Assessing earthquake rates and b-value given spatiotemporal variation in catalog completeness: Application to Atlantic Canada


  • Alexandre Plourde Geological Survey of Canada (Atlantic)



Spatiotemporal variations in the magnitude of completeness Mc make it challenging to confidently assess seismic hazard or even to simply compare earthquake rates between regions. In this study, we introduce new techniques to correct for heterogeneous Mc in a treatment of the eastern and Atlantic Canada earthquake catalog (1985--2022). We first introduce new methodology to predict Mc(x,t) based on the distribution of seismometers. Second, we introduce a modified maximum-likelihood estimator (MLE) for b (the b-value) that accounts for spatiotemporal Mc variation, allowing the inclusion of more earthquakes. Third, we compute the ratio of detected/predicted M>1 earthquakes as a function of Mc and apply it to create a calibrated M>1 event-rate map. The resulting map has advantages over a moment-rate map, which is effectively sensitive only to the very largest earthquakes in the dataset. The new MLE results in a modestly more precise b when applied to the Charlevoix Seismic Zone, and a substantial increase in precision when applied to the full Atlantic Canada region. It may prove useful in future hazard assessments, particularly of regions with highly heterogeneous Mc and relatively sparse catalogs.


Adams, J., & Basham, P. (1989). The seismicity and seismotectonics of Canada east of the Cordillera. Geoscience Canada, 16(1), 3–16.

Aki, K. (1965). Maximum likelihood estimate of b in the formula log N = a-bM and its confidence limits. Bull. Earthq. Res. Inst., Tokyo Univ., 43, 237–239.

Basham, P., & Adams, J. (1983). Earthquakes on the continental margin of eastern Canada: Need future large events be confined to the locations of large historical events. U.S. Geological Survey Open File Report, 83-843, 456–467.

Bent, A. (1994). The 1989 (MS 6.3) Ungava, Quebec, earthquake: a complex intraplate event. Bulletin of the Seismological Society of America, 84(4), 1075–1088.

Bent, A. (1995). A complex double-couple source mechanism for the Ms 7.2 1929 Grand Banks earthquake. Bulletin of the Seismological Society of America, 85(4), 1003–1020.

Bent, A. (2011). Moment magnitude (Mw) conversion relations for use in hazard assessment in eastern Canada. Seismological Research Letters, 82(6), 984–990.

Bent, A., & Hasegawa, H. (1992). Earthquakes along the Northwestern Boundary of the Labrador Sea. Seismological Research Letters, 63(4), 587–602.

Bent, A L and Voss, P (2022). Seismicity in the Labrador-Baffin Seaway and surrounding onshore regions. Geological synthesis of Baffin Island (Nunavut) and the Labrador-Baffin Seaway, Geological Survey of Canada, Bulletin 608, 379-387.

Yuxiang Cheng, Wenna Liu, Tianfu Xu, Yanjun Zhang, Xinwen Zhang, Yunyan Xing, Bo Feng, & Yi Xia (2023). Seismicity induced by geological CO_2 storage: A review. Earth-Science Reviews, 239, 104369.

Gerstenberger, M., Marzocchi, W., Allen, T., Pagani, M., Adams, J., Danciu, L., Field, E., Fujiwara, H., Luco, N., Ma, K.F., Meletti, C., & Petersen, M. (2020). Probabilistic seismic hazard analysis at regional and national scales: State of the art and future challenges. Reviews of Geophysics, 58(2), e2019RG000653.

Gutenberg, B., & Richter, C. (1944). Frequency of earthquakes in California*. Bulletin of the Seismological Society of America, 34(4), 185–188.

Haddon, R. (1995). Modeling of source rupture characteristics for the Saguenay earthquake of November 1988. Bulletin of the Seismological Society of America, 85(2), 525–551.

Halchuk, S., Allen, T., Rogers, G., & Adams, J. (2015). Seismic Hazard Earthquake Epicentre File (SHEEF2010) used in the Fifth Generation Seismic Hazard Maps of Canada. Geological Survey of Canada, Open File, 7724.

M Ishimoto, & K Iida (1939). Observations of earthquakes registered with the microseismograph constructed recently. Bulletin of the Earthquake Research Institute, 17, 443–478.

Kijko, A., & Smit, A. (2012). Extension of the Aki‐Utsu b‐Value Estimator for Incomplete Catalogs. Bulletin of the Seismological Society of America, 102(3), 1283–1287.

Kolaj, M., Adams, J., & Halchuk, S. (2020). Seismic hazard in southeastern Canada: uncertainty and controls on seismic hazard in a region of low-to-moderate seismicity. In 17th World Conference on Earthquake Engineering.

