Noise reduction by support vector regression with a Ricker wavelet kernel

We propose a noise filtering technology based on the least-squares support vector regression (LS-SVR), to improve the signal-to-noise ratio (SNR) of seismic data. We modified it by using an admissible support vector (SV) kernel, namely the Ricker wavelet kernel, to replace the conventional radial basis function (RBF) kernel in seismic data processing. We investigated the selection of the regularization parameter for the LS-SVR and derived a concise selecting formula directly from the noisy data. We used the proposed method for choosing the regularization parameter which not only had the advantage of high speed but could also obtain almost the same effectiveness as an optimal parameter method. We conducted experiments using synthetic data corrupted by the random noise of different types and levels, and found that our method was superior to the wavelet transform-based approach and the Wiener filtering. We also applied the method to two field seismic data sets and concluded that it was able to effectively suppress the random noise and improve the data quality in terms of SNR.