevant part in the noise model can be removed at the same time. Then the improved data and noise model have been used in the process of adaptivefiltering.In this thesis, we studied the variation of the fractal dimension, when theamplitude, phase and frequency of the signal have changed, and research thedifference of the P-wave and S-wave in the theoretical seismic data. Hausdorffdimension is shown that it has strong noise immunity, and it can well suppressrandom noise and pick first arrival. At the same time, the adaptive noise cancelingtechnology is verified that it has a good effect on de-noising in the multi-componentseismic data by theoretical and practical seismic data. Finally, under the constraintsof the Hausdorff dimension, adaptive filtering has achieved good results by the testof the theoretical and practical seismic data. Thus we can indicate that the method iscorrect and effective.