Spatial Temporal Distribution of b-value (STDB)

A versatile b-value calculator. Used for calculating time and space variations of b-values, it includes eight Mc calculation methods and four b-value calculation methods. Additional functions include synthetic seismic catalogs for seismic events, and more.

STDB is an extremely simple b-value calculator that includes most algorithms on the market, and the grouping between different algorithms is flexible and efficient. Just import a seismic catalog.

Earthquake Catalog Format (the following numbers represent column numbers):

1.Year 2.Month 3.Day 4.Hour 5.Minute 6.Latitude 7.Longitude 8.Magnitude

When estimating the b-value using the STDB calculator, refer to:

Weicheng Gong, Huayuan Cheng, Yajing Gao, Qing Li, and Yunqiang Sun (2023). Spatial-Temporal Distribution of b-value in the Eastern Tibetan Plateau. (in revision)

STDB calculator's main features:

1. Calculate the b-value for the entire catalog
2. Compute the b-value as a function of time
3. Determine the b-value as a function of space
4. Generate a synthetic earthquake catalog (additional feature)
5. Perform iterative sampling on the catalog (additional feature)

STDB calculator involves the following Mc calculation methods:

1. The Maximum Curvature technique (MAXC) (Wiemer & Wyss, 2000)
2. The goodness-of-fit test (GFT) (Wiemer & Wyss, 2000)
3. The Mc by b-value stability (MBS) (Cao & Gao, 2002)
4. The improved Mc by b-value stability (MBS-WW) (Woessner & Wiemer, 2005)
5. The entire-magnitude-range (EMR) (Woessner & Wiemer, 2005)
6. The median-based analysis of the segment slope (MBASS) (Amorese, 2007)
7. The harmonic mean of the magnitudes (MAH) (Godano, 2017)
8. The Normalized Distance test (NDT) (Lombardi, 2021)

STDB calculator involves the following b-value calculation methods:

1. linear least squares regression (LSR) (Pacheco et al., 1992)
2. maximum likelihood estimation (MLE) (Aki, 1965)
3. B-Positive (van der Elst, 2021)
4. K-M slope (KMS) (Li et al., 2023; Telesca et al., 2013)

Functions involved in the STDB calculator's synthetic seismic catalog:

1. OK1993 model Ogata & Katsura (1993)
2. WW2005 model Woessner & Wiemer (2005)

Other references

Aki, K. (1965). Maximum likelihood estimate of b in the formula logN=a-bM and its confidence limits. Bulletin of the Earthquake Research Institute, University of Tokyo, 43, 237-239.

Amorese, D. (2007). Applying a change-point detection method on frequency-magnitude distributions. Bulletin of the Seismological Society of America, 97(5), 1742-1749. https://doi.org/10.1785/0120060181

Cao, A., & Gao, S. S. (2002). Temporal variation of seismic b-values beneath northeastern Japan island arc. Geophysical Research Letters, 29(9), 1334.https://doi.org/10.1029/2001GL013775

Godano, C. (2017). A new method for the estimation of the completeness magnitude. Physics of the Earth and Planetary Interiors, 263, 7-11. https://doi.org/10.1016/j.pepi.2016.12.003

Gulia, L., & Wiemer, S. (2019). Real-time discrimination of earthquake foreshocks and aftershocks. Nature, 574(7777), 193-199. https://doi.org/10.1038/s41586-019-1606-4

Li, L., Luo, G., & Liu, M. (2023). The K-M Slope: A Potential Supplement for b-Value. Seismological Research Letters. https://doi.org/10.1785/0220220268

Lombardi, A. M. (2021). A Normalized Distance Test for Co‐Determining the Completeness Magnitude and b‐Value of Earthquake Catalogs. Journal of Geophysical Research: Solid Earth, 126(3). https://doi.org/10.1029/2020jb021242

Ogata, Y., & Katsura, K. (1993). Analysis of temporal and spatial heterogeneity of magnitude frequency distribution inferred from earthquake catalogues. Geophysical Journal International, 113(3), 727-738. https://doi.org/10.1111/j.1365-246X.1993.tb04663.x

Pacheco, J. F., Scholz, C. H., & Sykes, L. R. (1992). Changes in frequency-size relationship from small to large earthquakes. Nature, 355(6355), 71-73. https://doi.org/10.1038/355071a0

Telesca, L., Lovallo, M., Ramirez-Rojas, A., & Flores-Marquez, L. (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(24), 6571-6577. https://doi.org/10.1016/j.physa.2013.08.078

van der Elst, N. J. (2021). B‐Positive: A Robust Estimator of Aftershock Magnitude Distribution in Transiently Incomplete Catalogs. Journal of Geophysical Research: Solid Earth, 126(2). https://doi.org/10.1029/2020jb021027

Wiemer, S., & Wyss, M. (2000). Minimum magnitude of completeness in earthquake catalogs: Examples from Alaska, the western United States, and Japan. Bulletin of the Seismological Society of America, 90(4), 859-869. https://doi.org/10.1785/0119990114

Woessner, J., & Wiemer, S. (2005). Assessing the quality of earthquake catalogues: Estimating the magnitude of completeness and its uncertainty. Bulletin of the Seismological Society of America, 95(2), 684-698. https://doi.org/10.1785/0120040007