Rigorous slip uncertainty estimates using principal components analysis (PCA): An example from the San Andreas fault, California

Veronica B. Prush, & Michael E. Oskin

Published September 11, 2022, SCEC Contribution #12449, 2022 SCEC Annual Meeting Poster #103

Quaternary fault slip rate calculations require a measurement of landform offset due to fault activity and an age for the offset feature. Though offset landforms along fault traces are readily identifiable in tectonically active landscapes, reconstruction for Quaternary slip rates requires identification and mapping of contacts that 1) can be correlated and reconstructed unambiguously across the fault, 2) have an interpretable formation age that is as instantaneous as possible, and 3) may be dated, either directly or by age-bracketing, using appropriate materials for geochronology. A lack of community-wide standards for reporting piercing line offset uncertainty results in ambiguous constraints on slip rate determinations. This ambiguity presents challenges when assessing regional slip rate datasets, e.g., when identifying slip rate gradients along significant fault zones. If not identified, these ambiguities may propagate to modeling studies, resulting in erroneous assessments of fault hazard and regional strain distribution. We introduce a Matlab-based principal components analysis (PCA) methodology for straightforward reconstruction of offset landforms across faults. All that is required for this analysis is a digitized set of piercing lines and estimates of fault geometry (dip, strike, and surface trace) to allow for piercing line reconstruction. The algorithm determines the best-fit projection of piercing lines to the fault and reports the total offset, the estimated slip vector, and a formal estimate of uncertainty that is based solely on projection of the piercing lines to the fault. We demonstrate the technique using the Wallace Creek slip rate site along the San Andreas fault. This methodology allows for a statistically rigorous approach to estimating uncertainty that can be used at any location where a digitized map of piercing lines exists. Application of this technique to slip rate determinations will support standardization efforts for slip rates across the community.

Key Words
Slip rates, offset uncertainty, San Andreas fault

Citation
Prush, V. B., & Oskin, M. E. (2022, 09). Rigorous slip uncertainty estimates using principal components analysis (PCA): An example from the San Andreas fault, California. Poster Presentation at 2022 SCEC Annual Meeting.

Related Projects & Working Groups
Earthquake Geology