THINKING INSIDE THE BOX: MODELLING SLIP RATE VARIABILITY USING GEOLOGIC CONSTRAINTS

Geologic slip rates are typically constrained by a single offset feature with an associated age averaged over multiple earthquake cycles. As such, geologic slip rates represent cumulative fault behavior, and only approximate the true behavior of faults over multiple seismic cycles. Given that recent studies suggest incremental (i.e., time-transgressive) slip rates collected at a single site can vary by ~200-500%+, the event-by-event slip and inter-event time curves, which form a stair-step pattern (i.e., “earthquake path”), is critical for understanding fault behavior from both a fault evolution and tectonics standpoint, as well as from a hazard modelling perspective. Using a range of mean single event displacements and a range of mean inter-event times, coupled with a range of coefficients of variation (COVs) about those means, we derive these earthquake paths through displacement-time space. We generate many stair-step patterns through displacement-time space with variable input data and assess their fit through both synthetic and geologically observed data. We then sample only these paths that intersect the known displacement-time measurements, and then take the density of these paths that are permissible given data constraints. This density measurement therefore represents the suite of possible earthquake paths that describe the data, and provides an estimation of earthquake paths that satisfy the data constraints. The uncertainty associated with this density measurement is a physically rooted, geologically informed estimate. As such, this modelling approach inherently addresses natural variability of the system which is expressed as variability in earthquake magnitude and frequency through time. Currently, that variability is not explicitly addressed by slip rate error estimates, as these typically only rely on uncertainties associated with the offset and age measurements. This method can be applied to datasets that contain multiple dated offset features where slip rate is non-constant through time, as well as to sites with a single dated offset. Consistent error calculations for slip rates such as the method outlined here provide standardization for use in hazard models (i.e., USGS National Seismic Hazard Model).