Translations:Ricker wavelet/11/en

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We see that 12 of the roots have an absolute value of unity. Any root with absolute-value unity corresponds to a two-length equal-delay wavelet in the composition of the discrete Ricker wavelet being considered. We do not like equal-delay wavelets for reasons put forth earlier in this chapter. We want all the two-length constituent wavelets to be either strictly minimum-delay wavelets or strictly maximum-delay wavelets (Robinson et al., 1978[1]). We therefore modify the Ricker wavelet by adding a little bit of white noise to the center value of the autocorrelation function - say, 1% of this value - which is an operation called prewhitening. In other words, we multiply the center value of this autocorrelation function by 1.01. The modified Ricker wavelet now becomes

  1. Robinson, E. A., D. Loewenthal, and S. Treitel, 1978, Numerical testing of minimum-delay, positive- real, and positive-definite digital filters: Journal of Computational Physics, 29, 421–430.