A feasibility study for inverting reflection coefficients for a single-interface model consisting of a shale overlying a fractured sand is presented. To characterize the medium contact from amplitude versus scattering angles (AVA) behavior associated with the reflection from a particular interface, in view of the anisotropy, wide-angle scattering data are required. However, wide-angle scattering turns the inverse problem into an essentially nonlinear one. The inverse problem is hence analyzed with a global optimization procedure—a genetic algorithm with constraints. The key to making a genetic algorithm work for our AVA inverse problem appears to be a proper parameterization of the direct scattering problem and introducing a parameter hierarchy. These reduce the complexity of the misfit function occurring in the optimization procedure and let this function become convex over a relatively large range of medium parameter values. We illustrate how well our approach performs with a single-interface example representing a shale/fractured-sandstone contact. In this example, we assume the overburden, i.e., the shale, to be known; we allow the data to be contaminated with noise.