Inherent Asymmetry in Reporting Geologic Slip Rates

Nathan A. Toke

Published September 11, 2022, SCEC Contribution #11967, 2022 SCEC Annual Meeting Poster #083 (PDF)

Slip rates are fundamental data for understanding individual faults and fault system interactions. Slip rates are difficult to constrain because they require both accurate geometrical correlations of offset ‘piercing point’ features (e.g., landforms, strata, archeological structures) and the presence of datable material to estimate the age of the offset feature. Offset and age data contain multiple forms of uncertainty that must be accounted for when estimating a slip rate. A robust approach is to infer a probability density function (PDF) to describe the uncertainty in distance and time. When convolving two symmetrical offset and age PDFs, the resulting slip rate PDF will always be asymmetrical with the peak probability skewed toward the lower side of the range. The skew depends primarily on the percent of uncertainty in the age of the offset. I argue that slip rates with greater than 5 percent skew in their PDF should not be reported with symmetrical error bounds. To achieve this level of symmetry, less than ~15 percent uncertainty in the age of the offset feature must be achieved (e.g., 1000 +/- 150 years or 20,000 +/- 3000 years). Thus, the age of late Holocene landforms must be very well constrained as compared to those from the late Pleistocene. In either case, age uncertainty increases with the age of landforms studied. Rarely, archeological sites or historical markers yield precise piercing point ages. More commonly, calibrated radiocarbon ages for individual samples span 100–400-year intervals (at the 95% confidence interval) and thus well-constrained piercing point ages span 200–800 years. Optically Stimulated Luminescence and Cosmogenic Radionuclide sample ages tend to yield uncertainties in the range of 1,000-10,000 years. So, constraining a piercing point with less than a 2,000-year age uncertainty is not likely using these methods. Thus, we should be careful about adequately constraining the age of landforms in slip rate studies and due to the limitations of our methods nearly all slip rate uncertainties should be reported with asymmetrical uncertainty bounds.

Key Words
slip rate, reporting, uncertainty, asymmetry

Citation
Toke, N. A. (2022, 09). Inherent Asymmetry in Reporting Geologic Slip Rates. Poster Presentation at 2022 SCEC Annual Meeting.

Related Projects & Working Groups
Earthquake Geology