“…The presence of fluids in rock discontinuities at different scales, e.g., joints, could strongly affect acoustic wave propagation in the Earth's crust [1]. Understanding wave responses to fluid-filled rock joints is of great importance to many kinds of practical engineering applications, such as reservoir detection and characterization, geothermal exploration and extraction, underground engineering appraisal, exploration seismology and earthquake engineering [2][3][4][5][6]. For instance, seismic wave attenuation and velocity can be used to determine the fracture specific stiffness, which is a key parameter to characterize alternations of a facture induced by fluid flow [7].…”