Abstract - The relation between maximum displacement and length provides important information about the scaling properties of faults and earthquakes. Displacement-length plots typically reveal slopes of 1-1.5 for ancient fault systems and 1 for historical earthquakes. Active normal faults in the Taupo rift, however, provide slopes of 0.5-0.7 for paleoearthquakes and faulted volcanic surfaces ranging up to ca. 60 ka in age, with slopes of 1 or greater on older surfaces. The low slopes are attributed to two principal factors: increased variability of displacement rates on short-time scales and sampling bias. Fault interaction and displacement transfer in the rift locally enhances or diminishes the growth of individual faults, a complexity in behaviour which introduces an increase in the scatter of displacement-length relationships derived from progressively younger horizons, representing shorter time scales (horizons range from 2,000 to 300,000 years in age). The bulk of our data are from a digital elevation model of displaced geomorphic surfaces with a vertical resolution of ~2 m, which leads to an under-sampling of small faults and a reduction in lengths of at least 100-200 m on younger mapped surfaces. Both of these sampling artefacts introduce a systematic under-sampling of low displacement-length faults particularly for those faults with lengths of <1 km, and therefore lead to a decrease in the slope of the displacement-length relation.
In this talk we investigate the extent to which earthquake faulting is capable of reproducing the increased scatter on displacement-length plots for data representing progressively shorter time scales. Using a stochastic model in which earthquake populations ranging from power-law (i.e. Gutenberg-Richter) to nearly characteristic (i.e. same-sized) are placed over a fault surface, we show that, contrary to general opinion, it is not possible to define earthquake scaling from conventional trench data (i.e. kinematic constraints from trenches across active faults). Our model contrasts with classic slip-dependent or time-dependent earthquake models, which are underpinned by assumptions of how slip accumulates at each point on a fault surface, and instead examines the accumulation of slip over the entire fault surface. Despite its simplicity, we show that it is capable of reproducing the variability in displacement-length relationships on different scales, and therefore of providing a rationale for the unpredictable nature of earthquake accumulation. This model combined with sampling biases is capable of explaining the derived relationships between displacement and length.
Abstract of talk given to:
Tectonic Studies Group Annual Meeting, La Roche-en-Ardenne, Belgium, January 2008.