On the Integrated Surface Uplift for Dip‐Slip Faults

Abstract

Interferometric Synthetic Aperture Radar observations often provide maps of vertical displacement that can be integrated to estimate an uplift volume. Relating this measure to source processes requires a model of the deformation. Bignami et al. (2019) argue that the negative uplift volume associated with the 2016 Amatrice–Norcia, central Italy, earthquake sequence requires a coseismic volume collapse of the hanging wall. Using results for dip‐slip dislocations in an elastic half‐space we show that V_(uplift)=(P/4)(1−2ν)sin(2δ) in which P is the seismic potency, ν is the Poisson’s ratio, and δ is the fault dip, consistent with an earlier result of Ward (1986). For reasonable estimates of net potency for the 2016 Amatrice–Norcia sequence, this simple formula yields uplift volume estimates close to that observed. We conclude that the data are completely consistent with elastic dislocation theory and do not require a volume collapse at depth.