TheK−MSlope: A Potential Supplement forb-Value

Abstract

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.

A test on methods for Mc estimation and spatial-temporal distribution of b-value in the eastern Tibetan Plateau

“…However, its computation is susceptible to various factors, casting doubt on the accuracy of the b-value (especially when seismic catalogs are incomplete or the network for monitor earthquakes is severely disturbed). Alternative and validation methods for the b-value have been proposed (Guttorp, 1987;Parsons, 2007;Telesca et al, 2013;Lombardi, 2021;van der Elst, 2021;Li et al, 2023), such as the maximum likelihood method (Aki, 1965), the 10.3389/feart.2024.1335938 least square method (Guttorp, 1987), K-S slop (Telesca et al, 2013;Li et al, 2023), and the B-Positive method (van der Elst, 2021). In most cases, the maximum likelihood method derived by Aki (1965) is still the preferred method:…”

“…The K-M slope (KMS) obtained from the visibility graph analysis measures the topological connectivity of an event (with magnitude M) to other events (Telesca et al, 2013). The VGA method analyzes the topology of a time series (Li et al, 2023):…”

“…In addition, although the definition of the b-value is clear and the calculation method is straightforward, it can be significantly biased due to various factors, leading to the invalidity of the b-value. Currently, there are methods for calculating the b-value (Aki, 1965;Pacheco et al, 1992;Sandri and Marzocchi, 2007;Telesca et al, 2013;van der Elst, 2021;Li et al, 2023), such as maximum likelihood estimation (MLE) (Aki, 1965), linear least squares regression (LSR) (Pacheco et al, 1992;Sandri and Marzocchi, 2007), B-Positive (van der Elst, 2021), and K-M slope (KMS) (Telesca et al, 2013;Li et al, 2023). These methods significantly enhance the accuracy of the b-value through supplementation and validation.…”