Quantification of true displacement using apparent displacement along an arbitrary line on a fault plane

Abstract

This paper introduces some approaches to determine the true displacement ( S t) using an apparent displacement ( S m) measured from an arbitrary line on a fault plane. The considered parameters are the pitch of slip lineation ( γ), the pitch of a cutoff ( β), the apparent displacement along the observation line ( S m), and the pitch of the observation line on the fault plane ( φ). We analyzed the following cases. First, if the apparent displacement is taken as the true displacement, the degree of overestimation or underestimation of the true displacement can be calculated. The displacement cannot be obtained along the null line because the pitch of the observation line ( φ) is equal to the pitch of the cutoff of the marker ( β). Second, the total true displacement can be obtained not only along the slip direction but also along another particular line depending on the values of γ and β. Third, if the apparent displacements from two non-parallel markers can be measured, the slip direction can be estimated. We apply the methods to calculate the extensions due to the normal faults of San Miguelito in Mesa Central, Mexico. The results indicate that the largest fault strain reaches ca. 0.50 and the smallest fault strain is ca. 0.08. Also, the isolated faults show more regular strain profiles along the fault strikes than the faults with overlapping or intersecting geometries.