# Dictionary:Ricker wavelet

(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.

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

The amplitude *f(t)* of the Ricker wavelet with peak frequency *f _{M}* 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