Earth scientists can forecast the size and frequency of the aftershocks following Canterbury’s September 2010 earthquake. But this is very different from earthquake prediction. This article is based on a presentation to the 2011 NZ Skeptics Conference.
Since the moment of the magnitude 7.1 earthquake in Christchurch on 4 September, GNS scientists have been using models based on aftershock statistics to ‘forecast’ the expected range of aftershocks of given magnitudes. Not to be confused with earthquake ‘predictions’, which require specific magnitudes, locations, depths, times, and methodological reproducibility estimates to be useful, this forecast model is based on a modified version of the long-established Omori’s Law for aftershocks, which states that the rate of aftershocks is proportional to the inverse of time since the mainshock. Thus, depending on the values of parameters specific to certain regions, whatever the odds of an aftershock are on the first day, the second day will have approximately half the odds of the first day and the tenth day will have approximately one tenth the odds of the first day. These odds can be summed over various time scales, and the longer the time scale, the higher the probability, even though the probability decreases with time.
At present, these forecasts commonly look something like this:
“The expected number of aftershocks of magnitude 5.0 and above for the next month is 0-2, with an expected average of <1”.
Of course, one could dress this up differently using the same model applied over a full year, taking into account a reducing number of expected aftershocks, and the statement would look something like this:
“The probability of a magnitude 5.0 and above aftershock over the next year is ~82 percent”.
We have had 31 magnitude ≥ 5.0 events since September, the frequency of which has declined systematically following our large earthquakes in September and February. So to say that there is a near certainty of an event occurring somewhere in this range in the next year is no surprising conclusion, because the unfortunate reality of aftershock sequences is that earthquakes decrease in frequency but not magnitude. Remember also that this takes into account the entire aftershock zone, spanning an area from the eastern foothills of the Southern Alps, to offshore east of Christchurch, to Rangiora and throughout the Banks Peninsula; it doesn’t forecast the likelihood of one of these events occurring beneath your house. Large aftershocks have been recorded as far west as the Porter’s Pass area.
The probability of larger earthquakes (M<6) is a bit trickier, although the methodology behind the statement:
“There is a 10 per cent chance of a magnitude 6.0 to 6.4 quake in the next year”
is the same.
To generate an earthquake of M ≥ 6, it is helpful to know whether there are faults that are long enough and ‘connected’ enough to be able to do this, and whether these faults have ruptured in big earthquakes in the past. One way to explore this is to image faults in the subsurface using geophysical methods such as reflection seismic, gravity, and aeromagnetics. These can be combined with ‘relocations’ of aftershocks and by analysing the extent to which seismic waves are ‘guided’ by fault networks, which collectively help to refine the internal structure and strength of fault zones.
The Gap
The ‘Gap’ is a term used in reference to the region of intense and continuing aftershock activity between the eastern end of the Greendale Fault that ruptured in the 4 September Darfield earthquake and the western end of the Port Hills Fault that ruptured in the 22 February Christchurch earthquake.
Analysis of earthquake data and geophysical seismic reflection surveys indicates that the Gap is not a simple continuation of either the east-west striking Greendale or ENE-WSW striking Port Hills Faults. Instead, it is a complicated zone of NE-SW to E-W oriented, steeply SE dipping faults with a total length of up to 10-12 km that is defined by an array of aftershock earthquakes that range in depth from 2 km to greater than 10 km.
Preliminary interpretations of seismic surveys indicate that a series of faults in the Gap have ruptured at various times over the past several hundred thousand years. Based on the length of the aftershock zone and the types of deformation we see in the seismic sections, we estimate that this region has probably experienced major earthquakes in the range of Mw 6-6.3 in the geologic past. Such events appear to be very infrequent, ie, recurring only once every 10,000 years or more, because even sediments that are millions of years old are only subtly deformed. We do not see any evidence for a surface rupturing earthquake in the last 5000-10,000 years or so based on interpretations of air photos from this area.
The Gap has been seismically active throughout the Canterbury earthquake sequence, from immediately following the September mainshock to the present. There have been two earthquakes of M > 5 and 23 earthquakes of M > 4 in the gap since 4 September.
The total seismic energy release in this Gap (seismic moment) is less than the total energy released in the adjacent Port Hills and Greendale Faults. In the simplest interpretation, the total seismic energy release from the Gap would eventually fit a ‘smoothed’ profile between the Greendale and Port Hills Faults. This is not necessarily required, but it is something that would best fit our models for how fault slip accumulates across fault systems through time. ‘Filling the Gap’ could occur via a continuing series of smaller earthquakes, as has been the case so far, or via a larger event, possibly as large as a low magnitude 6 to high magnitude 5. From what we understand about the behaviour of earthquakes in this area to date, it seems most likely to us that this region will continue to release seismic energy in the form of smaller earthquakes rather than an isolated large one, although this possibility still remains.
