Determining kernels in linear viscoelasticity.

In this work, we investigate the inverse problem of determining the kernel functions that best describe the mechanical behavior of a complex medium modeled by a general nonlocal viscoelastic wave equation. To this end, we minimize a tracking-type data misfit function under this PDE constraint. We perform the well-posedness analysis of the state and adjoint problems and, using these results, rigorously derive the first-order sensitivities. Numerical experiments in a three-dimensional setting illustrate the method. • Kernel recovery method for general nonlocal viscoelasticity. • Minimization of a tracking-type data misfit function governed by non-local viscoelastic wave equations. • Rigorous derivation of first-order sensitivities. • Numerical experiments in three-dimensional settings. [ABSTRACT FROM AUTHOR]