Sunday, June 2

Earthquakes, Patterns and Predictions

Yesterday’s post was a ringer. What you were actually looking at was a random distribution of earthquakes that I generated using the R statistical package. The earthquakes themselves are real (at least the magnitude), representing the 3,776 earthquakes over magnitude 4 between January 1 and May 24. However, I had R assign a random day between 1 and 144 (1/1-5/24) to each earthquake. Many of you saw through my ruse, but did some of you start to convince yourself that there was a coherent pattern in this data? Maybe that some of the larger earthquakes occurred within a few days of the new moon? Maybe that lulls were happening during full moons? Did it seem plausible? That is because humans love to find patterns, especially in large data sets. We don’t even know we’re doing it (notice how Mary can show up on a potato chip?) Yet, here we are, always looking for patterns and an explain for the distribution of events or objects.
In geology, there is probably no bigger a subject than “pattern recognition” (or lack thereof) in earthquake prediction, to the point that some claim they can predict when and where an earthquake will strike. Sadly, we just can’t do that with our current technology and knowledge of the Earth, but people still fall prey to believing in these false patterns.
Human brains are good at seeing patterns, whether it be to see the ripe fruits to pick in a tree, to notice the snake ready to strike or to see that elephant in the sky when you’re looking at clouds. Our ancestors were those who survived and thrived because they were able to see the patterns in their environment to find food, avoid predators, and get a mate. One idea is that our brains want to see patterns, even false ones, so as not to miss the right pattern when it comes along — because if you miss that pattern for “snake”, you might end up dead. This ability mixed with culture became superstition, which in itself is pattern recognition, although the patterns can be false.
Work by Foster and Kokko (2009) models the behavior of people when it comes to superstitious beliefs (i.e., patterns that are false) and found that people should be apt to accept a false pattern if the cost of accepting that pattern is lower than the cost of not accepting the false pattern. Foster and Kokko (2009) sum this up by saying:
The evolutionary rationale for superstition is clear: natural selection will favour strategies that make many incorrect causal associations in order to establish those that are essential for survival and reproduction … the inability of individuals—human or otherwise—to assign causal probabilities to all sets of events that occur around them will often force them to lump causal associations with non-causal ones
Or, in other words, it is better to believe wrong and right things (and thus get all the right things) than accidentally miss some of the right things. For example, many traditional cultures have pregnancy taboos.  Many pregnancies don’t make it, and the causes aren’t often clear. However, people try to see some sort of pattern. It is low cost to believe that women should not eat certain foods, avoid the full moon, and never butcher an alligator if any of those things just might aid in the survival of her child. Low cost for believing in some good and some bad stuff in trade for high evolutionary rewards. Thus, cultures adopt taboos for pregnant women that may seem silly, because it was difficult to see which of the few taboos actually has a causal relationship (if any). Granny wants you to do them all, just to be on the safe side.
So, your brain is hypersensitive to patterns because you inherited this ability from your ancestors.  If great great great Grandma Ape wasn’t hyper about patterns, she wouldn’t have survived long enough to be your ancestor. However, the cost is that we tend to try to see things that aren’t always there.  That is what happened when you looked at the random 2013 earthquake data.  We can’t actually see the causal probabilities for the distribution of earthquakes because they are so complex, so instead we try to fit them to easier relationships, like the phase of the moon.
This might help explain why people will believe in their own method to predict earthquakes/eruptions or believe other’s models without adequate understanding. There have been a number of studies into why people believe conspiracies (again, a pattern that has a false basis) or see patterns when none exist. We all want to see patterns in the data, events or objects, but sometimes the pattern isn’t there or it is contained in much more complex layers that can be difficult or impossible to understand based on our current level of information about the processes involved.
The Real 2013 Earthquake Distribution
Now, here is the real distribution (honestly), with some of the largest (M7+) earthquakes labeled:

