Estimation of average to maximum displacement ratio by using fault displacement-distance profiles

• The ratio between average and maximum displacement for different types of faults is calculated.
• The values of ρ increases when continuous deformation is included in the total displacement.
• The value of ρ varies over time and usually decreases at the immediate linkage stage.
• The most frequent values of ρ are between 0.6 and 0.7.
• The analysis of 205 profiles indicates that most profile shapes are between the triangular and mesa types.

Fault displacement is an important factor in the study of discontinuous deformation. Considering that the values of average displacement (Dav) and maximum displacement (Dmx) are linearly related by Dav = ρDmx, we calculate the values of ρ estimated from 205 published displacement-distance profiles. The following results are obtained: (a) the value of ρ is largest for the mesa-type or flat-topped (M-type) profiles; (b) the value of ρ increases when ductile (continuous) deformation is added to the displacement profile; (c) generally, the value of ρ for a linked fault array is smaller than that for segmented faults in the array, i.e., the value of ρ changes with fault evolution, and at the stage where linkage occurs, the value of ρ becomes smaller; (d) the simulation results indicate that for an ellipse function, the value of ρ varies from 0.667 to 0.785. For trapezoid (M-type) profiles, the value of ρ is from 0.5 to 1, depending on the ratio of the upper base to the lower base. For best fit polynomial curves, the value of ρ can be less than 0.5; (e) the values of ρ more frequently observed in the published profiles are between 0.6 and 0.7; the average value is 0.6023 and the standard deviation 0.1123. These data indicate that the displacement-distance profiles are hybrids from the triangular profile to the elliptical or mesa profile. The average value (0.6023) would be useful to determine the average displacement in cases where not enough displacement data can be obtained. Finally, the value change of ρ with fault evolution can be used to quantitatively evaluate the level of interaction between segmented faults.