Blind identification using the kurtosis with applications to field data

In this paper we present an estimation method for a non-minimum phase MA, AR or ARMA models. This method is based on the maximum kurtosis property. First the spectrally equivalent minimum-phase (SEMP) filter is estimated from the output statistics, then the kurtosis allows us to localise the zeros of the true transfer function from the zeros of its SEMP filter. For ARMA process we adopt two ways of identification, the first uses a residual times series approach (RTS) and the second uses a minimum-phase-allpass decomposition. On a field seismic data, we compare the deconvolution results using the proposed methods and the minimum-phase approach. Using data from held underwater explosions we show the interest of modelling the secondary waves of the gas bubble, using a non-causal AR filter.