Wavelet parameter and phase estimation using cumulant slices

A simple, closed-form expression relates one-dimensional output cumulant statistics with the parameters of a known-order moving-average wavelet. Based on this relationship the author obtains unique parameter and phase estimates of autoregressive moving-average seismic wavelets. The input reflectivity sequence is assumed to be non-Gaussian, independent, and identically distributed. The wavelet is not assumed to be minimum phase and is allowed to include all-pass factors. The seismogram is contaminated by additive-colored Gaussian noise. Simulations demonstrate that the algorithm works well for moderate-size data records with a relatively low signal-to-noise ratio