The real distribution of earthquakes between January 1 and May 24, 2013. Graph by Erik Klemetti using USGS Earthquake data.
That is a lot of M4+ earthquakes — 3,776 to be exact. So that means each day, there are, on average, ~26 magnitude 4 or larger earthquakes on the planet. This means anyone who claims that we’re likely to have an earthquake on Earth on a given day is right — we are (it just isn’t very predictive). Now, most of the earthquakes are M4-5, so noticeable to the region near the earthquake but rarely devastating, but wow, just the normal seismicity of the planet is remarkable.
There are a few things you can notice in this real dataset. First, it isn’t a true random probability distribution — that earthquakes are really randomly distributed through time. This is likely due to clusters of foreshocks and aftershocks associated with large earthquakes. Just look at the peak around the M8 Tonga earthquake (on February 6 – Day 37) — there are many more earthquakes in the day before and after than any other 2-3 period of 2013. However, as Eneva and Hamburger (1989)concluded in a study looking at earthquakes in Central Asia, it you remove the fore/aftershocks of large earthquakes from any earthquake distribution, the rest of the earthquakes are randomly distributed through time.
Now, there are many who want to ascribe predictive powers to the moon phase or distance when it comes to earthquake distributions. Let’s take a look at those graphs:

All M4+ earthquakes between January 1 and May 24, 2013. The lunar phases are listed above the earthquakes, with open circles = full moon, crossed circles = new moons. Graph by Erik Klemetti using USGS earthquake data.
Here (above) are the earthquakes with moon phases listed along the top. There is no clear match between new or full moons and the occurrence of earthquakes or their magnitude. There are some new moons (such as in February) where activity when up, but also new moons (such as in March) where nothing changed. If you want to construct a predictive model, that doesn’t bode well. Kennedy and others (2004) did a statistical test of this “syzygy” and found no correlation between moon phase and earthquakes in the San Francisco area — at least not enough to make it anything close to a predictive tool for earthquakes. Earth tides — the result of flexing of the Earth’s crust due to the gravitational relationship between the Earth and the Moon (think ocean tides) — does seem to play some role in trigger some earthquakes, but as Cochran and others (2004) and Metivier and others (2009) found, it is only during the strongest of those tides and only on small, shallow earthquakes. So, it seems that something as simple as moon phases cannot be used to predict when and where an earthquake will occur.

