*This post is authored by Nate Taylor.*

Recently, equally great statesmen Kim Jong Un and Donald “Jong” Trump met in Singapore for a brief discussion on how they plan to split their Nobel prize winnings, their favorite burgers, and (assuming they got to it) the complete, verifiable, and irreversible dismantlement (CVID) of the Korean Peninsula. The lack of specifics notwithstanding, if CVID were to happen, South Korea and its partners would require as much insight as humanly possible about the nature and extent of the North Korean nuclear arsenal.

Unfortunately, the best source of information we have on North Korea’s nuclear capabilities are the distant rumblings of North Korean nuclear tests picked up by seismic monitoring stations belonging to the Comprehensive Test Ban Treaty Organization (CTBTO)’s International Monitoring System (IMS), the United States Geological Survey (USGS), or NORSAR (a Norwegian seismological monitoring organization with a mandate to monitor for nuclear explosions). Seismologists measure these rumblings using a measurement known as “mb” or “magnitude of the body wave.” (The richter scale has fallen out of fashion.) If these waves are the result of a nuclear explosion, seismologists can use a number of techniques and equations to derive a yield estimate from their seismological measurement. Here is one such equation, which is used by NORSAR to estimate the yield of North Korean nuclear tests:

mb = 0.75log(yield) + bias correction

It’s important to remember how the equations relating seismic signal to nuclear yield were developed. This 1988 OTA report sums up the process in chapter 7 “Estimating the Yields of Nuclear Explosions.” The “bias correction” is a correction for the geologic conditions of *specific *nuclear test sites. The U.S. first developed its yield estimate equations using nuclear explosions at its Nevada test site, i.e., scientists would detonate an explosive device with a known yield, measure the seismic signal, and then come up with an equation to fit the seismic signal to the yield.

But if the U.S. tried to use the same equation it developed for the Nevada test site to measure an explosion from Russia’s nuclear test site in Semipalatinsk, then it would end up overestimating the Semipalatinsk yield because the geologic conditions around Semipalatinsk are quite different. Specifically the upper mantle around the Nevada test site is hotter than the mantle around Semipalatinsk. A hotter mantle means a more elastic mantle, and a more elastic mantle means greater seismic vibration absorption.

So how does one create an equation suitable for Semipalatinsk? In 1988 the Soviet Union sent a team of scientists to Nevada, and the U.S. sent a team of scientists to Semipalatinsk to create and verify equations calibrated to one another’s test sites. These experiments were known as the joint verification experiments (JVE). They were done to facilitate the ratification of the 1974 Threshold Test Ban Treaty (TTBT), which limited all nuclear tests to less than 150 kilotons. It had been signed by the Soviet Union and the U.S., but not ratified because neither side trusted the other not to cheat. The JVE satisfied both sides’ concerns, and the TTBT went into force in 1990.

But back to North Korea. The CTBTO, NORSAR, and the USGS all have different mb measurements for each of the North’s declared nuclear tests. (It should be noted that nuclear test monitoring is not part of USGS’s mandate. The Air Force Technical Applications Center is the US government agency directly responsible for nuclear test monitoring, but does not release its findings to the public.) NORSAR assigns a bias correction of 4.3 (so the full equation is mb = 0.75log(yield) + 4.3), the same as for the Novaya Zemlya test site in Russia. Through the magic of spreadsheets we can make the following chart:

Before we move on, it’s important to note that neither the CTBTO, nor the USGS makes official yield estimates. The USGS does not make yield estimates because their mandate is seismic activity. The CTBTO does not make yield estimates because the CTBTO, per *its* mandate, treats all nuclear explosions as equally serious regardless of their size. So, to be clear, the USGS and CTBTO yield estimates are not “officially” from the USGS/CTBTO, rather they are the result of me plugging their mb estimate into NORSAR’s yield estimate equation.

But back to the chart, seems simple right? The values are *basically *in line with what you’d expect. The first test explosions are tiny by nuclear weapons standards, and increase as the program gets more advanced over time, ending with a test that’s an order of magnitude larger than the previous tests, lending credence to North Korea’s claim that it was a two-stage thermonuclear device. The yields derived from the USGS’s mb estimates are higher than the other two organizations’, but not by too much, save for one notable outlier. For North Korea’s most recent test, the USGS-derived yield stands at a whopping 464 kt as opposed to the more reasonable seeming (but still high) yield of 250 kt derived from the CTBTO and NORSAR’s mb estimate.

To understand how a small difference in mb input could lead to a large difference in yield output, let’s rework NORSAR’s equation so the yield is on one side, and graph the relationship between yield and mb. I’ve also indicated where each organization’s mb estimate for each test falls on that graph.

Y=10^((mb-4.3)/.75)

Now we can clearly see how a small change in our mb input can have a drastic effect on our yield output, *especially *once we get up above input mbs of around 5.6. (We can also see that while Kim 3 was indisputably larger than Kim 2, there is disagreement as to whether Kim 4 was larger than Kim 3.) This is all from an equation developed for another test site, and which assumes that each explosion was carried out at a standard minimum burial depth of 120 meters.

