Time-varying earthquake hazard in the Wellington region

Abstract

In the simplest and most common method of estimating earthquake hazard, it is assumed that the hazard does not change with time. This assumption is not realistic if one considers that after a fault has moved in an earthquake, the stress on the fault is reduced. It will take some time (perhaps many decades or centuries) for stress to build up before another similar earthquake could occur. This thinking leads to a method of estimating earthquake hazard in which the probability of an earthquake occurring on a particular fault varies with time, starting from when it last ruptured. Also, studies of patterns of earthquake occurrence, revealed by high-quality catalogues, show that most large earthquakes are preceded in the long term, ie, over years or decades, by an increase in the rate of occurrence of small earthquakes. This has led to another method in which the hazard varies with time. In this method, the probability of large earthquakes increases after many small earthquakes occur.

These two methods have been applied to estimate the hazard in the Wellington region.

In the fault-hazard method, everything that is known about the past history of the four main earthquake faults in the Wellington region (how far the faults have moved over very long times, when they last ruptured and how big the earthquakes on the fault are) has been taken into account. Using this method, we estimate the probability for the occurrence of very severe earthquake shaking in the Wellington urban area over the next 100 years. Although less than 20%, it is found to be 50% higher than the common method indicates.

In the earthquake-pattern method, the whole catalogue of recent earthquakes down to small magnitudes has been used to show how strongly they indicate that moderate-to-large earthquakes may be imminent in the Wellington region. This method does not indicate an increased hazard in the Wellington urban area at present. It does show that the probability of moderate-to-large earthquakes occurring on the southern side of the Cook Strait is higher than normal.

Further studies are needed to improve the data and methods used here. This will allow forecasts that are more reliable.

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Technical Abstract

Time-varying earthquake hazard in the Wellington region has been estimated using two different approaches, one from earthquake geology and fault-rupture recurrence-time modelling, and the other from long-term precursory seismicity patterns revealed by high-quality earthquake catalogues and space-time point-process modelling.

For the four major active faults of the Wellington region in the upper plate – the Wellington Fault, the Wairarapa Fault, the Ohariu Fault and the Shepherds Gully-Pukerua Bay Fault – existing data on long-term average slip-rate, the mean single-event displacement, and the times of known past ruptures have been assembled, and their uncertainties assessed. These data have been used to estimate the time variation, over the next 100 years, of the probability of rupture of each fault under the exponential, Weibull, lognormal and inverse Gaussian recurrence-time distributions, allowing for uncertainties in data and parameters. In the case of the Wellington, Ohariu and Shepherds Gully-Pukerua Bay Faults, the probability is higher under the Weibull, lognormal and inverse Gaussian models, in which the hazard is intrinsically time-varying, than under the exponential model, in which the hazard is intrinsically static. In the case of the Wairarapa fault, the reverse is true.

For theoretical reasons, the inverse Gaussian model is preferred, and it has been used to adjust the probabilities of occurrence of maximum accelerations exceeding 0.3g and 0.7g in the Wellington region over the next 100 years, starting from the database of the national seismic hazard model. At 0.3g, the probability in the Wellington urban area is increased from about 0.5 to between 0.55 and 0.6. At 0.7g the proportional increase in probability is larger, from about 0.1 to between 0.12 and 0.18. This result is mainly due to an increase in the estimated probability of rupture of the Wellington Fault over the next 100 years.

Major shallow earthquakes near to plate boundaries are usually preceded in the long term by a marked increase in the rate of occurrence of minor earthquakes in the same locality. This is called the precursory scale increase phenomenon. In the precursory scale increase phenomenon, the magnitude of the largest precursory earthquakes can be used to predict the magnitude of the major earthquake, the time interval between the onset of precursors and the major earthquake, and the area occupied by the precursors, major earthquake and aftershocks. Reliably identifying the precursory scale increase phenomenon pattern before the major earthquake occurs is difficult, but a point-process model (EEPAS) has been developed in which every earthquake is regarded as a long-term precursor, according to scale, of larger ones to follow. This model has been fitted to the New Zealand catalogue and successfully tested on the catalogues of California and Japan.

Estimates of the current earthquake occurrence-rate density in the Wellington region under the EEPAS model, at magnitudes ranging from 6.0 to 7.5, do not show any elevated rate density in the vicinity of the major faults of the Wellington region. They do show an elevated rate density in the northern South Island which could affect the ground-shaking hazard in the Wellington region.

Further research is needed to improve the data available for fault-recurrence modelling, by reducing the uncertainties of the mean single-event displacement and slip-rate, and identifying the times of recent prehistoric ruptures of the faults. Likewise, further research is needed to strengthen forecasts under the EEPAS model, by improving its ability to distinguish precursory earthquakes from others that are not precursory.