Proceedings of the 12th International INQUA meeting on paleoseismology, active tectonic and archaeoseismology

The 3DEC equations assume that the longer the target fracture is, the larger displacement will occur on it. This assumption comes from the observation in structural geology, that cumulative displacement on faults is directly proportional to fault length. Distance from the PF to the fracture is deemed irrelevant in 3DEC. For historical surface ruptures, the situation is reversed. We are interested only in displacement-per- event on the PF and DF, not cumulative displacement. For all DFs and most PFs, we don’t even know the cumulative displacement. But we believe that the major control on DF displacement is distance to the PF, not length of the DF. To my knowledge, no paleoseismologist has regressed DF displacement against DF length using the SURE or FDHI databases, although it could easily be done. Another complication for historic reverse faults, is that Nurminen 2020 equations predict median (50%-ile) displacements on DFs, whereas Moss 2022 equations predict 95%-ile displacements. Moss’s equation for DF displacements as a fraction of PF maximum displacements (d/Dmax), yield unrealistically large DF displacements, much larger than Nurminen’s regression equations based on magnitude and PF-DF distance. Finally, Nurminen’s equation for DF displacement includes three independent variables; earthquake magnitude, distance from PF to DF, and displacement on the PF at a point closest to the DF. ln(Y) = a + b 1 (ln(s)) + c1(ln(D N )) + d 1 (m) where: Y, displacement on DF; s, distance from PF to DF; D N , displacement on PF closest to DF; and m, earthquake magnitude. The empirical coefficients a, b1, c1, and d1 vary depending on whether the DF is on the PF footwall or hanging wall. In both FW and HW, the largest coefficient (most important control) is d1, earthquake magnitude. On the FW coefficient b1 (distance) is the second-strongest control, whereas on theHWit is a very weak control. Fälth et al. (2015), Hökmark et al. (2019) and others had predicted 3DEC off-fault displacements in several scenario earthquakes deemed possible at Forsmark. For the same scenario earthquakes, I calculated empirical DF displacements from equations of Nurminen (2020) and Moss (2022) [for reverse events] and Petersen at al. (2011) for strike-slip events. In every case, empirical estimates were many times larger (5 to 20 times) than 3DEC estimates (see McCalpin, 2024 for details). Summary of 3DEC displacements versus Empirical Displacements For the case of local area, low-angle faults (like ZFMA2, M5.6), empirical displacement values are all larger than the Falth et al. (2015) values (Fig. 2). Falth’s median displacement value at a distance of 200 m was 5 mm. In six scenarios using Nurminen’s 2020 equation and Davg values as DN, median (50%-ile) displacements at 200 m distance ranged from 29 mm to 54 mm, or 580% to 1080% of Falth’s values. At higher %-iles our displacement values grew even larger than Falth’s. We also ran two simulations (same magnitude and distances as above) with the new Moss et al. (2022) equation for distributed displacements during reverse ruptures, which predicts d/Dmax at various distances. Compared