Study of least squares support vector regression filtering technology with a new 2D Ricker wavelet kernel

To suppress the random noise in seismic data, the least squares support vector regression (LS-SVR) filtering technology with a new 2D Ricker wavelet kernel is proposed in this paper. Firstly, we prove that the 2D Ricker wavelet kernel is an admissible support vector kernel. The proposed 2D Ricker wavelet kernel takes into account the characteristics of seismic data in the time-space domain. And the kernel parameters of the 2D Ricker wavelet kernel reflect the dominant frequency of seismic data in time domain and the wavenumber of seismic data in space domain, which will help the difficult problem of parameters selection for LS-SVR. Then by solving a quadratic optimization problem with constrains, we can obtain the regression function so as to compute the filtered output. The simulation experiments on synthetic records show that compared with the LS-SVR using ID Ricker wavelet kernel and the common f-x prediction filtering method, the proposed method can suppress the random noise more efficiently, and enhance the continuity of events greatly. An example on a real seismic data processing also proves the effectiveness of the proposed method. So the LS-SVR with the 2D Ricker wavelet kernel can be used to attenuate the random noise in seismic data.