Model reduction approaches to forward and inverse elastic wave problems with active sources in fractured reservoirs. One of the challenges of modeling and inversion of the elastic wave responses in presence of hydraulic fractures is multi-scale nature of the problem. We address this issue by employing recently developed model reduction approaches. Reduced order models (ROMs) approximate transfer functions of large-scale linear dynamical systems by small equivalent ones. Their matrices can be geometrically interpreted as finite-difference operators discretized on so-called optimal grids or alternatively, spectral projection approximations. That allows us to substitute fine-scale fractured models by low dimensional approximants. Based on model reduction methods, we developed multiscale mimetic 3D elastic forward solver and direct imaging algorithm. In this talk we describe both of them and illustrate their application for models with hydraulic fractures. Contributors: Alexander Mamonov, Dzevat Omeragic, Olga Podgornova, Andrew Thaler, Mikhail Zaslavsky, Smaine Zeroug