# A study of Ricker wavelets in MS Excel

There, I said it, and aloud: ‘EXCEL’!

I got this idea of making a modern (no, I am NOT kidding) educational tool to interactively construct and study Ricker wavelets after reading William Ashcroft’s A Petroleum Geologist’s Guide to Seismic Reflection. The book is a gem, in my opinion (I discovered it thanks to a blog post by Matt Hall a couple of years ago) and comes with some interesting tools on a DVD, which are unfortunately a bit outdated. So I went back to my old Geophysics Bible (Yilmaz’ book Seismic Data Analysis), and mashed a few ideas up; you can Please feel free to use it, peruse it, and abuse it, in your classes, labs, nightmares, etcetera…

The tool is fairly simple. In Sheet 1 the user enters the dominant frequency of the desired Ricker wavelet, as shown in the middle of Figure 1. From that informatin the wavelet is constructed using the equation A = g^2 * 1/exp g^2 where g is the ration between frequency f  (in increments of 5 Hz up to an arbitrary 125 Hz – but this could be easily changed!) and the dominant frequency f1 just entered.  frequencies. The frequency spectrum of the wavelet is shown as a graph.

Figure 1

In Figure 2 I show the same Sheet, but for a wavelet of dominant frequency equal to 50 Hz.

Figure 2

A number of ancillary graphs, shown in Figure 3, display individual building blocks of the formula A = g^2 * 1/exp g^2.

Figure 3

In Sheet 2 the user can view a plot of the wavelet in the time domain,  add Constant phase shifts and Linear phase shifts, and experiment with different combinations of them, as shown in Figures 4-7, below.

Figure 4

Figure 5

Figure 6

Figure 7

Finally, Sheet 3 displays a plot of the wavelet, and of the individual frequency components that make it up. Have fun!!!

Figure 8

### References and further playing

A Petroleum Geologist’s Guide to Seismic Reflection, William Ashcroft, 2011, Wiley.

Seismic Data Analysis, Öz Yilmaz, 2001, Society of Exploration Geophysicists.

To plot a wavelet [in Python]. blog post by Evan Bianco.