SimpleFWI

This code provides the basic building blocks to test optimization algorithms on seismic inverse problems. The canonical seismic waveform inversion problem is given by

$$\min_{m} \sum_{i} \frac{1}{2}||P^TA(m)^{-1}q_i - d_i||_2^2 + \frac{\alpha}{2}||Lm||_2^2,$$

where $A(m)$ is the discretized Helmholtz operator $\omega^2 m + \nabla^2$ with absorbing boundary conditions, $P$ is the sampling operator, $q_i$ are the source vectors, $d_i$ are the observed data and $L$ is the discretized $\nabla$.

The main function is misfit.m, which takes as input the medium parameters $m$ and the data $d_i$ (and definitions of $P$, $q_i$, $\omega$ etc.) and returns the misfit value, its gradient and a function handle to compute the action of the Gauss-Newton hessian.

For an example, see /examples, which uses a simple BB iteration to solve the optimization problem. To run these, you need to install the SPOT library: https://github.com/mpf/spot

Feel free to contact me with any questions, suggestions, etc.

Tristan van Leeuwen - [email protected]