Dictionary:Ricker wavelet

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(rik’ ∂r) A zero-phase wavelet, the second derivative of the Gaussian function or the third derivative of the normal-probability density function. A Ricker wavelet is often used as a zero-phase embedded wavelet in modeling and synthetic seismogram manufacture. See Figure R-14. Named for Norman H. Ricker (1896–1980), American geophysicist.

Segr14.jpg

FIG. R-14. Ricker wavelet. (a) Time-domain and (b) frequency-domain representations.


The amplitude f(t) of the Ricker wavelet with peak frequency fM at time t is given by,

.

The frequency domain representation of the wavelet is given by,

Where,

and .

The mean frequency and the median frequency .

Sometimes the period (somewhat erroneously referred to occasionally as the wavelength) is given as 1/f, but since it has mixed frequencies, this is not quite correct, and for some wavelets is not even a good approximation. In fact, the Ricker wavelet has its sidelobe minima at

These minima have the value