A HOS-based blind deconvolution algorithm for the improvement of time resolution of mixed phase low SNR seismic data

A blind deconvolution technique using a modified higher order statistics (HOS)-based eigenvector algorithm (EVA) is presented in this paper. The main purpose of the technique is to enable the processing of low SNR short length seismograms. In our study, the seismogram is assumed to be the output of a mixed phase source wavelet (system) driven by a non-Gaussian input signal (due to earth) with additive Gaussian noise. Techniques based on second-order statistics are shown to fail when processing non-minimum phase seismic signals because they only rely on the autocorrelation function of the observed signal. In contrast, existing HOS-based blind deconvolution techniques are suitable in the processing of a non-minimum (mixed) phase system; however, most of them are unable to converge and show poor performance whenever noise dominates the actual signal, especially in the cases where the observed data are limited (few samples). The developed blind equalization technique is primarily based on the EVA for blind equalization, initially to deal with mixed phase non-Gaussian seismic signals. In order to deal with the dominant noise issue and small number of available samples, certain modifications are incorporated into the EVA. For determining the deconvolution filter, one of the modifications is to use more than one higher order cumulant slice in the EVA. This overcomes the possibility of non-convergence due to a low signal-to-noise ratio (SNR) of the observed signal. The other modification conditions the cumulant slice by increasing the power of eigenvalues of the cumulant slice, related to actual signal, and rejects the eigenvalues below the threshold representing the noise. This modification reduces the effect of the availability of a small number of samples and strong additive noise on the cumulant slices. These modifications are found to improve the overall deconvolution performance, with approximately a five-fold reduction in a mean square error (MSE) and a six-fold reduction in convolution noise of 10 dB of the SNR. © 2009 Nanjing Institute of Geophysical Prospecting.