siamesefwi

Siamese Full waveform inversion

This example reproduce the siamese fwi (Omar et al., 2024), which use a network to map the data into a latent space and then compare them. The network is trained to minimize the difference between the latent space of the predicted and observed data.

Theory

For conventional FWI, the objective function is defined as the difference between the observed and synthetic data:

$$ J(\mathbf m) = \frac{1}{2} \sum_{s,r}^{} \left| d_{\text{obs}}^i - d_{\text{syn}}(\mathbf m)^i \right|^2 $$

The siamese fwi, on the other hand, uses a network to map the data into a latent space, so we will have:

$$ \mathbf z_{obs}^{latent} = \mathcal F(\mathbf d_\text{obs}; \theta) $$

and

$$ \mathbf z_{syn}^{latent} = \mathcal F(\mathbf d_\text{syn}; \theta) $$

where $\mathcal F$ is the network and $\theta$ are the network parameters. Both synthetic and observed data are mapped into a same latent space with a single network, that is why it is called siamese.

The objective function of siamese fwi is defined as the difference between the latent space of the predicted and observed data:

$$ J(\mathbf m) = \frac{1}{2} \sum_{s,r}^{} \left| \mathbf z_{\text{obs}}^{latent} - \mathbf z_{\text{syn}}^{latent} \right|^2 $$

Run the example

The configuration file is configure.py. You can change the parameters in this file to test the example.

First, we need to simulate the observed. The script forward.py is used to that.

python forward.py

Scripts fwi_classic.py and fwi_siamese.py are used to run the conventional L2-based and Siamese-based FWI, respectively. You can either run it in an interactive window for checking the intermediate results or run it in the background.

Note

I only have one 2080Ti, cannot test the full Marmousi model, so I use a downsampled for testing. This test still to be done.