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

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Abstract

The power-law exponent (n) in the equation: D=cL 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 (10−2–105 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 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.

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Acknowledgements

This work was supported by projects D.01003, F30617 of the Mexican Institute of Petroleum and CONACYT-33087-T, PAPIIT IN102602-3. This manuscript benefited greatly from thorough reviews by Agust Gudmundsson and Jorn H. Kruhl. We are also thankful for helpful suggestions of improvement by N.H. Dawers and Conrad Childs.

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Authors and Affiliations

  1. Eje Central Lázaro Cárdenas, Instituto Mexicano del Petróleo, No. 152, Col. San Bartolo Atepehuacan, 07730, México, México

    S-S. Xu & L. G. Velasquillo-Martínez

  2. Centro de Geociencias, Universidad Nacional Autónoma de México, Apartado Postal 1-742, 76001, Querétaro, México

    S-S. Xu, A. F. Nieto-Samaniego & S. A. Alaniz-Álvarez

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  1. S-S. Xu
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  2. A. F. Nieto-Samaniego
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Xu, SS., Nieto-Samaniego, A.F., Alaniz-Álvarez, S.A. et al. Effect of sampling and linkage on fault length and length–displacement relationship. Int J Earth Sci (Geol Rundsch) 95, 841–853 (2006). https://doi.org/10.1007/s00531-005-0065-3

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