3-D earthquake surface displacements from differencing pre- and post-event LiDAR point clouds

The explosion in aerial LiDAR surveying along active faults across the western United States and elsewhere provides a high-resolution topographic baseline against which to compare repeat LiDAR datasets collected after future earthquakes. We present a new method for determining 3-D coseismic surface displacements and rotations by differencing pre- and post-earthquake LiDAR point clouds using an adaptation of the Iterative Closest Point (ICP) algorithm, a point set registration technique widely used in medical imaging, computer vision and graphics. There is no need for any gridding or smoothing of the LiDAR data and the method works well even with large mismatches in the density of the two point clouds. To explore the method's performance, we simulate pre- and post-event point clouds using real ("B4") LiDAR data on the southern San Andreas Fault perturbed with displacements of known magnitude. For input point clouds with ~2 points per square meter, we are able to reproduce displacements with a 50 m grid spacing and with horizontal and vertical accuracies of ~20 cm and ~4 cm. In the future, finer grids and improved precisions should be possible with higher shot densities and better survey geo-referencing. By capturing near-fault deformation in 3-D, LiDAR differencing with ICP will complement satellite-based techniques such as InSAR which map only certain components of the surface deformation and which often break down close to surface faulting or in areas of dense vegetation. It will be especially useful for mapping shallow fault slip and rupture zone deformation, helping inform paleoseismic studies and better constrain fault zone rheology. Because ICP can image rotations directly, the technique will also help resolve the detailed kinematics of distributed zones of faulting where block rotations may be common.