ARTICLE

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

XIAOYING DENG1 DINGHUI YANG2 TAO LIU3 BAOJUN YANG4
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1 Department of Electronic Engineering, Beijing Institute of Technology, Beijing 100081, P. R. China. xydeng@bit.edu.cn,
2 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China. dhyang@math.tsinghua.edu.cn,
3 Military Representative Office of PLA in Second Research Institute of CASIC, Beijing 100854, P. R. China.,
4 Department of Geophysics, Jilin University, Changchun 130026, P. R. China. yangbaojun@jlu.edu.cn,
JSE 2011, 20(2), 161–176;
Submitted: 22 July 2010 | Accepted: 21 December 2010 | Published: 1 May 2011
© 2011 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

Deng, X., Yang, D., Liu, T. and Yang, B., 2011. Study of least squares support vector regression filtering technology with a new 2D Ricker wavelet kernel. Journal of Seismic Exploration, 20: 161- 176. 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 1D Ricker wavelet kerne] 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.

Keywords
2D Ricker wavelet kernel
least squares support vector regression
seismic data
random noise reduction
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing