Bayesian estimation of b-value in Gutenberg-Richter relationship: a sample size reduction approach

One of the most widely used relationships for prediction of b-value is the Aki-Utsu relationship, which is based on the maximum likelihood estimating. This method has some limitations that can lead to inaccurate estimations of b-value. The need for an accurate estimate of mean earthquake magnitude for the whole seismic catalog samples is one of them. Given that the data in seismic catalogs are usually incomplete, the obtained mean value is far from the actual value, and consequently, the value of the parameter b estimated from the Aki-Utsu relationship will not be reliable enough. In this paper, a Bayesian approach is proposed for b-value estimation to reduce the minimum required sample size. To evaluate the accuracy of the proposed method, catalogs with mostly less than 200 sample sizes were simulated with Monte Carlo method. For each of the catalogs, the b-values were estimated and errors were found and compared to those of the classic methods. The results show a considerable reduction in b-value estimation error, and significant decrease in the minimum sample size required for a reliable estimation.

Automated summary

This paper proposes a Bayesian approach for b-value estimation to reduce the minimum required sample size and improve estimation accuracy. Simulation results using the Monte Carlo method show a significant reduction in b-value estimation error and minimum sample size requirement.