Modified Fast Independent Component Analysis And Its Application On Noise Attenuation For Seismic Data

Independent component analysis (ICA) derived from blind source separation (BSS) is a new method for finding underlying factors or components from multivariate (multidimensional) statistical data. The goal of ICA is to recover the unobserved source signals without any prior information given only the sensor observations that are unknown linear mixtures of the independent sources. Recently, because of a few assumptions on surroundings, ICA has become one of the exciting new topic, both in the field of data mining and more generally in image processing, feature extraction, telecommunications, financial time series analysis.This paper briefly described the development of ICA, applications and the status quo, discussed the ICA in detail on the principles and implementation process, systematic introduced of the current ICA algorithms, as well as several major intrinsic link between them, focusing on fast independent component analysis algorithm (FastICA), did an analysis on the FastICA algorithm and found that the most time-consuming part of algorithm is the calculation of Jacobian matrix for the Newton iteration, and in order to reduce the calculation of Jacobian matrix in the iterative process and adapt to changes in data requirements, this paper introduced an improved method (M-FastICA), the FastICA algorithm combines multiple iterations of these many iterations, In these many iterations, only calculate one Jacobian matrix, which is uased in the following iterative process, Thus only one iteration in a number of Jacobian matrix to adapt to changes in data iteration purposes, greatly enhance the convergence rate of iterative. Also as a result of combination of many iterative process, this method can increase the volume of each iteration, reduce the need for convergence of the iteration, avoid oscillation of the situation, so the algorithm has a better convergence performance. Because the M-FastICA algorithm depends on the initial weights, added the relaxation factor in the algorithm, the purpose is to improve the algorithm to the dependence of the initial weight, this is the LM-FastICA algorithm. the algorithm to the dependence of the initial weight. In order to verify the feasibility of algorithms, respectively, did simulations on the analog signals and image signals ,and the simulation results show that the single M-FastICA method uased more time-consuming than FastICA, however, because the M-FastICA method reduced the number of iterations, therefore, the whole M-FastICA method is still improve the convergence rate, the corresponding computation time is also reduced. In general, M-FastICA methods and methods of LM-FastICA separation performance in improving the convergence speed with the original method is basically the same as FastICA.Seismic data is the important information resource of geological prospect and exploration. Random noise in seismic reflection data can be introduced by various sources and is often a problem in geophysical data visualization because it obscures fine details and complicates identification of image features. Among them, the denoising problem is the most prominent problem in seismic exploration.At present, about the seismic signal de-noising method focused on the following two aspects: First, in the denoising process , how to enhance signal not only in the horizontal direction can be enhanced with the phase axis, and can enhance the seismic record section with a larger tilt angle of axis, or bending the phase axis. Because most of the noise attenuation methods are based on the seismic record section in the horizontal direction of relevance, which often result in seismic records of the level of section with an axis to be strengthened, and the greater the tilt angle of axis, or bending with the phase axis will be weakened. Therefore we have to find a new de-noising method, or improve on the existing denoising methods. In order to effectively suppress the noise and can further enhance the signal to noise ratio with an in-phase axis with tilt angle and the bending of with the phase axis. Second, find a de-noising method for the seismic signals with different frequency bands. Because seismic records' different frequency components have different signal to noise ratio. Different frequency components of the signal to noise ratio have different role in improving the resolution. The loss of the effective high-frequency component of the seismic signal increases with depth increasing. So signal to noise ratio in the high-frequency is low. Therefore, the seismic signal denoising should be treated differently for different frequency components, which requires the research methods should have the characteristics of frequency. In this paper, based on the analysis of the characteristics of seismic signals, introduce the ICA method to seismic signal processing, achieve the de-noising of exploration seismic signals. FastICA first method has been applied to a single Ricker denoising, after analysis and verify the feasibility of the algorithm, and then applied FastICA on phase axis, multi-phase axis of the seismic data and a number of complex seismic data. The simulation results show that ICA can be a good method in the elimination of post-stack noise, so that a larger section to improve the quality and improve signal to noise ratio of the seismic data, so the independent component analysis has broad application prospects in seismic data processing.