Just for general information, I decided to do a statistical analysis of the likelihood of a mag 3.2 to mag 4.0 quake in the San Francisco bay region
in a given period. I feel that this might help us to appreciate the likelihood of Mr Thomas’ prediction being right on the basis of pure chance --
as this is the assessment criteria often used to determine the validity of such predictions.
To do an analysis like this, you need a good database that holds records of quakes by magnitude, time and location, and that (preferably) also allows
you to choose variables within those criteria and search a given are for a specific time and magnitude range. The NEIC database is good for this, so
that’s the one I used.
I did a search with these variables:
Location: I used
this page about San Francisco Bay on Wikipedia to obtain the coordinates of
37.717 N, 122.283 W. (Note: I rounded up the lat coordinates from 37.7166. It makes very little difference to the overall result. Also, the longitude
figure is input in the search as a minus number. All “West“ longitudes are minus. If we used a non-minus number then we‘d be on the wrong side
of the world but at the same latitude.)
Area of search: this is always an arbitrary choice. I felt that if a quake occurred within 64 kilometers (around 40 miles) of the Bay’s coordinates
then it would be fair enough to accept it as in the right area, even if not all points 40 miles away are actually considered to be part of the Bay
region. So, I chose the “circle” search format with the above coordinates as the centre and gave the radius of the circle as 64 km.
Magnitude: Mr Thomas’ prediction states the quake should be between magnitude 3.2 and 4.0, so they are low- and high-range figures I input in to
NEIC search facility.
Time frame: The larger the amount of data with such varibale things as seismic events, the better chance of getting a reasonable figure for averaging.
The NEIC database holds data from 1973 onwards. A check showed that there was only 1 quake in the above range in that year, which occurred on Dec 29.
So, as the time frame is quite large, I made the start date Oct 12, 1973 and the end date Oct 11, 2010, to give a period of exactly 37 years.
True, I could have taken the start date as of the first quake (ie Dec of 73), but the percentage difference in total time is minimal and in the final
result we’re only looking for a rough percentage likelihood of the event, not minute fractions of a percent.
Inputting the above parameters yields a list of 245 earthquakes. In other words, over the past 37 years, there have been 245 quakes in the range of
mag 3.2 to mag 4.0 within about 40 miles of the Bay’s defined coordinates. As posting the complete data list would take up a huge amount of space
(and maybe several posts to fit it all in here), I’ve instead posted a screen shot of the main section of the results page here:
Also, if you click on
this link to the NEIC search page you’ll be
able to input the parameters yourself and confirm my results.
Okay, that’s the prelim. Now we do the sums…
A total of 245 quakes in 37 years works out at 6.621 quakes per year. Purely from a statistical point of view, we can also calculate the average
number of days from one quake to the next. If there are 6.621 quakes per year and each year has 365 days*, then we simply do 365/6.621 and get a
figure of 55.127 days. Simply put, this means that the odds of a quake in that magnitude range occurring in the given area work out at 1.818%
(recurring).
*I’m ignoring leap years for sake of this exercise and just using a standard 365-day year. As I mentioned before, it makes a trivial amount of
difference for the figures we need in this exercise.
So, ball park figure: on the basis of known data, there is only around a 2% chance that a quake will occur in that region today, Oct 12, 2010. If it
happens (and therefore Mr Thomas would be right) then I’ll be pretty impressed.
Incidentally, there have only been 16 quakes of precisely mag 4.0 in that same region and time frame. Just 16 in 37 years. So the odds of a mag 4.0
occurring there on any given day are very small indeed. Even if we do a rough calculation and (again) ignore the few extra days from leap years, 37
years is 13,505 days. With just 16 quakes in all that time it comes out at (statistically) one quake roughly every 844 days!
On the other hand, what if a quake occurs there today, but it’s say a mag lower -- like a 2.2? Well, as you all know, the lower the magnitude the
quake, the more of them there are. In this case, using the same parameters and just changing the low-range mag from 3.2 to 2.2, the number of quakes
in the region jumps from 245 to 826. Even so, the odds are still not very favorable. If we use the same methods of calculation and do 826/37, we get
22.324 quakes per year. To get the day interval, we use 365/22.324 and get the figure of 16.35 days. (Aren’t calculators wonderful?
) So, the
odds on a given day are around 6.12%.
If you’re not asleep yet, then thank you for reading through all of this. I hope it helps to explain a bit more about the difficulties we’re up
against in trying to make accurate predictions. It also explains why it’s poor science to keep moving goalposts (so to speak) by revising the
prediction’s data. It’s far better to pick a reasonable time frame and stick to.
Further, it helps to show why we are sometimes pretty excited when we get a prediction right and the odds of doing so were down in the single-digit
range. And in case any newcomers are wondering (and you’re right to wonder!), we don’t predict quakes in very low mag ranges for places that
typically have them on an almost daily basis. We tend to steer away from that sort of thing as it serves no real purpose.
Regards,
Mike
EDIT to add: no sooner have I posted this but on checking back on the quakeprediction.com site, I find that Mr Thomas has revised his prediction for
SF Bay. Now he's tightened up the mag range (which greatly reduces the odds of its occurrence) and also changed the data for the percentages, but
additionally, he's now made the prediction for a two-day period instead of the single day he'd posted a few hours ago.
Anyway, here's the screen shot:
The source for the above image is
here. As usual, this image will drop off the site when the next revision
is posted.
Mike
edit on 12/10/10 by JustMike because: Added the edit as stated above.