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488 Danilo R. Velis and Mauricio D. Sacchi<br />

There are also some equivalent formulae based <strong>on</strong> fourthorder<br />

statistics.<br />

However, direct methods based <strong>on</strong> a single slice of higherorder<br />

covariance or moment functi<strong>on</strong>s do not provide any<br />

filtering to reduce the effects of the errors derived from the<br />

fact that these functi<strong>on</strong>s are simple estimates, thus the above<br />

equati<strong>on</strong> is not practical from a computati<strong>on</strong>al point of view<br />

(Mendel 1991). The same argument applies to the estimati<strong>on</strong><br />

of the reflectivity <strong>using</strong> the MTDS.<br />

REFERENCES<br />

Lu W. 2005. N<strong>on</strong>-<strong>minimum</strong>-<strong>phase</strong> <strong>wavelet</strong> estimati<strong>on</strong> <strong>using</strong> sec<strong>on</strong>dand<br />

third-order moments. Geophysical Prospecting 53, 149–<br />

158.<br />

Mendel J. 1991. Tutorial <strong>on</strong> higher-order statistics in signal processing<br />

and system theory: Theoretical results and some applicati<strong>on</strong>s.<br />

Proceedings of the IEEE 79, 278–305.<br />

Nikias C.L. and Mendel J.M. 1993. Signal processing with<br />

higher-order spectra. IEEE Signal Processing Magazine 10, 10–<br />

37.<br />

C○ 2006 European Associati<strong>on</strong> of Geoscientists & Engineers, Geophysical Prospecting, 54, 487–488

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