You know what’s hype? Full-waveform inversion.

If you’re in geophysics specifically involved in some sort of inversion, you want to be doing FWI. It’s what the cool kids do.

You know what’s the problem? Cool kids really like to be an exclusive club. The same thing is happening in Machine Learning and Deep Learning. Fast.ai has particularly set their slogan “Making Neural Networks uncool again” as to say, you too can learn using deep learning algorithms without being superintelligent.

The fantastic people from Imperial College around Gerard Gorman have taken it on themselves to make FWI uncool again. They publish a three part open access series in Geophysics. They present end to end code examples with all the explanations.

The basic problem of FWI is getting a high-resolution velocity model from seismic data. Usually we start from a prior low-resolution velocity model. Making a forward seismic model of the data. Then estimating the misfit to the measured seismic and iteratively reducing that misfit.

You do this with something called this adjoint wave equation. In the acoustic case this is relatively easy. As soon as our data gets more complicated it gets harder to get the adjoint wave equation.

All those research centers working on FWI are working to make the wave equation solved more realistic or the calculation more efficient. Here is your entrance point to the beautiful world of partial differential equations to get velocity models.

## The Forward Pass

Find their paper here:

https://library.seg.org/doi/abs/10.1190/tle36121033.1

I could foolishly call this the easy part. This generates shot gathers from the velocity model.

## The Adjoint Method

Find paper two here:

https://library.seg.org/doi/abs/10.1190/tle37010069.1

This is where we compare the generated seismic and try to minimize the misfit.

## The Optimization

Paper three is not out yet and I will not spoil it for you. February is approaching fast. You can look forward to some amazing work in the Julia language with the JUDI framework.

#### Would you like FWIs with that?

#### Jesper Dramsch

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