But none of the DPRK’s nuclear tests took place at a depth of 120 meters, they in fact took place at depths greater than that, and at depths that we can now estimate with a fair degree of accuracy. A recent and exciting development in the field of obsessing over North Korean nuclear tests was North Korea showing journalists a map of the Punggye-ri test complex with authentic locations for each test. This was done in accordance of the North Korean tradition of every ten years gathering journalists to watch it blow up a piece of nuclear infrastructure it no longer needs.

By using this map, and digital elevation data gathered by NASA and Japan’s Ministry of Economy Trade and Industry (METI) from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) mission, we can estimate to a reasonable degree of certainty the depth of burial of each nuclear test. Here is the 3D model I made, using the ASTER data gathered on the Punggye-ri test site, to estimate the depth of burial for each test.

Now what use is knowing depth of burial if our yield estimate equation doesn’t take depth of burial into account? In 2013 two Chinese researchers, Miao Zhang and Lianxing Wen, created an equation with steps taken to more precisely calibrate it to the North Korean test site and to take depth of burial into account. I should note here, that as a non-expert in seismology, I am in no way qualified to comment on their methods for calibrating the equation. I am making the assumption that, because it was published in a respected peer reviewed publication, their conclusions and methods are sound. Here is their equation:

mb = 1.0125log(yield) – 0.7875log(depth) + 5.887

If we plug in the CTBTO’s mb estimates we get the following chart (I’ve included the NORSAR equation yields for comparison’s sake).

The first thing we notice is that Zhang and Wen’s equation are giving us higher yield results overall. To understand Zhang and Wen’s equation a bit better, let’s plot how Zhang and Wen’s yield estimates vary with mb input, and compare it to how NORSAR’s equation varies according to mb input. (Note: I set the depth for Zhang and Wen’s equation to a constant 650 meters.)

So we can see that Zhang and Wen’s equation will tend to give us higher values at the lower end of the yield spectrum, and lower values at the higher end of the yield spectrum. Overall, we see a similar level of sensitivity to mb input as NORSAR’s equation that gets higher as the mb inputs get larger. Now let’s see how Zhang and Wen’s equation varies with depth, when you keep the mb input constant.

This graph tells us that Zhang and Wen’s equation responds more (though not perfectly) linearly to depth of burial variation. This does not mean that we shouldn’t be as precise as possible when determining our burial depth, but it does tell us that an error in burial depth couldn’t be responsible for an error approaching an order of magnitude, whereas an error in mb can. It also tells us that the ASTER data’s vertical margin of error of 17 meters should not have a huge effect on our yield estimates.

So what’s the right answer? Which equation should we be using? I’m going to avoid the always annoying answer of “it depends,” and instead respond with the possibly more annoying “we shouldn’t be thinking of it in those terms.” These equations serve two purposes for the nuclear wonk who isn’t a seismology expert: (1) they let us know that the DPRK’s last (and hopefully final) test was an order of magnitude larger than the previous tests, (2) they loosely bound our yield estimates, and (3) show a pattern of generally increasing yields over time.

So we find ourselves, as we often do in this type of analysis, back where we started, with a wide range of estimates and few ways to bound them further, but with a better idea of *why *we can’t bound them further. We can certainly make informed speculation (who’s going to stop us?) as to which end of the bound the yield most likely was based on our assessments of North Korean nuclear weaponeering ability, and North Korean fissile material stocks.

How much does the precise yield really matter? As a final macabre note, it is worth noting that the difference between a 200 kt burst and a 300 kt burst isn’t as big as one might think. According to Alex Wellerstein’s Nukemap, a 200 kt airburst in the middle of Manhattan would kill around 1,000,000 people, and a 300 kt airburst would kill around 1,200,000 people. This difference would obviously matter to those 200,000 people, but it doesn’t provide North Korea with any additional deterrence value. The devil here, it seems, is at the strategic level, not in the details.

Citations:

Hecker, Siegfried S, editor. *Doomed to Cooperate*. Vol. 1, Bathtub Row Press, 2016

U.S. Congress, Office of Technology Assessment, eism”c Verification of Nuclear Testing Treaties, OTA-ISC-361 (Washington, DC: U.S. Government Printing Office, May 1988)

“Summing up the Nuclear Test in North Korea on 3 September 2017.” *NORSAR*, NORSAR, 22 Sept. 2017, www.norsar.no/in-focus/summing-up-the-nuclear-test-in-north-korea-on-3-september-2017-article1554-863.html

“Summary of DPRK Nuclear Tests.” *CTBTO*, CTBTO, Sept. 2017, www.ctbto.org/the-treaty/developments-after-1996/2017-sept-dprk/

“M 6.3 Nuclear Explosion – 21km ENE of Sungjibaegam, North Korea.” *U.S. Geological Survey*, U.S. Geological Survey, earthquake.usgs.gov/earthquakes/eventpage/us2000aert#executive

Zhang, M., and L. Wen (2013), High-precision location and yield of North Korea’s 2013 nuclear test, Geophys. Res. Lett., 40, 2941–2946, doi:10.1002/grl.50607c

Wellerstein, Alex, “Nukemap,” accessed 1 June 2018, http://nuclearsecrecy.com/nukemap/

Test site map courtesy of Michael Greenfield (@SkyGreenfield) and Sky News.

Nice article!

And I can see that you make good use of Python ;-). Very useful tool.