Ricker wavelet

The Ricker wavelet is a model seismic wavelet, sometimes called a Mexican hat wavelet.

Analytic expression
The amplitude A of the Ricker wavelet with peak frequency f at time t is computed like so:


 * $$A = (1-2 \pi^2 f^2 t^2) e^{-\pi^2 f^2 t^2} $$

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


 * $$\pm \frac{\sqrt{3/2}}{f\pi} $$

These minima have the value


 * $$A_\mathrm{min} = -\frac{2}{e^{3/2}} $$

Make one in Python
Here's a snippet from an IPython Notebook by Evan: