Lavrent’ev-Type Equations and Systems in the Inverse Problem of Reconstructing Viscoelastic Medium Memory

We consider a nonlinear coefficient inverse problem related to partial reconstruction of the memory matrix of a viscoelastic medium from the results of probing the medium with a family of wave fields excited by point sources. A spatially non-overdetermined formulation is studied, for which the manifolds of point sources and detectors do not coincide and have a total dimension of 3. The requirements for these manifolds are established that ensure the unique solvability of the inverse problem. The results are achieved by reducing the problem to a chain of coupled systems of linear integral equations of the Lavrent’ev type.