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## Determining the picking position

We choose the convention that the picking position of a wavelet is the first break of the minimum phase part and the ending point of the maximum phase part. The minimum phase part is causal and the maximum phase part is anti-causal:
 (4)
where and are generally complex with their norm less than one, and Nmin+Nmax=N. Clearly, this choice ensures that for a minimum phase wavelet, the first break of the wavelet is picked, and that for a zero phase wavelet, the center point of the wavelet is picked.

To estimate n0, we need to examine the phase response of S(Z). Let be the phase spectrum of ,and the phase spectrum of . Equating the the phase spectra of the two sides of equation (3) yields
 (5)
Because w(n) is a real sequence and has causal minimum phase and anti-causal maximum phase parts, its phase spectrum is anti-symmetric with respect to :

Using this condition, we can solve equation (5) for n0 as follows:
 (6)
By setting , we see that n0 is the phase delay of the received signal at the Nyquist frequency:

Next: Calculating the phase spectrum Up: THEORY Previous: THEORY
Stanford Exploration Project
12/18/1997