“3D_Fault_Offsets,” a Matlab Code to Automatically Measure Lateral and Vertical Fault Offsets in Topographic Data: Application to San Andreas, Owens Valley, and Hope Faults

Abstract

Measuring fault offsets preserved at the ground surface is of primary importance to recover earthquake and long‐term slip distributions and understand fault mechanics. The recent explosion of high‐resolution topographic data, such as Lidar and photogrammetric digital elevation models, offers an unprecedented opportunity to measure dense collections of fault offsets. We have developed a new Matlab code, 3D_Fault_Offsets, to automate these measurements. In topographic data, 3D_Fault_Offsets mathematically identifies and represents nine of the most prominent geometric characteristics of common sublinear markers along faults (especially strike slip) in 3‐D, such as the streambed (minimum elevation), top, free face and base of channel banks or scarps (minimum Laplacian, maximum gradient, and maximum Laplacian), and ridges (maximum elevation). By calculating best fit lines through the nine point clouds on either side of the fault, the code computes the lateral and vertical offsets between the piercing points of these lines onto the fault plane, providing nine lateral and nine vertical offset measures per marker. Through a Monte Carlo approach, the code calculates the total uncertainty on each offset. It then provides tools to statistically analyze the dense collection of measures and to reconstruct the prefaulted marker geometry in the horizontal and vertical planes. We applied 3D_Fault_Offsets to remeasure previously published offsets across 88 markers on the San Andreas, Owens Valley, and Hope faults. We obtained 5,454 lateral and vertical offset measures. These automatic measures compare well to prior ones, field and remote, while their rich record provides new insights on the preservation of fault displacements in the morphology.

Reevaluation of the Late Pleistocene Slip Rate of the Haiyuan Fault Near Songshan, Gansu Province, China

“…Delineation of various terrace features and their offsets at the Xuanma Wan site by the method in Stewart et al ().…”

“…Reconstruction showing offset measurements of the base of T4/T1′ riser, (a) the lower bound of 58 m by a far‐field fault‐perpendicular line projection and (b) the upper bound of 70 m by the method in Stewart et al ().…”

“…If instead we project the base of the T4/T1′ from the far‐field, the offset may be as small as 58 m (Figures b and e). If the method in Stewart et al () is used, the base of T4/T1′ riser is offset by 68.0 ± 2.4 m (black lines in Figures b and a), which is similar to the upper bound of our back slip estimate. The difference is mainly due to the distance to over which the marker is projected to the fault, which are defined as far‐field and near‐field on account of the geometry of the terrace riser extending from the fault zone.…”

“…The difference is mainly due to the distance to over which the marker is projected to the fault, which are defined as far‐field and near‐field on account of the geometry of the terrace riser extending from the fault zone. Again, using the method by Stewart et al (), the middle and the top of T4/T1′ is offset by 70 ± 1.1 m and 70 ± 1.5 m, respectively (white lines and dashed lines in Figures b and b and c). Combining all different scenarios and reconstruction of offset by back slip, the best estimate of the offset is determined to be 68 +3 / −10 m (Figure ).…”

Characteristic slip distribution and earthquake recurrence along the eastern Altyn Tagh fault revealed by high-resolution topographic data

“…Obtaining a sufficient and precise along-fault offset data set is vital to identify long-term earthquake recurrence behavior. Furthermore, knowledge of alongfault slip distribution during a single earthquake or multiple earthquakes is important for other reasons, including a better understanding of the relationship between earthquake size and coseismic displacements (e.g., Peltzer and Tapponnier, 1988;Tapponnier et al, 2001;Manighetti et al, 2005;Li et al, 2012;Stewart et al, 2018) and fault kinematics and fault mechanics (e.g., Armijo et al, 1989;Van der Woerd et al, 1998;Gaudemer et al, 1995;Manighetti et al, 2001;Replumaz et al, 2001;Van Der Woerd et al, 2002;Hubert-Ferrari et al, 2002;Manighetti et al, 2005;Stewart et al, 2018).…”