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Rupture length and paleo-magnitude estimates from point measurements of displacement - a model-based approach

Glenn P. Biasi, Ray J. Weldon, & Katherine M. Scharer

Published 2011, SCEC Contribution #944

We present a new method that allows paleomagnitude and paleorupture length to be estimated quantitatively given a measurement of rupture displacement at a point. Variability in rupture displacement along a rupture profile means that a typical paleoseismic displacement measurement constrains the average displacement only to within a factor of 3 or so. We use previously published results summarizing rupture variability, then apply a graphical method of identifying the relative likelihoods among a suite magnitudes, one of which must have caused the measured displacement. Results are developed for displacement observations from 1-6 meters using a magnitude range from 6.0 < M < 8.0. Probabilities of rupture length given displacement are developed at the same time. Smaller earthquakes can cause ground rupture, but we show that they would not influence likelihoods for 1 meter and larger displacements. Smaller displacements than 1 meter are also of potential interest, but will require extension of the method to include the declining probability that smaller magnitudes produce ground rupture. We then consider application of the length distributions to correlation of rupture evidence between sites. Dating evidence alone, even when excellent, does not provide a physical basis to relate rupture at one site to rupture at another. Ruptures, however, have an expected length, and thus do provide a physical basis for correlation. We present probability of correlation curves given rupture length and which may be combined with probabilities of rupture length to give a probability of correlation given a point displacement. Applications for quantitative probabilities of magnitude and length given a paleoseismic displacement measurement include probabilistic seismic hazard analysis, where probabilities of magnitude and length must be assigned to branches in the analysis.

Biasi, G. P., Weldon, R. J., & Scharer, K. M. (2011). Rupture length and paleo-magnitude estimates from point measurements of displacement - a model-based approach. Geological Society of America Special Paper, 479, 195-204.