A new quantitative technique is proposed for determining both the concentration and spatial extent of viscous dissipation in dynamic systems. When dissipation is distributed unevenly within a system, nonexponential response decays can result within certain frequency ranges. Unlike typical exponential decays that carry volume averaged information about the strength of dissipation, nonexponential decays carry information about both the strength and distribution of dissipation in the system. Two parameters describe the nonexponential decay process and can be directly related to the strength and spatial extent of the dissipation. It is proposed that fitting observed nonexponential decays to the predicted model may provide a method for the nondestructive determination of both the extent and severity of dissipation causing defects in materials. The presented work concentrates on acoustic systems and provides a test of the proposed concept. Theoretical predictions are presented and compared with numerical experiments to determine the effectiveness of the proposed approach.