# A Cheerful Wave(let)

### August 5th, 2017

The wavelets have been put in their rightful place at last. We've developed and coded an algorithm that allows a modeller to seek out specific regions of a model by extracting them from the wavelet domain. Since wavelets are geographically localised, we can use them to seek out and compare specific parts of a tomographic model, whether global or regional.

In addition, I've adapted the original algorithm for conducting the wavelet transform on a cubed sphere to improve computational efficiency and more importantly, to run using Python! The key step in doing so involved using MATLAB to generate a wide set of 3-D wavelet basis functions that can be accessed on a sphere.

I've since developed a general set of streamlined functions that work with any input velocity model and allow you to run the wavelet transform on it. Here's an example of what we can achieve if we look at different 'scales' (wavelengths) of a tomographic model.

This is an original velocity model developed by researchers at MIT.

This is the scaling function, or longest-wavelength structure of that model. We can generate this by running the wavelet transform on this model.

The real power of wavelets for us, however, lies when we combine the same areas of regional and global models. Stay tuned for that- it's only a matter of time.

## Comments

*You must be logged in to post a comment.*