Effect of sampling and linkage on fault length and length–displacement relationship

• Published in: International journal of earth sciences : Geologische Rundschau Vol. 95; no. 5; pp. 841 - 853
• Main Authors: Xu, S-S., Nieto-Samaniego, A. F., Alaniz-Álvarez, S. A., Velasquillo-Martínez, L. G.
• Format: Journal Article
• Language: English
• Published: Berlin Springer Nature B.V 01-09-2006
• Subjects: Trees
• ISSN: 1437-3254; 1437-3262
• DOI: 10.1007/s00531-005-0065-3

The power-law exponent (n) in the equation: D=cL ^sup n^, with D = maximum displacement and L = fault length, would be affected by deviations of fault trace length. (1) Assuming n=1, numerical simulations on the effect of sampling and linkage on fault length and length-displacement relationship are done in this paper. The results show that: (a) uniform relative deviations, which means all faults within a dataset have the same relative deviation, do not affect the value of n; (b) deviations of the fault length due to unresolved fault tip decrease the values of n and the deviations of n increase with the increasing length deviations; (c) fault linkage and observed dimensions either increase or decrease the value of n depending on the distribution of deviations within a dataset; (d) mixed deviations of the fault lengths are either negative or positive and cause the values of n to either decrease or increase; (e) a dataset combined from two or more datasets with different values of c and orders of magnitude also cause the values of n to deviate. (2) Data including 19 datasets and spanning more than eight orders of fault length magnitudes (10^sup -2^-10^sup 5^ m) collected from the published literature indicate that the values of n range from 0.55 to 1.5, the average value being 1.0813, and the peak value of n ^sub d^ (double regression) is 1.0-1.1. Based on above results from the simulations and published data, we propose that the relationship between the maximum displacement and fault length in a single tectonic environment with uniform mechanical properties is linear, and the value of n deviated from 1 is mainly caused by the sampling and linkage effects.[PUBLICATION ABSTRACT]