The K-M Slope: A Potential Supplement for b-Value

The b-value of the Gutenberg-Richter law describes the relationship of size and frequency distribution of earthquakes. Its variations may be related to stress state, hence has been used for short-term earthquake forecasting. However, estimation of b-value faces many uncertainties, making it difficult to interpret b-value changes as tectonic signals or statistical artifacts. Some recent studies have suggested that the b-values of some seismic catalogs are proportional to the K-M slope (KMS) obtained from the visibility graph analysis. If confirmed, the KMS may provide additional constraints to the b-value and its variations. In this study, we used synthetic seismic catalogs that obey various probability distributions to demonstrate that the proportional relationship between KMS and b-value is universal and stable, and that the KMS/b ratio is dependent on the catalog size. We found that the KMS estimation can perform better than the commonly used b-value estimation methods, especially when the catalogs are incomplete or have variations in the magnitude-frequency relations. We proposed an improved KMS method to ensure that the KMS value provides pure magnitude information and is not affected by the occurrence time or orders of the events. We used the KMS to estimate the spatiotemporal variations of b-value in the northeastern Tibetan plateau; the results are consistent with those derived from traditional b-value estimation methods. We suggest that the KMS can be used as a verification of or a supplement to the b-value.