Figure S1. Back slipping and visual assessment of channel reconstruction (A). Hillshade plot for the offset gully with fault trace (in turquoise), profile lines (in red and blue), channel trend of upstream and downstream channel segment (in yellow), and riser trend (in purple). (B) and (C) are back slipped hillshade plot and slope plot by optimal displacement amount (~100 m) for visual assessment of the reconstruction. (D) Projected topographic profiles based on channel morphology. Top shows red profile with overlay of optimal back slip (maximum goodness of fit) blue profile. (E) The GoF as a function of horizontal back slip. The maximum GoF presented the back-slip value.

Figure S2. (a) Geomorphologic interpretation in the Huangcaoba site, along the central segment of the FHF. The location of the Huangcaoba site is showed in Figure 2. (b) Terrace T1 was displaced by three north-verging faults forming three north-facing scarps in 0.8±0.1 m, 1.5±0.2 m and 1.3±0.2 m high (from north to south), respectively. (c) and (d) are the trench log and interpretation. Red-white stick in 1 m height as the scale. (e) The result of calibration of radiocarbon age to calendar years. The red dotted line represent the time of the 1609 Hongyazi earthquake. U5 was faulted, which indicates that the 1609 earthquake ruptured range front fault in the Huangbaoba site. (d) Close-up view of samples in the mudstone/ fine sand and coarse sand rhythm layer. The trench result of the Huangcaoba had been submitted for the Journal of “Seismology and Geology”.

Figure S3. Google image and photos along the eastern segment of the FHF. Red arrows point to the active fault traces. To the easternmost of the FHF, the landform is characterized by a direct contact between bedrock mountain and piedmont alluvial fans (e.g. B, C, and D). And we did not find any evidence of active faults on the alluvial fan surface and terraces of some small gullies, suggesting a less active or inactive fault. The yellow points represent the locations of field geological survey.