# Can a 99.9% probability of an M≥ 5 earthquake within a 3-year period be verified?

Paper:

Obviously there has been much discussion on the viability of earthquake prediction. This recent paper presents some rather bold claims:

The calculated probability for a M ≥ 6 earthquake within a circle of radius 100 km, and over the 3 years following 1 April 2015, is 35%. For a M ≥ 5 earthquake within a circle of radius 100 km, and over the 3 years following 1 April 2015, the probability is 99.9%

On the other hand, the USGS is saying those figures are too high:

The USGS conducts its own look at quake risk in California — the most recent version is called Uniform California Earthquake Rupture Forecast, Version 3. Jones said that, according to those models, there is only an 85 percent chance of a magnitude 5 or 6 quake in the same region over a three-year period. "It's nowhere near a 99.9 percent number," Jones said. USGS released a statement on its Facebook page saying that the lack of details on how this number was reached "makes a critical assessment of this approach very difficult."

The LA Times has it reported here: http://touch.latimes.com/#section/-1/article/p2p-84786019/ , which says:

The study’s lead author, Jet Propulsion Laboratory principal research scientist Andrea Donnellan, said in an interview that the 99.9% figure was not a central conclusion of the paper and should not be viewed as an official forecast. “As scientists, we were not putting out an official forecast. We were putting out something in a paper to test,” Donnellan said. Donnellan said she considers the 99.9% number a test of a model, or algorithm, on the probability of future earthquakes. “We never said in this paper we were predicting an earthquake. And we said that's the probability of an event," Donnellan said. "There is still a 0.1% chance it won't happen. So we need to test it. And that's what we are doing as scientists."

Has anyone verified this study? Is there anything wrong with it? How were they able to arrive at such a high probability?

• I don't understand your last question. They explain how they get to that probability on page 7. In the very paper you linked to. So what are you actually asking? And the corrected article has been online for 15 days, the original for only 2 months. Which isn't much time to verify a paper (unless you can normally produce a confirmation paper and get it published a handful of weeks - can you? Link please.) Did you do any search for papers that cited it? Oct 22 '15 at 3:36
• 85% or 99%, basically it is going to happen. Remember, EQ's in the 5 range happen fairly often and are not that big a deal. The more interesting prediction is the 35% for a major EQ in the 6 range. We are overdue for one of those by a number of measures. Oct 22 '15 at 16:59
• For anyone looking into model verification, Oreskes, et al. (1994) Verification, Validation, and Confirmation of Numerical Models in the Earth Sciences. is worth a read. The take home message: Verification of earth system science models (or any model really, in the extreme) is not possible, since we only ever really have one replicate, and the answer is boolean (it did happen or it didn't happen). That last quote just seems stupid to me. I'm with Aabaakawad though - if I had a >80% prediction that I thought was reliable, I'd start preparing regardless. Feb 11 '16 at 0:31
• I am a bit late to the party, but wanted to add some things. Well there are formal ways to evaluate binary probability forecasts, for example the Brier score which are well used in meteorology and related disciplines for decades. On the other hand, evaluating this one single forecast means that the sample size is exactly 1, so inference based on this very small sample is questionable. Regarding the question how they arrive at such probabilities, there is extensive use of numerical models, see for example the work at SCEC Apr 14 '16 at 8:34

Based on Probabilistic Seismic Hazard Analysis the probability of an earthquake of magnitude $m$ occurring at the source is obtained with the Truncated Exponential Distribution can be given by

$$P(M > m) = \int_{m}^{m_{max}} \frac{\beta e^{-\beta (m - m_{min})}}{\left( 1 - e^{-\beta (m_{max} - m_{min})} \right)}dm$$

where :

$m$ is the magnitude; $m_{min}$ is the minimum magnitude of earthquakes in source; $m_{max}$ is the maximum magnitude of earthquakes in source; $P(M > m)$ is the probability of occurrence of an earthquake with magnitude $M$ larger than $m$; $\beta = b \ln(10)$; $b$ is the slope in the Gutenberg–Richter (G–R) magnitude–frequency relation.

Additional Read : Gutenberg Richter Law - why exponential distribution was used

• Thanks for the equation... but could you answer the question?
– f.thorpe
Dec 12 '15 at 12:48
• If you have some background in statistics you can set lower and upper bounds and use this equation to calculate probability within some margin of error .This will also depend on the number of samples you have in that interval. Also It seems to me that your doubt is concerning some lines in the last paragraph.could you point out exactly which line ? Dec 12 '15 at 16:32