In our recent works [65,66], we demonstrate via the frameworks of linear sampling and boundary integral equations the feasibility of non-iterative, 3D seismic waveform tomography of heterogeneous fractures. This includes both (i) geometric fracture reconstruction and (ii) quantitative mapping of its shear and normal specific stiffness distributions — reflecting e.g. the fracture aperture, surface roughness, and the presence (if any) of an interphase such as fluid or proppant. One such synthetic example is shown in the image above, showing the reconstruction and characterization of a cylindrical fracture endowed with a “cheetah” pattern of normal specific stiffness.