The big 6

Another M3 earthquake last night  (M3.0 05:45UTC 180km NW
of OK city),  a quick review of what our tiny geophone has picked up in the past couple of weeks.

Looking at some of these all on the same scale we start to see some patterns  ... most of these earthquakes are happeneing 100-200km away, at these distances seismic signals start to have a distinct pattern with P and S waves arriving a different times ... the delay being because P waves travel faster than S waves ... at 150km this gives a delay of about 20 seconds ...  

California rocks again

The last week or two have seen a sudden increase in earthquakes in California.   For the first time in several years California is once more having more eathquakes than Oklahoma.

13 OK earthquakes >M2.5 in past 7 days

48 CA earthquakes >M2.5 in past 7 days

While this is  worrying for people living in California it is somehow reassuring for a geoscientist.   Earthquakes are supposed to happen in California, that is what we have been teaching kids for the past 40 years or so since plate tectonics was discovered.

If we look in a bit more detail (USGS Earthquakes website is great for doing this )  we see that the vast majority of these Californian earthquakes have happened in a place called Bombay beach and are associated with a NE-SW trending fault under the lake.

Most earthquakes happening at Bombay beach on a NE-SW fault

This fault is related to the great San-Andreas fault system which runs through Calfornia, so people are inevitably asking ... is this the precursor to "THE BIG ONE", which in California means an earthquake >M7  which is likely to happen every 10 years or so (that Gutenberg-Richter relatioinship again) .   Unfortunately such swarms of small earthquakes are just as likely to not be followed by a big earthquake as to be the precursor, this particlur fault at has a history of producing small swarms with no big one following but that does not mean this will be the case now.  Seismologists in California  try to adjust their short term risk forecasts to take account of such swarms maybe being a precursor but the overall risk is still low (less than 1% ) so not  a usable piece of information to help people in their day to day lives.

Why worry more about earthquakes in California than Oklahoma ?

It is all to do with maximum likely earthquake magnitude and fault lengths.    Earthquakes start to become dangerous once their magnitude goes over M5, once they reach M7 they can be devastating.   California, sitting as it does on a tectonic plate boundary has a massive fault system running through it (the San Andreas) which is thousands of km long.   It has a history of M7+ earthquakes (6 in the last 40 years) and there is a possibility that they could reach M8 if the whole San Andreas fault slips at once.  

Fault length is the reason.  The thing that really decides how big an earthquake is is the total size of  the fault that ruptures (well really fault area x slip length)  this leads to another useful rule of thumb (seismologists seem to have a lot of thumbs !)

Empirical (fancy name for rule of thumb) relationship between earthquake magnitude and rupture length

      So a M4 earthquake ruptures a fault less than 1km long  whereas a M7 earthquake ruptures a fault about 100km long.   Or from a geoscientists point of view you need to have a pre-existing fault system at least 100km long to enable a M7 earthquake to happen.   There are plenty of these in California but not so many in Oklahoma (or they are much older and well buried).   So in California we are pretty much guaranteed to have an M7+ earthquake in the next twenty years or so,   maybe the next one will be preceded by a swarm of smaller earthquakes or maybe it will happen out of the blue.  No wonder seismologists are starting to pay lots of attention to California at the moment.   

What are the chances ?

Ben has been monitoring earthquakes in Oklahoma for about 10 days now ... in that time there have been about 8 earthquakes > M3   and about half of these have been registered on our trusty geophone.

(seismologists look away ! our window-sill sensor on the third floor !)

  But how long will Ben have to wait until he feels an earthquake ?   Chatting to people in the hotel it seems that  M5+ events even 160+ km away cause shaking strong enough to be easily felt.

It turns out that there is a pretty good rule of thumb that seismologists can use to estimate how frequently earthquakes occur in a given location (seismologists call it the Gutenberg-Richter Law ) It seems that for most places for most of the time earthquake size and frequency of  occurence follow a simple power of 10 rule (roughly).   For every decrease in magnitude of one unit, the number of earthquakes increases by a factor of 10.  So if there have been 8 earthquakes >M3 in the last 10 days there were probably 80 earthquakes >M2  (unfortunately we cannot detect earthquakes this small with our geophone and even the Oklahoma Geological Survey only guarantee measuring earthquakes  >M2.5 )

Looking back over the past year there have been 567 earthquakes >M3 in Oklahoma  37 >M4 and 3 >M5

The past year's earthquakes >M3 in Oklahoma 

(You can have a play at making your own maps at http://ds.iris.edu/ieb/ )

so you would expect there to be an earthquake >M5 every 100 days or so,

But Ben is only planning on being in Oklahoma for 70 days so does this mean he won't feel one ?   Well not necessarily ... earthquakes tend to occur at fairly random times so we need to start thinking about probabilities ...  Time to do some MATHS !!! 

Let's start by thinking about the probability of a M5+ earthquake occuring somehwere in Oklahoma state today as 1 in 100 (or 0.01) .... this means that the probability of an earthquake not occurring to day must be 99 in 100 (or 0.99) .  (It turns out that measuring the probability of an earthquake not occurring is a more useful way at solving this problem) 

Now if we consider the probability that two consecutive days won't have a M5+ earthquake we have to multiply the probability of this happening on each day so the probability is 0.99 x 0.99 = 0.9801 

So the probability that an earthquake not happeneing for 70 consecutive days should be 

0.99 x 0.99 x 0.99 .........   (70 times)   which is 0.99 ^70   = 0.494   i.e. roughly 50%   or 1 in 2 

So if there is a    50 % probability that an earthquake >M5 will not happen for 70 consecutive days then there will also be a 50% probability that there will be an earthquake >M5 occuring in a consecutive 70 day period.