The processes governing fault rupture are somewhat complicated, but our scientific understanding of these processes continues to improve. One could ask, “Why should the Gap behave one way during one earthquake sequence and a different way in another?” The answer is that the order and the direction in which adjacent faults rupture, the areas of these ruptures, and the processes that go on between large earthquakes, such as fault rock healing and fault closure, all influence the rupture behaviour of an individual fault segment. The overall pattern since September has been an eastward propagation of major earthquakes, starting with the Darfield earthquake in September, then the Port Hills fault rupture in the February earthquake, then the June earthquake even further east. If the sequence had started in the east and propagated west, it is entirely possible that some of these faults may have behaved differently.
Marine surveys by NIWA immediately offshore of Christchurch have revealed additional faults, some of which have had small earthquakes on them during this seismic sequence. The lengths of these faults suggest that some are capable of generating earthquakes as large as or larger than the 22 February event, however, the increased distance from Christchurch would reduce the impact on the city for a similar-sized event. In the face of our seismic realities, the best way forward is to take this opportunity to make Christchurch one of the world’s most earthquake-resilient cities.
Geologic analogies
This is my favourite geologic analogy for the Canterbury earthquake sequence. On April 23, 1992, the Mw 6.1 Joshua Tree earthquake rocked the Californian desert east of the San Andreas Fault. Two months later, on June 28, 1992, the Mw 7.3 Landers earthquake occurred in the same region, with an epicentre located approximately 40 km north of the Joshua Tree epicentre. Three hours after the Landers event, the Mw 6.2 ‘Big Bear’ aftershock occurred some 40 km to the west. On 16 October 1999, seven years after the Landers event, the Mw 7.1 Hector Mine earthquake occurred, with an epicentre some 40 km north of the Landers epicentre.
This area is adjacent to a section of the San Andreas Fault (America’s version of our Alpine Fault) that had not had a major earthquake since 1812 (one segment) and 1680 (another segment), just as our Alpine Fault does not appear to have ruptured in a major earthquake since 1717.
Palaeoseismologic estimates of the recurrence intervals of clusters of earthquakes in the Mojave Desert near the Landers rupture are in the range of 5000 to 15,000 years (Rockwell et al., 2000), similar to the expected range of recurrence intervals of active faults in our Canterbury Plains. So a situation like this is possible, although we would obviously prefer that the region settled down without the occurrence of any more big events.
Where to from here?
We’ll do our best to provide the best scientific information possible. Wait for the information to come from scientists regarding the earthquake history, likely lengths, and ‘connectivity’ of faults in our region. Then take into account whether you want to occupy your time with fear of the next big one, which may or may not eventuate in the next few years or more, or get on with your life while learning lessons about being prepared for earthquakes.
Could the magnitude and location have been predicted?
Generally, when considering the maximum magnitude in an aftershock sequence, seismologists refer to Bath’ s Law, which states:
“The average difference in magnitude between a mainshock and its largest aftershock is 1.2, regardless of the mainshock magnitude”.
This is a generalisation based on analysis of global earthquake datasets, recognising that each aftershock sequence is different and there are many exceptions to the rule. Let’s look at how Bath’s Law predicts the largest aftershock magnitude for some of New Zealand’s largest earthquakes.
| Earthquake |
Date |
Magnitude |
Largest Aftershock(s) |
| Hawke’s Bay |
1931 |
7.8 |
6.9, 5.9 |
| Pahiatua |
1934 |
7.5 |
5.7 |
| Wairarapa |
June 1942 |
7.0 |
4.7 |
| Wairarapa |
December 1942 |
6.0 |
4.7 |
| Gisbourne |
1966 |
6.2 |
5.0 |
| Inangahua |
1968 |
7.1 |
6.0 |
| Arthur’s Pass |
1994 |
6.7 |
6.1 |
| Table 1. A comparison of the magnitude of some NZ earthquakes and their largest aftershocks |
Table 1 shows mainshock-aftershock comparisons for some large New Zealand earthquakes.
The average difference between the largest aftershock and mainshock for this small New Zealand dataset is 1.2, consistent with Bath’ s Law. Prior to 22 February 2011, the largest difference between the 2010 Darfield 7.1 mainshock and largest aftershock (5.6(, that occurred only about 20 minutes after the mainshock, was 1.5. There was reason to be optimistic, as this difference had been seen from other events; however all scientists working on the Darfield earthquake acknowledged that a larger aftershock was still possible. Unfortunately, our fears were confirmed, with the 22 February magnitude 6.3 aftershock (0.8 point difference from mainshock, perhaps higher than predicted from a simplistic interpretation of Bath’s Law( and the June 13 6.0 event.
