Research on wavelet estimation via cumulant-based arma model approach

On the assumption that the seismic wavelet is non-causal and mixed phase, ARMA (autoregressive moving average) model was utilized to describe the seismic wavelet, and a cumulant-based parametric estimation approach which synthesized both the linear (matrix equation)and nonlinear(cumulant matching) methods was proposed to estimate the wavelet parameters. In this approach, the cumulant matching approach is used for accurate parameter estimation, with the basis of the initial guess that generated from matrix equations. Theoretic analysis and numerical simulation demonstrate the feasibility of this approach. Compared with the potential computational error of the linear methods, this approach can improve parameter estimation precision. Moreover, it extracts wavelet with high computational efficiency by avoiding the use of cumulant matching method under MA (moving average) model description, and reduces the complexity of initial guess via ARMA model matching approach.