Interactive Retro-Deformation of Terrain for Reconstructing 3D Fault Displacements

Planetary topography is the result of complex interactions between geological processes, of which faulting is a prominent component. Surface-rupturing earthquakes cut and move landforms which develop across active faults, producing characteristic surface displacements across the fault. Geometric models of faults and their associated surface displacements are commonly applied to reconstruct these offsets to enable interpretation of the observed topography. However, current 2D techniques are limited in their capability to convey both the three-dimensional kinematics of faulting and the incremental sequence of events required by a given reconstruction. Here we present a real-time system for interactive retro-deformation of faulted topography to enable reconstruction of fault displacement within a high-resolution (sub 1m/pixel) 3D terrain visualization. We employ geometry shaders on the GPU to intersect the surface mesh with fault-segments interactively specified by the user and transform the resulting surface blocks in realtime according to a kinematic model of fault motion. Our method facilitates a human-in-the-loop approach to reconstruction of fault displacements by providing instant visual feedback while exploring the parameter space. Thus, scientists can evaluate the validity of traditional point-to-point reconstructions by visually examining a smooth interpolation of the displacement in 3D. We show the efficacy of our approach by using it to reconstruct segments of the San Andreas fault, California as well as a graben structure in the Noctis Labyrinthus region on Mars.