2D Acoustic Frequency-domain FWI

This is a 2D full waveform inversion code using simultaneous encoded sources based on first- and second-order optimization methods developed in Amsalu's Thesis.

Forward modelling: solves a two-dimensional wave-equation in frequency domain $$ \frac{\partial }{\partial x}\left(\frac{1 }{\rho}\frac{\partial }{\partial x} p(\omega) \right) +\frac{\partial }{\partial z}\left(\frac{1}{\rho}\frac{\partial }{\partial z} p(\omega) \right) + \frac{\omega^2}{\kappa} p(\omega) = f(\omega) $$ where, $\kappa = \rho v^2$ is the bulk modulus, $\rho $ is the density, $v$ is the velocity, $p$ is the pressure field, $\omega$ is the angular frequency and $f(\omega)$ is the source signature.

After discretization, the acoustic wave equation can be written in a compact matrix form as
$$ A({\bf x}, {\bf m}, \bf \omega){\bf p}({\bf x }, {\bf x}_{s},\omega) ={\bf f(\omega)} \delta({\bf x} - {\bf x}_{s}), $$ where $ A({\bf x}, {\bf m}, \omega) $ is the discretized Helmholtz equaton, $ {\bf p}( {\bf x}, {\bf x}_{s},\omega) $ is a complex pressure field for a shot located at $ {\bf x}_{s} $.