Ground motion simulation of hypothetical earthquakes in the upper North Island of New Zealand

The problem

Almost half of New Zealand's population lives in the Auckland, Waikato and Bay of Plenty regions. Seismic hazard there is lower than elsewhere in the country, because the crust deforms slowly and earthquakes are infrequent (Stirling et al., 2012). Two known faults nevertheless lie close to these cities. The Kerepehi Fault extends along the Hauraki Rift, from Matamata to beneath the Firth of Thames. The Wairoa North Fault lies in the Hūnua Ranges, southeast of Auckland. A strong earthquake on either fault would therefore affect a large share of the country's people and economy.

Hazard estimates usually rely on empirical ground motion prediction equations. These formulas, fitted to recorded earthquakes, predict shaking from inputs such as magnitude and distance (Bradley, 2013). They do not represent the geology between a fault and a particular town. Our goal was to simulate the largest credible earthquakes on both faults, including the effect of soft sediment basins.

What we did

We used a physics-based simulator (Graves and Pitarka, 2016). For slow shaking, below 1 Hz (one cycle per second), it computes seismic waves travelling from the rupturing fault through a three-dimensional model of the crust. For faster shaking, from 1 to 50 Hz, it uses a statistical approximation. A correction accounts for soil in the top 30 m.

Individual strands of the Kerepehi Fault rupture about once every 6000 years (Persaud et al., 2016). But the 2016 Kaikōura earthquake showed that at least 21 faults can rupture together (Clark et al., 2017). We therefore modelled a worst case, one 140 km plane spanning all the onshore and offshore segments, with an estimated magnitude of Mw 7.3. For the 27 km Wairoa North Fault, we estimated Mw 6.6. We ran each scenario eight times with different random patterns of slip on the fault, to estimate a mean and range of shaking at each site.

We compared the simulations with 17 records from five small earthquakes nearby. They slightly overestimated the strength of shaking and slightly underestimated its duration. However, these biases were small compared with the scatter between records, typically a factor of 1.6 to 4.5.

What we found

For the Kerepehi Fault scenario, shaking next to the fault exceeds Modified Mercalli Intensity (MMI) 8, described as severe. At Ngātea, above the deepest part of the basin near the Firth of Thames, the mean is MMI 9.5 (violent), the highest of the 22 locations we tabulated. At most locations, there is a 90% chance that shaking from a future earthquake of this kind would be within one MMI unit of the mean.

The basins amplify slow shaking, with periods longer than 1 s. Hamilton and Huntly are both about 40 km from the fault, but Hamilton sits above a basin. At a 2 s period, its spectral acceleration is two to three times that at Huntly, and its mean intensity is MMI 6.9 against 6.2. This is because, in our model, seismic waves travel two to three times slower in the basin sediment than in the surrounding rock. However, the statistical approximation used above 1 Hz does not include basins. The simulated faster shaking therefore shows no basin amplification.

In Auckland, the Wairoa North Fault scenario gives a peak ground acceleration of 0.45 g, almost half the acceleration of gravity (g), at the Mangatawhiri Dam, an earthen dam in the Hūnua Ranges that holds part of the city's water supply. The airport receives 0.22 g and the CBD 0.15 g. At the dam, simulated shaking would likely exceed the level used to check its safety, which is the shaking expected about once in 10 000 years (McQuarrie, 2012). This is not surprising, because the Wairoa North Fault has an estimated return period of more than 20 000 years. However, little is known about its earthquake history.

Road, rail, fuel and electricity lines converge between Takanini and Drury, about 10 km from the fault. Both scenarios give 0.2 to 0.4 g in south Auckland, similar to the 0.17 to 0.27 g used in an earlier infrastructure assessment (AELG, 2014). It found that road and rail on poor soils could take weeks to months to repair.

Stop-banks along the Waihou and Piako rivers protect dairy farmland in the Hauraki Depression from flooding. The Kerepehi scenario gives peak accelerations of 0.4 to 0.5 g there. In the 2010–11 Canterbury earthquakes, liquefaction of foundation soils cracked stop-banks (Green et al., 2011). We suggest that damage would depend on whether local soils lose strength during shaking, for example through liquefaction.

We also tested whether a shallow source and soft sediments could explain the unusually strong shaking in the 1976 M 5.0 Korakonui earthquake (Eiby, 1977). Our simulated intensity contours were smaller in extent than those mapped from damage reports, even for an event one magnitude unit larger. These two factors alone are therefore unlikely to explain the mapped intensities. However, the method used to map the 1976 contours may have overestimated intensity.

Limitations

These are illustrative scenarios for disaster planning, with no probability attached. An earthquake closely resembling either one is unlikely in our lifetime. The main shortcoming is the single plane used for a Kerepehi rupture involving several separate segments. This mainly affects near-fault shaking at Matamata and Ngātea. We did not model the South Auckland Basin, which could amplify slow shaking in Pukekohe. Whether liquefaction occurs, or a dam is damaged, depends on local soils and structures. Engineering investigations could reduce that uncertainty.

Glossary

Moment magnitude (Mw) is a measure of earthquake size based on the fault area and the amount of slip.

Modified Mercalli Intensity (MMI) is a scale of local shaking effects, from MMI 5 (moderate) through 6 (strong), 7 (very strong) and 8 (severe) to 9 (violent). We converted simulated ground velocity to MMI using a published correlation (Worden et al., 2012).

Peak ground acceleration is the largest acceleration of the ground at a site during an earthquake.

Spectral acceleration is the peak acceleration of a simple structure that sways with a given natural period, the time for one full sway, such as 1 or 2 s. A building's natural period depends on its size, height and construction material.

g is the acceleration due to gravity, 9.81 m/s².

Hz (hertz) is a unit of frequency, one cycle per second.

A sediment basin is a depression in the bedrock filled with soft sediment, in which seismic waves travel slowly.

A stop-bank is an earth embankment built along a river to contain floods.

Liquefaction is the loss of strength of water-saturated sandy or silty soil during shaking.