Tangential cone condition for the full waveform forward operator in the elastic regime: the non-local case

We generalize results of [M. Eller and A. Rieder, Inverse Problems 37 (2021) 085011] from the acoustic to the elastic wave equation. That means we show injectivity of the Fréchet derivative of the parameter-to-state map for a semi-discrete seismic inverse problem in the elastic regime. Here, the parameter space is spanned by functions which have a global support in the propagation medium (the non-local case) and are locally linearly independent. As a consequence we derive local conditional wellposedness of this nonlinear inverse problem. Furthermore, the tangential cone condition holds, which is an essential prerequisite in the convergence analysis of a variety of inversion algorithms for nonlinear illposed problems.