This illustrates that, while we can use historical examples to help us predict possible aftershock magnitudes, each sequence can be different, depending on the length (or more accurately, the potential rupture area) of faults throughout the area, the strength of the faults, how close they are to their breaking points, and how things like stress transfer and fluid pressures associated with the mainshock or other aftershocks influence these faults. This illustrates how important it is to know the location and length of other faults in the vicinity of Christchurch and offshore before we even discuss putting billions of dollars into a rebuild. This can be done relatively inexpensively with existing technology. Shouldn’t we know the location and magnitude potential of other faults throughout this region, and model how they may have been stressed or de-stressed following our big earthquakes before buildings are even designed?
To summarise, the magnitude of the 6.3 could not have been exactly predicted, but something within this magnitude range was always possible and all scientists involved in this event recognised this. We were hopeful it would not occur. A glance through some of the largest New Zealand earthquakes from the last century indicates considerable variability in the magnitude of the largest aftershock, but an aftershock of this large magnitude compared to the mainshock is not unprecedented (eg the 1994 Arthur’s Pass earthquake sequence(.
Earthquakes and the moon: should we worry?
- No one has predicted the recent earthquakes in Canterbury. Vague quotes about dates of ‘increased’ activity plus or minus several days, without magnitudes, locations, and exact times do not constitute prediction. Consider this: Ken Ring’s probability of getting a prediction correct based on perigee/apogee new moon/full moon for 2010 was 63 percent. That’s 230 out of 365 days that fall on some day that he would argue influences earthquake activity. For days that combine several factors of new moon/perigee etc, he missed out on several predictions and nothing unusual happened on those days. (ie 30 January, 14 February, 27 February, 29 March, 14 June, 12 July, 10 August, and so on for his liberal interpretation of the aftershock sequence). This does not constitute ‘prediction’. It is opportunistic and meaningless self-promotion.
- Consider your chances of getting a ‘prediction’ correct given this unscientific definition of prediction. On average, New Zealand gets around 330 earthquakes of M4-4.9 every year, 26 M5-5.9s per year, two M6-6.9s per year, and one M 7-7.9 every three years (see stats on Geonet). If unspecific about magnitude and location, then your chance of ‘predicting’ an earthquake that is likely to be locally felt and recorded is greater than 90 percent (based on the simplified method of assuming each earthquake occurs on a different day, which isn’t the case, but you get the picture). This of course goes up immediately following a major earthquake like our 7.1 where the occurrence of large events is high. We had 203 earthquakes greater than 4 in the Canterbury region close to the 7.1 rupture in the six months since 4 September. So one’s chances of ‘prediction’ are actually quite high.
- If we had been specifically predicting large earthquakes (M>6) on the faults near Christchurch that ruptured on 4 September and 22 February using the moon over the last several thousand years, we would have been wrong many thousands of times, with a success rate of ‘zero’, even invoking the broad criteria cast by invoking all of the possible moon scenarios listed above.
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There is no clear correlation between the largest aftershocks in the Darfield earthquake aftershock sequence and diurnal tides. Some of our largest earthquakes have occurred near high tide and some near low.
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Consider implementation of this ‘predictive’ strategy. Should we evacuate an area every time the moon is on its closest approach, is full or new, is moving rapidly, is at its maximum declination or is crossing the equator? Imagine the fear and frustration of such an approach, particularly given the unspecified times, locations, and magnitudes of the supposed ‘imminent’ events. Without a basic understanding of how faults generate earthquakes, where the faults are, at what stage they are at in the seismic cycle, and how they have been affected by prior activity, where should we evacuate and where should we go to? This would require several evacuations a month of ‘unspecified areas’ to other ‘unspecified areas’.
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Since humans first looked into the sky and felt the effects of earthquakes, they have wondered if the moon and planets are in some way responsible for major earthquakes. As early as 1897, scientists began to pose hypotheses about moon-earth earthquake connections and test them in honest and rigorous way. After all, the moon still gets earthquakes in the absence of plate tectonics, so perhaps there is some validity to this claim.
While some astrologers may feel isolated from the scientific community, this shows a true lack of appreciation for all of those dedicating significant effort to this issue. Many of these findings from studies comparing earthquake catalogues to tides have been published in high-quality journals such as Science (eg, Cochran et al, 2004) and some scientists have argued based on statistical data from global earthquakes for an influence of tides on earthquake activity under certain circumstances, such as beneath the oceans and within active volcanoes. Some scientists have even argued for a small correlation (perhaps an increased earthquake likelihood of 0.5 to 1 percent) between smaller, shallower continental earthquakes and ‘solid earth tides’ (changes in the shape of our planet due to the gravitational pull of the moon).
This is peer-reviewed but controversial research; it does not make it so, but it has undergone scrutiny and will continue to do so. This is the scientific process. To this end, I have a postgraduate student conducting high-level geologic and statistical research on the Canterbury aftershock sequence, including spatial, temporal, and mechanistic relationships with lunar parameters. You can bet that any results, regardless of the outcome, will be published for all to see and openly scrutinise.
