Differential LiDAR (Light Detection and Ranging) from repeated surveys has recently emerged as an effective tool to measure three-dimensional (3D) change for applications, such as quantifying slip and spatially distributed warping associated with earthquake ruptures, and examining the spatial distribution of beach erosion after hurricane impact. Currently, the primary method for determining 3D change from LiDAR is through the use of the iterative closest point (ICP) algorithm and its variants. However, all current studies using ICP have assumed that all LiDAR points in the compared point clouds have uniform accuracy. This assumption is simplistic given that the error for each LiDAR point is variable, and dependent upon time varying factors such as target range, angle of incidence, and aircraft trajectory accuracy. Therefore, to rigorously determine spatial change, it would be ideal to model the random error for every LiDAR observation in the differential point cloud, and use these error estimates as apriori weights in the ICP algorithm. To test this approach, we implemented a rigorous LiDAR observation error propagation method to generate estimated random error for each point in a LiDAR point cloud, and then determine 3D displacements between two point clouds using an anisotropic weighted ICP (A-ICP) algorithm. The algorithm was evaluated by qualitatively and quantitatively comparing point clouds with synthetic fault ruptures between a uniform weight and anistropically weighted ICP algorithm. Then post-earthquake slip is estimated for the 2010 El Mayor-Cucapah Earthquake (EMC), using pre- and post-event LiDAR. Based on the analysis, Moving Window A-ICP is able to better estimate the synthetic surface ruptures, and provides a smoother estimate of actual displacement for the EMC earthquake.