Lamontagne, M., Beauchemin, M., & Toutin, T. (2003). Earthquakes in the Charlevoix seismic zone, Quebec. International Journal on Hydropower & Dams, 10(2), 98–99.

Lamontagne, M., Keating, P., & Perreault, S. (2003). Seismotectonic characteristics of the Lower St. Lawrence Seismic Zone, Quebec: insights from geology, magnetics, gravity, and seismics. Canadian Journal of Earth Sciences, 40(2), 317-336.

Mahani, A., Kao, H., Walker, D., Johnson, J., & Salas, C. (2016). Performance evaluation of the regional seismograph network in northeast British Columbia, Canada, for monitoring of induced seismicity. Seismological Research Letters, 87(3), 648–660.

Mignan, A., Werner, M., Wiemer, S., Chen, C.C., & Wu, Y.M. (2011). Bayesian estimation of the spatially varying completeness magnitude of earthquake catalogs. Bulletin of the Seismological Society of America, 101(3), 1371–1385.

Mignan, A. (2012). Functional shape of the earthquake frequency-magnitude distribution and completeness magnitude. Journal of Geophysical Research: Solid Earth, 117(B8), B009347.

Mizrahi, L., Nandan, S., & Wiemer, S. (2021). The effect of declustering on the size distribution of mainshocks. Seismological Research Letters, 92(4), 2333–2342.

Munro, P., Halliday, R., Shannon, W., & Shieman, D. (1988). Canadian Seismograph Operations –- 1986. Geological Survey of Canada, Paper 88-16.

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.

Yosihiko Ogata, & Ken'ichiro Yamashina (1986). Unbiased estimate for b-value of magnitude frequency. Journal of Physics of the Earth, 34(2), 187-194.

Page, R. (1968). Aftershocks and microaftershocks of the great Alaska earthquake of 1964. Bulletin of the Seismological Society of America, 58(3), 1131–1168.

Plourde, A., & Nedimovic, M. (2021). Earthquake depths, focal mechanisms, and stress in the Lower St. Lawrence Seismic Zone. Seismological Research Letters, 92(4), 2562–2572.

Schorlemmer, D., & Woessner, J. (2008). Probability of detecting an earthquake. Bulletin of the Seismological Society of America, 98(5), 2103–2117.

Schultz, R., Skoumal, R., Brudzinski, M., Eaton, D., Baptie, B., & Ellsworth, W. (2020). Hydraulic fracturing-induced seismicity. Reviews of Geophysics, 58(3), e2019RG000695.

Si, Z., & Jiang, C. (2019). Research on parameter calculation for the Ogata-Katsura 1993 model in terms of the frequency-magnitude distribution based on a data-driven approach. Seismological Research Letters, 90(3), 1318–1329.

Stallone, A., & Falcone, G. (2021). Missing earthquake data reconstruction in the space-time-magnitude domain. Earth and Space Science, 8(8), e2020EA001481.

Taroni, M. (2021). Back to the future: old methods for new estimation and test of the Gutenberg-Richter b-value for catalogues with variable completeness. Geophysical Journal International, 224(1), 337–339.

Toda, S., & Stein, R. (2018). Why aftershock duration matters for probabilistic seismic hazard assessment. Bulletin of the Seismological Society of America, 108(3A), 1414–1426.

Utsu, T. (1965). A method for determining the value of" b" in a formula log n= a-bM showing the magnitude-frequency relation for earthquakes. Geophys. Bull. Hokkaido Univ., 13, 99–103.

Tokuji Utsu (1966). A statistical significance test of the difference in b-value between two earthquake groups. Journal of Physics of the Earth, 14(2), 37-40.

Elst, N. (2021). B-Positive: A robust estimator of aftershock magnitude distribution in transiently incomplete catalogs. Journal of Geophysical Research: Solid Earth, 126(2), e2020JB021027.

Weichert, D. (1980). Estimation of the earthquake recurrence parameters for unequal observation periods for different magnitudes. Bulletin of the Seismological Society of America, 70(4), 1337–1346.

Wetmiller, R., Adams, J., Anglin, F., Hasegawa, H., & Stevens, A. (1984). Aftershock sequences of the 1982 Miramichi, New Brunswick, earthquakes. Bulletin of the Seismological Society of America, 74(2), 621–653.

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.

Yu, H., Liu, Y., Harrington, R., & Lamontagne, M. (2016). Seismicity along St. Lawrence paleorift faults overprinted by a meteorite impact structure in Charlevoix, Québec, eastern Canada. Bulletin of the Seismological Society of America, 106(6), 2663–2673.



How to Cite

Plourde, A. (2023). Assessing earthquake rates and b-value given spatiotemporal variation in catalog completeness: Application to Atlantic Canada. Seismica, 2(2).