A Normalized Distance Test for Co-Determining the Completeness Magnitude and b-Value of Earthquake Catalogs

The spatial-temporal variations of b-value in the Gutenberg-Richter's relation are understood as stress meter and premonitory indicator of strong events. The characterization of the Gutenberg-Richter's relation is complicated by the difficulty of identifying the completeness magnitude Mc, since its inaccurate estimate may lead to biased conclusions on b-value. Therefore, many methods have been proposed to estimate b-values and their changes, but no agreement has been reached on which is the most appropriate algorithm. Here a principled statistical framework is presented for discerning and quantifying variations in the Gutenberg-Richter Law on empirical data. A new approach, called Normalized Distance (ND) test, is proposed, combining maximum-likelihood estimates with a goodness-of-fit test and bootstrap resampling. The proposed method is evaluated on synthetic data and compared with the most used approaches. The main result is that the ND test provides better estimates of Mc and b-value respect to all other methods. Finally, the same algorithms applied to the most recent Italian sequence provide contradictory results, indicating that detected b-value fluctuations may be apparent.