Uncertainities in estimation of extrapolated annual occurrence rate of earthquakes using logical tree

Abstract

The logical tree methods are used for evaluate quantitatively relationship between frequency and magnitude, and deduce uncertainties of annual occurrence rate of earthquakes in the periods of lower magnitude earthquake. The uncertainties include deviations from the self-similarity of frequency-magnitude relations, different fitting methods, different methods obtained the annual occurrence rate, magnitude step used in fitting, start magnitude, error of magnitude and so on. Taking Xianshuihe River source zone as an example, we analyze uncertainties of occurrence rate of earthquakes M ≥ 4, which is needed in risk evaluation extrapolating from frequency-magnitude relations of stronger earthquakes. The annual occurrence rate of M ≥ 4 is usually required for seismic hazard assessment.

The sensitivity analysis and examinations indicate that, in the same frequency-magnitude relations fitting method, the most sensitive factor is annual occurrence rate, the second is magnitude step and the following is start magnitude. Effect of magnitude error is rather small.

Procedure of estimating the uncertainties is as follows: (1) Establishing a logical tree described uncertainties in frequency-magnitude relations by available data and knowledge about studied region. (2) Calculating frequency-magnitude relations for each end branches. (3) Examining sensitivities of each uncertainty factors, amending structure of logical tree and adjusting original weights. (4) Recalculating frequency-magnitude relations of end branches and complementary cumulative distribution function (CCDF) in each magnitude intervals. (5) Obtaining an annual occurrence rate of M ≥ 4 earthquakes under given fractiles.

Taking fractiles as 20% and 80%, annual occurrence rate of M ≥ 4 events in Xianshuihe seismic zone is 0.643 0. The annual occurrence rate is 0.631 8 under fractiles of 50%, which is very close to that under fractiles 20% and 80%.