K–M slope (KMS) is a parameter derived from Visibility Graph Analysis (Lacasa et al., 2008; Telesca et al., 2013). We verify that there is a positive between KMS and b-value from Gutenberg–Richter law. Thus, it can be used to estimate the b-value.
The most efficient script to calculate b-values using the KMS method is "KMS_Improved_DC_algorithm.m". One only needs to input the magnitude sequence to get a b-value. The script (the time complexity is O(n*logn)) uses the Divide & Conquer (DC) strategy (Lan et al., 2015).
Some other dispensable programs:
- The Matlab code to calculate KMS_0 (KMS/b ratio) under a given catalog size. --KMS2b_ratio.m
- The Matlab code to calculate the temporal evolution of the b-value by KMS and the improved KMS methods. The earthquake data in the northeastern Tibetan Plateau from 1980 to 2020 (Catalog_out.txt) is the input of the code and can be freely replaced. --Temporal_bvalue_by_KMS.m
- A relatively fast (compared with the above two scrips, the time complexity is O(n^2), where n is the catalog size) Matlab code for calculating the b-value of a given magnitude sequence based on the improved KMS method. The script is still based on the classic definition of a visibility graph. --KMS_Improved_tradditional.m
For estimating the b-value using the KMS method, please refer to:
- Linxuan Li, Gang Luo, and Mian Liu (2023). The K–M slope: a potential supplement for b-value. Seismological Research Letters 94, 1892-1899. doi: 10.1785/0220220268.
- Linxuan Li and Gang Luo (2024). Can we obtain reliable seismic b-values for real-time catalogs? Geophysical Journal International 237(3), 1554–1566. doi: 10.1093/gji/ggae124.
Other references:
- Lucas Lacasa, Bartolo Luque, Fernando Ballesteros, Jordi Luque, and Juan Carlos Nuño (2008). From time series to complex networks: The visibility graph. Proceedings of the National Academy of Sciences 105(13), 4972-4975. doi: 10.1073/pnas.0709247105.
- Luciano Telesca, Michele Lovallo, Alejandro Ramirez-Rojas, and Leticia Flores-Marquez (2013). Investigating the time dynamics of seismicity by using the visibility graph approach: Application to seismicity of Mexican subduction zone. Physica A: Statistical Mechanics and its Applications 392(23), 6571-6577. doi: 10.1016/j.physa.2013.08.078.
- Xin Lan, Hongming Mo, Shiyu Chen, Qi Liu, and Yong Deng (2015). Fast transformation from time series to visibility graphs. Chaos: An Interdisciplinary Journal of Nonlinear Science. 25:083105. doi: 10.1063/1.4927835.
Contact: Linxuan Li. lxli@caltech.edu or lucas.linxuan.li@gmail.com