The relationship between displacement and length of faults: a review

The relationship between maximum displacement ( d max) and fault length ( L) has been studied extensively, mainly in attempts to understand how fault geometry varies over different length scales. Individual data sets are sampled over limited length scales, and values of d max and L are generally poorly correlated, thus relationships are usually postulated on the basis of combining different data sets. There are problems in sampling both d max and L in a consistent manner over these different length scales, especially where different data collection methods are used (e.g., field and seismic reflection data). Failure to resolve low-displacement tips and damage zones leads to underestimates of L, and exclusion of fault drag leads to underestimates of d max. Measurement of non-central fault traces leads to underestimates of both d max and L and an underestimate of d max/ L. In this paper, we examine factors that control the measured displacement–fault length relationships of natural faults. We suggest that there may be systematic differences between the d max/ L ratios where length is measured parallel or normal to the displacement vector, and where the growth histories of individual faults vary due to the nature and number of slip events, linkage, and reactivation. Controlling factors also include material properties and fault types. It is explained how each controlling factor contributes to the d max/ L ratio and should be considered in the statistical analysis of fault data.