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

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 À2 -10 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 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.

Scaling and paleodepth of compaction bands, Nevada and Utah

“…The values of band thickness and length used in this paper are the total band dimensions (rather than the semithicknesses and semilengths reported and used by Tembe et al [2008] and others), following the convention in displacement-length scaling studies [e.g., Watterson, 1986;Cowie and Scholz, 1992;Dawers et al, 1993;Westaway, 1994;Cartwright et al, 1995;Clark and Cox, 1996;Fossen and Hesthammer, 1997;Gross et al, 1997;Marrett, 1996;Olson, 2003;Gudmundsson, 2004;Xu et al, 2006;Schultz et al, 2006;Fossen et al, 2007]. Displacement-length scaling relations for the compaction bands were obtained from values of length L and maximum thickness T max , here associated with the maximum displacement, D max , for consistency with analogous studies of other structures [e.g., Schultz et al, 2006;Fossen et al, 2007] (see discussion in section 4.2).…”

Segmentation and Interaction of Normal Faults in Central Greece

“…The published values for D of individual datasets ranges from 0.67 to 2.07 (e.g., Cladouhos and Marrett, 1996;Xu et al, 2006). Changes of D-value are due to both measurement and natural process (e.g., Yielding et al, 1996).…”

Effects of Physical Processes and Sampling Resolution on Fault Displacement Versus Length Scaling: The Case of the Cantarell Complex Oilfield, Gulf of Mexico

“…The results of the analysis of global data also suggest that the relation between displacement and length is approximately linear (e.g. CLARK and COX 1996;XU et al 2006). Therefore, while no consensus exists, many researchers accept that n = 1.…”