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Research on wavelet extraction via linear equation approach based on higher-order cumulant
DAI Yong-shou, WEI Lei, HUO Zhi-yong
(College of Information and Control Engineering in China University of Petroleum,Dongying 257061, Shandong Province, China)
Abstract:
Based on the assumption that the wavelet is non-causal and mixed phase, both the moving average (MA) and autoregressive moving average (ARMA) models were introduced to fit the seismic record. A linear equation approach based on higher-order cumulant was employed to extract the wavelet and evaluate the adaptability of each model. Numerical simulations demonstrate that the ARMA model provides a parsimonious, more efficient signal model for fitting seismic trace than the MA model does. The cumulant-based linear equations approach is not sensitive to Gaussian colored noise, but strongly relies upon the accuracy of the trace cumulant estimates. If the estimated error and variance of trace cumulants are moderate, the cumuiant-based linear equations approach combined with the ARMA model description of the seismic record is appropriate for non-causal, mixed phase wavelet extraction. The real seismic data examples demonstrate possible uses of the method.
Key words:  sesmic record  higher-order cumulant  wavelet extraction  autoregressive moving average  linear equation approach