Institute of Geophysics, University of TehranJournal of the Earth and Space Physics2538-371X42120160521Erratic seismic noise attenuation by weighting of rank reduced Hankel matrixErratic seismic noise attenuation by weighting of rank reduced Hankel matrix63735567710.22059/jesphys.2016.55677FAMoslemHashemiGraduateHamid RezaSiahkoohiProfessor of Physics of the EarthAliGholamiHead of Computer ServicesJournal Article20150202The presence of noise in geophysical measurements has undesirable effects on the seismic data. One of the important problems in seismic data processing is attenuation of the noise to the desired form and keeping the original signal. Contamination of seismic data with noise prevents obtaining a proper image of geological structures and seismic data interpretation. In some of the receivers the noise has erratic values and the amplitude is large in relation to other receivers, surprising and do not follow a Gaussian distribution. In reality, not all observed data follow the Gaussian distribution. There may be a group of atypical data that are far away from the majority of data. Atypical data are referred to as outliers or gross errors, which follow other distributions or there is no clear distribution to describe them. These are called erratic noises that do not follow the Gussian distribution. Conventional methods for noise suppression assume Gaussian noise distribution and their performance decreases in the case of erratic noise. The rank reduction based techniques are applied to attenuate weak random seismic noise in a least squares sense. The rank reduction methods are very sensitive to erratic noises and the different results provide. Even a little of erratic noises extremly degrades the performance of the rank reduction methods. More robust estimates are needed such that they are acceptable even when the data do not strictly follow the given distribution. The non-Gaussian and erratic noise are usually produced by wind, incorrect polarity, cultural and traffic noises and so on. In order to solve this problem a new filter based on repeating the reduction of the rank of Hankel matrix is introduced. The method is called iteratively reweighted rank reduction (IRRR). This method is combination of iterative weighted least squares procedure (IRLS) and weighting low-rank approximations (WLRA). In this method after transferring data into the frequency domain, for each constant frequency slice an individual Hankel matrix is created and then by using singular value decomposition (SVD) a rank reduced matrix is obtained. Later on using the iterative algorithm, until the desired convergence is achieved, the combined weight values are obtained from the original matrix and rank reduced matrix. Parameter that controls the convergence of the method is the weighting function. The role of weighting function is reducing or completely removing of the erratic noise from data. Here the weighting function we used was Tukey’s Biweight function. In order to maintain the statistical performance and the ability of the method we define regulation parameter τB. Regulation parameter is calculated based on the estimates to the median and the median absolute deviation. These two estimates are not sensitive to erratic noise. The advantage of this method in comparison to the other rank reducing methods is the attenuation of erratic noise and at the same time random noise. This method is application to 2D and 3D seismic data. Performance of the method was tested on synthetic and real seismic data. The results showed superior performance of the method in attenuating erratic noises.The presence of noise in geophysical measurements has undesirable effects on the seismic data. One of the important problems in seismic data processing is attenuation of the noise to the desired form and keeping the original signal. Contamination of seismic data with noise prevents obtaining a proper image of geological structures and seismic data interpretation. In some of the receivers the noise has erratic values and the amplitude is large in relation to other receivers, surprising and do not follow a Gaussian distribution. In reality, not all observed data follow the Gaussian distribution. There may be a group of atypical data that are far away from the majority of data. Atypical data are referred to as outliers or gross errors, which follow other distributions or there is no clear distribution to describe them. These are called erratic noises that do not follow the Gussian distribution. Conventional methods for noise suppression assume Gaussian noise distribution and their performance decreases in the case of erratic noise. The rank reduction based techniques are applied to attenuate weak random seismic noise in a least squares sense. The rank reduction methods are very sensitive to erratic noises and the different results provide. Even a little of erratic noises extremly degrades the performance of the rank reduction methods. More robust estimates are needed such that they are acceptable even when the data do not strictly follow the given distribution. The non-Gaussian and erratic noise are usually produced by wind, incorrect polarity, cultural and traffic noises and so on. In order to solve this problem a new filter based on repeating the reduction of the rank of Hankel matrix is introduced. The method is called iteratively reweighted rank reduction (IRRR). This method is combination of iterative weighted least squares procedure (IRLS) and weighting low-rank approximations (WLRA). In this method after transferring data into the frequency domain, for each constant frequency slice an individual Hankel matrix is created and then by using singular value decomposition (SVD) a rank reduced matrix is obtained. Later on using the iterative algorithm, until the desired convergence is achieved, the combined weight values are obtained from the original matrix and rank reduced matrix. Parameter that controls the convergence of the method is the weighting function. The role of weighting function is reducing or completely removing of the erratic noise from data. Here the weighting function we used was Tukey’s Biweight function. In order to maintain the statistical performance and the ability of the method we define regulation parameter τB. Regulation parameter is calculated based on the estimates to the median and the median absolute deviation. These two estimates are not sensitive to erratic noise. The advantage of this method in comparison to the other rank reducing methods is the attenuation of erratic noise and at the same time random noise. This method is application to 2D and 3D seismic data. Performance of the method was tested on synthetic and real seismic data. The results showed superior performance of the method in attenuating erratic noises.https://jesphys.ut.ac.ir/article_55677_91942d07e630836c4520338605cfa6e0.pdf