Translations:Ricker wavelet/17/en

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What is the component signal for the modified Ricker wavelet? Consider the above absolute values of the roots of the modified Ricker wavelet: one-half of them are greater than one, whereas the other half are less than one. Take the 11 roots with absolute values greater than one. With these 11, form a polynomial. The coefficients of this polynomial make up what we shall call a component wavelet (Robinson and Treitel, 1985[1]). This component wavelet is necessarily a minimum-delay wavelet because (by construction) each root of its Z-transform polynomial has magnitude greater than one (Figure 23). In Figure 23, we also show the time-reverse of this component wavelet, which is necessarily a maximum-delay wavelet.

  1. Robinson, E. A., and S. Treitel, 1985, The right-half autocorrelation theorem, in O. D. Anderson, J. K. Ord, and E. A. Robinson, eds., Time series analysis, theory and practice 6: North Holland Publishing Co., 105–132.