The Ricker wavelet is a model seismic wavelet, sometimes called a Mexican hat wavelet.
The amplitude A of the Ricker wavelet with peak frequency f at time t is computed like so:
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
Make one in Python
import numpy as np import matplotlib.pyplot as plt def ricker(f, length=0.128, dt=0.001): t = np.arange(-length/2, (length-dt)/2, dt) y = (1.0 - 2.0*(np.pi**2)*(f**2)*(t**2)) * np.exp(-(np.pi**2)*(f**2)*(t**2)) return t, y f = 25 # A low wavelength of 25 Hz t, w = ricker(f)
- scipy.signal.ricker — Scipy function for a Ricker wavelet, which takes a scale parameter a = 1/2πf (I think)
- Mexican hat wavelet — Wikipedia article
- Ryan, 1994. A choice of wavelets. CSEG Recorder September 1994.
- Ricker wavelet — Sheriff's Encyclopedic Dictionary