# Ricker wavelet

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

## Contents

## Analytic expression

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:

and

then

## Make one in Python

Here's a snippet from an IPython Notebook by Evan:^{[2]}^{[3]}

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)

## See also

## References

- ↑ Ricker wavelet in WolframAlpha
- ↑ To make a wavelet — an IPython Notebook.
- ↑ To plot a wavelet — Agile Geoscience blog post

## External links

- scipy.signal.ricker — Scipy function for a Ricker wavelet, which takes a scale parameter
*a*= 1/2π*f*(I think) - Mexican hat wavelet — Wikipedia article
- Ryan, 1994. A choice of wavelets. CSEG Recorder September 1994.
- Ricker wavelet — Sheriff's Encyclopedic Dictionary

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