The Canterbury sequence in the context of global earthquake statistics

Abstract

The Canterbury earthquake sequence is an on-going earthquake sequence, which started with the M7.1 Darfield earthquake on 4 September 2010. The three M≥6.0 aftershocks included the devastating M6.3 Christchurch earthquake on 22 February 2011, which resulted in 185 deaths and extensive damage. As a consequence of the earthquake sequence the New Zealand National Seismic Hazard model was expected to grossly underestimate the level of ground shaking for the Canterbury region for the coming decades due to on-going aftershock activity and the possibility of other triggered moderate to large earthquakes. Therefore a new time varying earthquake hazard model, the EE model, was developed.

Our project set out to investigate the Canterbury sequence in the context of global earthquake statistics. We had two main objectives:

1. Use aftershock parameters derived from global earthquake catalogues to provide bounds for earthquake rates in the Canterbury region for the coming years and decades.
2. Investigate how unusual late and large aftershocks are as observed in the Canterbury sequence.

During our project we realised that many earthquakes, including 14 in the magnitude band 5‑5.9 in the first 24h following Darfield, had not been reported in the initial GeoNet catalogue. We slightly changed focus from deriving aftershock parameters from the global catalogue, to modelling aftershocks in the Canterbury sequence to provide bounds for earthquake rates in the Canterbury region for the coming years and decades. The probability for one or more M≥ 6.0 earthquakes in the 50 years starting in September 2012 ranges from 50% to 93% depending on the model. We identified further work required to understand the time frame for which aftershock models can be usefully applied. We also identified further work required to better understand what effect the deficiencies of the real-time earthquake data have on the real-time forecasting models.

To investigate how unusual late and large aftershocks are (such as those observed in the Canterbury sequence) we used two global earthquake catalogues. For each catalogue we identified magnitude thresholds and time periods for which the data can be expected to be complete. We then searched for earthquake sequences using different search criteria. Depending on the search criteria, between 6 and 13 % of main shocks in the more complete catalogue had 3 or more aftershocks within 1.1 magnitude units as observed in the Canterbury sequence. Of these large earthquakes, around 20% had a larger relative distance than Christchurch to Darfield, and around 15% occurred later than 171 days. This confirmed that the M≥6.0 aftershocks in the Canterbury sequence occurred relatively far away from the main shock in space and time but this is not too unusual in global aftershock statistics.

We also searched for large aftershocks within 1.1 magnitude units of the main shock that occurred at least as late and far away as the Christchurch earthquake relative to the Darfield earthquake. In our most complete dataset and with the preferred search criteria, 2% of large earthquake fulfil these criteria. In the other dataset there were another couple of examples. This confirms that while the Christchurch earthquake occurred with a time delay of 171 days and 42 km from the Darfield epicentre, this is not too unusual in global earthquake occurrences.

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Technical Abstract

The Canterbury earthquake sequence has been a long-lived complex earthquake sequence, which started with the M7.1 Darfield earthquake on 4 September 2010. The three M≥6.0 aftershocks included the devastating M6.3 Christchurch earthquake on 22 February 2011, which resulted in 185 deaths and extensive damage. Due to on-going aftershock activity and the possibility of other triggered moderate to large earthquakes, the New Zealand National Seismic Hazard model was expected to grossly underestimate the level of ground shaking for the Canterbury region for the coming decades. Therefore a new time varying earthquake hazard model, called the EE model, was developed.

Our project set out to investigate the Canterbury sequence in the context of global earthquake statistics. We had two main objectives:

1. Use aftershock parameters derived from global earthquake catalogues to provide bounds for earthquake rates in the Canterbury region for the coming years and decades.
2. Investigate how unusual late and large aftershocks are, as observed in the Canterbury sequence.

During our project we realised that many earthquakes in the first 24h following Darfield, including 14 in the magnitude band 5‑5.9, had not been reported in the initial GeoNet catalogue. We slightly changed focus from deriving aftershock parameters from the global catalogue, to aftershock modelling in the Canterbury sequence to provide bounds for earthquake rates in the Canterbury region for the coming years and decades. We first illustrated the deficiency of the initial catalogue by comparing the GeoNet data downloaded in January 2012 with the mainly finalised catalogue in September 2012. We identified further work required to better understand what effect the deficiencies of the real-time earthquake data have on the real‑time forecasting models. We fitted the two relationships used in aftershock forecasting, the Omori-Utsu law for aftershock decay and the Gutenberg-Richter relation for the magnitude-frequency distribution of earthquakes, to three subsets of the catalogue following M≥6.0 earthquakes. The range of the fitted parameters exceeded what we would have expected from averaging global earthquake sequences. We used the fitted parameters to calculate the number of M≥6.0 earthquakes expected to occur in the 50 years starting in September 2012 for the different combinations of parameters. The expected number ranged from 0.6 to 1.1, and totalled 2.3 for all sub sequences, which is an upper bound estimate due to the dependence of the events. In comparison, the EE model expects about 1.3 M≥6.0 earthquakes in about the same area and time.

We also fitted the Epidemic Type Aftershock Sequence (ETAS) model to the Canterbury sequence. We used the estimated parameters, as well as generic aftershock parameters for New Zealand to simulate ETAS earthquake sequences for the two-year duration of the catalogue, as well as for 50 years starting in September 2012. The retrospective simulations are consistent with the observations. For the prospective simulations the expected number of M≥ 6.0 earthquakes in 50 years is up to six times higher than for the EE model. We identified further work required to investigate the applicability of aftershock models on the time-scale of decades, which is due to begin soon.

In summary, the probability for one or more M≥ 6.0 earthquakes in the 50 years starting in September 2012 ranges from 50% to 93% depending on the model and model parameters.

To investigate how unusual late and large aftershocks are as observed in the Canterbury sequence, we used two global earthquake catalogues. For each catalogue, we identified magnitude thresholds and time periods for which the data can be expected to be complete. We then searched for earthquake sequences using different search criteria. Depending on the search criteria, between 6 and 13 % of main shocks in the more complete catalogue had 3 or more aftershocks within 1.1 magnitude units, as observed in the Canterbury sequence. In space, the relative distance of Christchurch to the Darfield earthquakes was around the 80th percentile, and in time around the 85th percentile of all large aftershocks respective to their main shocks for the preferred search criteria. This confirmed that although the M≥6.0 aftershocks in the Canterbury sequence occurred relatively far away from the main shock in space and time these differences were not unusual in global aftershock statistics. We also searched for large aftershocks within 1.1 magnitude units of the main shock that occurred at least as late and far away as the Christchurch earthquake relative to the Darfield earthquake. In our best dataset, 2% of large earthquake fulfil these criteria. In the other dataset there were another couple of examples. This confirms that while the Christchurch earthquake occurred with a time delay of 171 days and 42 km from the Darfield epicentre, this is not unique in the context of global earthquake occurrences.