A Caltech Library Service

Coulomb threshold rate-and-state model for fault reactivation: application to induced seismicity at Groningen

Heimisson, Elías R. and Smith, Jonathan D. and Avouac, Jean-Philippe and Bourne, Stephen J. (2022) Coulomb threshold rate-and-state model for fault reactivation: application to induced seismicity at Groningen. Geophysical Journal International, 228 (3). pp. 2061-2072. ISSN 0956-540X. doi:10.1093/gji/ggab467.

[img] PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


A number of recent modelling studies of induced seismicity have used the 1994 rate-and-state friction model of Dieterich 1994 to account for the fact that earthquake nucleation is not instantaneous. Notably, the model assumes a population of seismic sources accelerating towards instability with a distribution of initial slip speeds such that they would produce earthquakes steadily in the absence of any perturbation to the system. This assumption may not be valid in typical intraplate settings where most examples of induced seismicity occur, since these regions have low stressing rates and initially low seismic activity. The goal of this paper is twofold. First, to derive a revised Coulomb rate-and-state model, which takes into account that seismic sources can be initially far from instability. Second, to apply and test this new model, called the Threshold rate-and-state model, on the induced seismicity of the Groningen gas field in the Netherlands. Stress changes are calculated based on a model of reservoir compaction since the onset of gas production. We next compare the seismicity predicted by our threshold model and Dieterich’s model with the observations. The two models yields comparable spatial distributions of earthquakes in good agreement with the observations. We find however that the Threshold model provides a better fit to the observed time-varying seismicity rate than Dieterich’s model, and reproduces better the onset, peak and decline of the observed seismicity rate. We compute the maximum magnitude expected for each model given the Gutenberg–Richter distribution and compare to the observations. We find that the Threshold model both shows better agreement with the observed maximum magnitude and provides result consistent with lack of observed seismicity prior to 1993. We carry out analysis of the model fit using a Chi-squared reduced statistics and find that the model fit is dramatically improved by smoothing the seismicity rate. We interpret this finding as possibly suggesting an influence of source interactions, or clustering, on a long timescale of about 3–5 yr.

Item Type:Article
Related URLs:
URLURL TypeDescription Itemopen source earthquake location information
Heimisson, Elías R.0000-0001-8342-7226
Smith, Jonathan D.0000-0002-1684-1344
Avouac, Jean-Philippe0000-0002-3060-8442
Bourne, Stephen J.0000-0003-2925-8411
Additional Information:© The Author(s) 2021. Published by Oxford University Press. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( Received 2021 September 14; in original form 2021 March 17. ERH formulated the main research questions in consultation with J-PA and SJB and ERH derived the threshold model, and carried out data and model comparison. ERH and JDS developed code and methods for data and model comparison and visualization. J-PA and SJB helped interpret results. ERH wrote the manuscript with input from all authors. ERH acknowledges support from the Geophysics Option Postdoctoral Fellowship at Caltech. JS was supported for this project by the NSF centre of Geomechanics and Mitigation of Geohazards (GMG). We gratefully acknowledge data and support from Nederlandse Aardoli Maatschappij (Jan Van Elk, Gini Ketellar and Dirk Doornhof), Shell Global Solutions (Stijn Bierman, Steve Oates, Rick Wentinck, Xander Campman, Alexander Droujinine and Chris Harris) and Koninkljjk Nederlands Meteorologisch Instituut for the open source earthquake location information. ( We thank the IUCRC program of the National Science Foundation for support though grant no. 1822214 to GMG. DATA AVAILABILITY. Data used in this paper, from which the stress model is derived, have been previously published in Smith et al. (2019). Seismic data and catalogues are provided by Koninkljjk Nederlands Meteorologisch Instituut (
Group:Center for Geomechanics and Mitigation of Geohazards (GMG), Division of Geological and Planetary Sciences, Seismological Laboratory
Funding AgencyGrant Number
Caltech Division of Geological and Planetary SciencesUNSPECIFIED
Geomechanics and Mitigation of Geohazards CenterUNSPECIFIED
Subject Keywords:Europe; Instability analysis; Earthquake hazards; Earthquake interaction, forecasting, and prediction; Statistical seismology; Dynamics and mechanics of faulting
Issue or Number:3
Record Number:CaltechAUTHORS:20220414-27838000
Persistent URL:
Official Citation:Elías R Heimisson, Jonathan D Smith, Jean-Philippe Avouac, Stephen J Bourne, Coulomb threshold rate-and-state model for fault reactivation: application to induced seismicity at Groningen, Geophysical Journal International, Volume 228, Issue 3, March 2022, Pages 2061–2072,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:114327
Deposited By: George Porter
Deposited On:15 Apr 2022 14:44
Last Modified:15 Nov 2022 15:15

Repository Staff Only: item control page