The falling weight deflectometer (FWD) test is a commonly used method for the evaluation of the structural performance of pavement systems. In the FWD test, a large weight is raised off the ground and dropped onto a rubber loading pad creating an impulse load representative of the real loading imposed by heavy traffic on the pavement. The excitation produced by the loading sets off waves in the pavement and underlying soil. Deflection time histories are gathered by an array of sensors placed at several nearby locations. The traditional method for interpreting the FWD data to backcalculate structural pavement properties involves extracting the peak deflection from each displacement trace of the sensors (deflection basin) and matching it through an iterative optimization method to the deflections predicted by a static model of the pavement. This approach is computationally efficient and, when the depths of the layers are known and their properties are largely homogeneous with depth, the procedure is effective in backcalculating layer properties. However, when the depths are uncertain or when the moduli vary within a layer, the static backcalculation scheme may not yield reliable results. The goal of this study is to investigate the feasibility and effectiveness of using the complete time history of the FWD test to overcome some of the limitations of the static backcalculation procedure, and recover pavement layer moduli distribution and thickness. The problem is also formulated as a numerical minimization problem, where the unknowns are the resilient moduli of thin "computational layers" that discretize the profile. The initial finding is that this optimization formulation regularized by constraints on the magnitude and spatial gradient of the moduli, coupled with a continuation scheme for imposing the regularization terms, can overcome the ill-posedness nature of the original optimization problem. The computational effort for solving this inverse problem, however, is very significant as it requires repeated calls to the expensive forward problem: an elastodynamic simulation in stiff heterogeneous media. Additional work is needed to speed up the forward problem to be able to perform a more comprehensive evaluation with field data.