Deriving fault-slip histories to test for secular variation in slip, with examples from the Kunlun and Awatere faults

Although offset and age data from displaced landforms are essential for identifying earthquake clusters and thus testing whether faults slip at uniform or secularly varying rates, it is not clear how the uncertainties in such measurements should be propagated so as to yield a robust fault-slip history (i.e., record of fault displacement over time). Here we develop a Monte Carlo approach for estimating the distribution of geologically reasonable fault-slip histories that fit the offset and age data from a population of dated and displaced landforms. The model assumes that the landforms share common faulting histories, the offset and age constraints are correct, and the fault has not reversed shear sense. Analysis of the model results yields both a precise average slip rate, in the case where a linear fit is applied to the data, and a best-fit fault-slip history, in the case where the linear constraint is removed. The method can be used to test for secular variation in slip because the uncertainty on this best-fit history is quantified. By applying the method to previously published morphochronologic data from faulted late Quaternary terrace risers along the Kunlun fault in China and the Awatere fault in New Zealand, we have assessed the extent to which our modeled average slip rates match previously reported values and the data support previous interpretations of uniform slip rate. The Kunlun data set yields average slip rates of 8.7 + 3.6/−2.1 mm/yr and 5.1 + 1.6/−1.2 mm/yr (68.27% confidence), for the central and eastern reaches of the fault, respectively, both of which match previously published slip rates. Our analysis further indicates that these fault reaches have both slipped uniformly over the latest Quaternary. In contrast, analysis of data from the Saxton River site along the Awatere fault reveals a mid-Holocene deceleration in slip rate from 6.2 + 1.6/−1.4 mm/yr to 2.8 + 1.0/−0.6 mm/yr. This result contradicts previous interpretations of uniform slip along the Awatere fault. The Monte Carlo method we present here for quantifying fault-slip histories using the offset and age data from a population of faulted landforms provides an important tool for distinguishing temporally uniform from secularly varying fault slip.

Research highlights► New Monte Carlo method measures precise average slip rates and fault-slip histories. ► The Monte Carlo method can test for secular variation in slip. ► Analysis confirms uniform slip rate along central and eastern Kunlun fault, China. ► Reveals factor of 2.2 mid-Holocene deceleration in slip rate along Awatere fault, NZ.