All M4+ earthquakes between January 1 and May 24, 2013. Lunar distance is marked across the top, with up triangles = perigee (closest), down triangles = apogee (farthest). Graph by Erik Klemetti using USGS data.
This figure (above) is earthquakes with lunar perigee (nearest) and apogee (farthest) positions marked. Much like the moon phases, there are no matches between the number and magnitude of earthquakes and the moon’s distance from the Earth. I discussed why this is likely true when we’ve had the so-called “Supermoon” that people where saying would cause a sharp increase in earthquakes and eruptions (hey look, we survived!) What both of these two plots suggest is that the distribution of earthquakes is not likely to be controlled by something as simple as lunar phase or distance.
Predicting Earthquakes
We could go on with a list of all sorts of external variables: solar flare activity, alignment of planets, gamma ray bursts, whatever. What becomes clear is that earthquake occurrence is likely much more dependent on the state of stresses on individual faults within the Earth rather than any forces coming from outside the Earth. Now, to anyone trying to predict earthquakes, this revelation must be maddening because the phase of the moon or solar flares are easy to observe (and use as a predictor). However, the state of stress on a fault at 50 km depth beneath Tibet?
That is something we don’t know and can’t know with our current level of technology. Remember, thefocus (hypocenter) of most earthquakes are at depths of tens to hundreds of kilometers below the surface, and we humans have only drilled into the uppermost few kilometers of the planet. Collecting data that can tell us the state of stress on all the known active faults alone is far beyond our current capabilities — and that is exactly what we need to be able to make accurate predictions of when an earthquake will occur on a given fault. As Geller (1997) and Geller and others (1997) conclude, we haven’t even come close to developing a reliable (and believable) method for predicting earthquakes. All of this adds up to this simple statement: prediction of earthquakes is currently impossible.
Does this mean that the quest to predict earthquakes (or future eruptions, for that matter) is in vain? Well, that becomes tricky. The short answer, with our current technology and knowledge of the Earth’s interior, is yes. Geller and others (1997) say that we should be putting our efforts into better mitigation against disasters by identifying areas prone to earthquakes rather than trying to predict when they might occur or, as Kagan (1997) suggests, building models for predicting aftershocks of large earthquakes. However, Wyss (1997) and Wyss (2001) disagree, and say that earthquake prediction could happen if only we continue to study it. Wyss (2001) points out that there is a stigma associated with studying earthquake/eruption prediction* amongst established geoscientists — as he puts it:
The dream of discovering how to predict earthquakes attracts individuals who put enormous energy into promoting unfounded ideas with the public and policy makers. Unfortunately, it takes a great deal of effort to show the flaws in highly advertised claims of success in earthquake prediction, and not all are able to understand the reasons for which the work is invalid.
Wyss (2001) says that the stigma associated with the study of earthquake or eruption prediction needs to be removed, because as our technology and understanding of the planet advances, so should our ability to predict these events — but not if no one is studying them. The problem lies in getting past thecharlatans and snake oil dealers who give a bad name to research into predictive models. They claim to predict when earthquakes are likely to strike (as I said above, they strike all the time) and then claim that any earthquake that occurs validates their prediction — it especially helps it one of the ~26 earthquakes M4 or greater that can occur each day happens near someplace populated.
So, we need to be very careful when we tread into earthquake (or eruption) prediction. There are many people out there on Twitter or the internet claiming to know how to predict earthquakes using some of the very methods I’ve just discussed. And people believe them, because they can present that they claim is a pattern and the cost of believing these “predictors” is low for most people. You can check out the “success” rates of some of these people claiming to have figured it out on Quack Predict, a website dedicated to outing these fake predictions and false earthquake prophets. However, as I’ve tried to lay out here, the cost in believing these people who don’t put their work up to peer scrutiny and don’t answer to when they are wrong (which is close to 98% of the time in most cases) can be high — it might prevent real research in earthquake or eruption prediction from occurring. Even beyond this more abstract reason, it can have real ramifications in public trust and preparedness in places where that unexpected earthquake occurs.
  • Cochran, E.S., 2004. Earth Tides Can Trigger Shallow Thrust Fault Earthquakes. Science 306, 1164–1166.
  • Eneva, M., Hamburger, M.W., 1989. Spatial and temporal patterns of earthquake distribution in Soviet Central Asia: Application of pair analysis statistics. Bulletin of the Seismological Society of America 79(5), 1457-1476.
  • Foster, K.R., Kokko, H., 2009. The evolution of superstitious and superstition-like behaviour. Proceedings of the Royal Society B: Biological Sciences 276, 31–37.
  • Geller, R.J., 1997. Earthquake prediction: a critical review. Geophysical Journal International 131, 425–450.
  • Geller, R.J. and others, 1997. Earthquakes Cannot Be Predicted. Science 275, 1616–0.
  • Kagan, Y.Y., 1997. Are earthquakes predictable? Geophysical Journal International 131, 505–525.
  • Kennedy, M., Vidale, J.E., Parker, M.G., 2004. Earthquakes and the Moon: Syzygy Predictions Fail the Test. Seismological Research Letters 75, 607–612.
  • Métivier, L., De Viron, O., Conrad, C.P., Renault, S., Diament, M., Patau, G., 2009. Evidence of earthquake triggering by the solid earth tides. Earth and Planetary Science Letters 278, 370–375.
  • Wyss, M., 1997. Cannot Earthquakes Be Predicted? Science 278, 487–490.
  • Wyss, M., 2001. Why is earthquake prediction research not progressing faster? Tectonophysics 338, 217–223.
* Wyss (2001) does make an interesting argument that volcanologists have it easy in the game of predicting earthquakes — as he claims that for volcanoes, we know the location, that the result is binary (eruption, no eruption), there are limited styles of eruption that might occur and that the timeframe of knowing an eruption might happen is short (days to weeks ahead of time). Not sure I buy his argument, but interesting to compare earthquake to eruption prediction.

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You can write whatever you want, but technically, the precise mathematical-statistical forecast of earthquakes based on information about the behavior of wild and domestic animals, birds, fish, and individuals available from 1995, with the advent of social networking.

THE STRUCTURE OF INPUT BIG DATA: API applications to social networks