Seismic wavelet estimation via a system identification method

On the assumption that the wavelet is causal and nonminimum phase, an autoregressive moving average (ARMA) model is introduced to fit the seismic trace. Seismic wavelet extraction is converted to parameters estimation of the ARMA model. Singular value decomposition (SVD) of an appropriate matrix formed by autocorrelation is exploited to determine the autoregressive (AR) order, and the cumulant-based SVD-TLS (total least squares) approach is proposed to obtain the AR parameters. The author proposes a new moving average (MA) model order determination method via combining the information theoretic criteria method and higher-order cumulant method. The cumulant approach is used to achieve the MA parameters. Theoretical analysis and numerical simulations demonstrate the feasibility of the wavelet extraction approach.