Semi-discrete Matrix Free Formulation of 3D Full Waveform Elastic Modeling and Inversion

In this work we derive the adjoint equations for the SEM model, which enables the incorporation of a generic data misfit functional. The key contributions of the study are a scalable computational strategy and a novel approach for matrix-free evaluation of the adjoint wavefield. The formulation enables computation of the adjoint wavefield, and consequently the gradient (or proximal function of which) of the objective function, while avoiding storage of the forward displacement field in memory. This algorithmic setup grants scalability in both weak and strong scaling tests.