Retrieval of Elastodynamic Green's Functions through Single-Sided Marchenko Inverse Scattering

The solution of the inverse scattering problem for the 1D Schrodinger equation is given by the Marchenko equation. Recently, a Marchenko-type equation has been derived for 3D acoustic wave-fields, whose solution has been shown to recover the Green's functions from points within themedium to its exterior, using only single-sided scattered data. Here we extend this approach to 3D vectorial waveelds that satisfy the elastodynamic wave equation, and recover Green's functions from points interior to an elastic, solid-state medium from purely external and one-sided measurements. The method is demonstrated in a solid-Earth-like model to construct Green's functions using only subsurface sources, from Earth-surface force and deformation sources and particle velocity and stress measurements.