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Conventional fracture-characterization methods assume the presence of a single set of cracks in the subsurface. We relax this assumption and demonstrate the feasibility of seismic characterization of multiple fracture sets. Our technique relies on recent findings indicating that multiple, differently oriented, possibly intersecting cracks embedded in an otherwise isotropic host rock result in nearly orthotropic effective media. Here, we estimate the governing parameters of crack-induced orthotropy from 3D, wide-azimuth, multicomponent seismic reflection data acquired over the tight-gas Rulison Field in Colorado. We translate azimuthal variations of the normal-moveout velocities into interval crack densities, fracture orientations, type of fluid infill, and velocities of P- and S-waves in an unfractured rock. Our inversion procedure identifies one set of cracks in the western part of the study area and multiple, likely intersecting fractures in its eastern part. We validate both our underlying theoretical model and the obtained estimates by two independent measurements: the estimated fluid-infill parameter indicates dry cracks as expected for the gas-producing sandstones at Rulison; and the obtained crack orientations are supported by well observations. As a by-product of fracture characterization, we build an orthorhombic velocity model of the Rulison reservoir.