We present a new three-dimensional (3D) approach to the analysis of fault scarps using high-resolution elevation models. Advances in topographic measurement techniques [e.g., lidar (light detection and ranging) and photogrammetric techniques] have allowed extensive measurement of single earthquake and cumulative scarps to draw conclusions about along-strike slip variation and fault slip history. The resulting slip distributions are almost always variable and noisy, but the cause is often unclear. We first present the results of sensitivity analysis to demonstrate significant apparent noise due to varying terrain and fault and measurement geometry (topographic slope attitude, fault dip and slip obliquity). We show, with a case study on the Hoshab fault, Pakistan, that oblique slip can have a significant effect on the measured apparent slip.
Individual planar geomorphic markers only constrain one component of the full 3D slip vector. We use the variation in apparent offset with marker geometry to constrain the slip vector in 3D. Combining multiple offset measurements along strike, we show that determining the slip vector is reduced to a simple linear formulation. We test our method using a terrestrial lidar data set from the ruptures on the Borrego fault from the 2010 El Mayor–Cucapah earthquake (Baja California, Mexico). Combining 22 observations, we estimate a throw of 1.56 ± 0.02 m and a lateral slip of 1.9 ± 0.3 m. The vertical slip estimate agrees well with previous studies, but the lateral slip is significantly smaller. In regions of steep varied topography or with oblique slip, our method will give enhanced slip resolution while standard methods will give biased estimates.