A dual formulation for time-domain wavefield reconstruction inversion

We illustrate a dual formulation for full-waveform inversion potentially apt to large 3-D problems. It is based on the optimization of the wave equation compliance, under the constraint of data misfit not exceeding a prescribed noise level. In the Lagrangian formulation, model and wavefield state variables are complemented with multipliers having the same dimension of data ("dual data" variables). Analogously to classical wavefield reconstruction inversion, the wavefield unknowns can be projected out in closed form, by solving a version of the augmented wave equation. This leads to a saddle-point problem whose variables are only model and dual data. As such, this formulation represents a model extension, and is potentially robust against local minima. The classical downsides of model extension methods and wavefield reconstruction inversion are here effectively mitigated: storage of the dual variables is affordable, the augmented wave equation is amenable to time-marching finite-difference schemes, and no continuation strategy for penalty parameters is needed, with the prospect of 3-D applications.

https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/rizzuti...