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
Apparent vs dominant frequency
We can use the trough-to-trough width of the Ricker to estimate the dominant frequency (i.e. the central frequency of the Ricker) from the apparent frequency (which will be driven by this trough-to-trough width). If 't' is the width in time:
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