Monday, March 21, 2011

In the Aftermath of the March 19 “Supermoon”

Not much happened, no major earthquakes, or clusters of minor earthquakes. Well, astrologer Richard Nolle actually cleared up his definition of what a “supermoon” is (compare with the wording here).

It turns out it’s any full Moon with a perigee closer than 361585 Km (a bit closer than the average perigee distance of 357372 Km). The justification for this distance is pretty much non existent, but even the closest “supermoons” have a tidal force only 4% greater than the “supermoon” cutoff. Also, recall that in Astronomical terms “Full Moon” is when the Sun and Moon are exactly aligned. For us ordinary folks wandering out in the evening, Full Moon is from Moonrise to Moonset on the night of the Astronomical Full Moon and I think this is the form of “Full Moon” that Nolle is using. In terms of wandering out and looking up at the Moon (and failing to see any actual difference without a telescope and a photographic record), this is perfectly okay.

However, in terms of earthquake generation, the alignment of the Moon and Sun is critical. You can imagine that the flexing of the Earth as the lithosphere tide (all 30cm of it) passes through the Earth might set off an earthquake that was already “ready to blow” as it were. Indeed, there is a week correlation between the lithospheric tides associated with Full/New Moon and a subclass of shallow earthquakes (increasing the probability of this subclass of earthquakes by less than 1%).

Buuuutttt. Remember a) the tidal force falls off the cube of the distance and b) the tidal bulge (both oceanic and lithospheric) depends on the sum of the Solar and Lunar tidal force and c) the further perigee is away from Astronomical Full Moon (when the Moon and Sun are exactly aligned), the Lunar tidal force opposes the Solar tidal force (that’s why neap tides, at the quarter Moon, when the Moon and Sun are at 90 degrees, are lower than the tides at full and New Moon when the Moon and Sun are aligned). So even if a “supermoon” has a perigee closer than average, if the perigee time is far from the alignment with the Sun, the tidal force (which is less than 5% greater than average anyway) will reduce the tide size rather than enhance it). Many of the “supermoons” listed by Mr. Nolle are not very super after all.

Chart of "supermoons" vs earthquake date for 2010, with "supermoons" marked. No alteration of earthquake pattern with "supermoon" status is seen (click to embiggen)

For example, Mr. Nolle lists the February 27, 2010 Full Moon as a “supermoon”. It is is 357831 Km away (about 3% greater tidal force than Nolles cut-off). But perigee occurs 18 h before the full Moon so the overall tidal force is lower.

Now Mr. Nolle points out that the February 27, 2010 Full Moon occurs not far from a 8.8 magnitude quake. However, in any given year there are 1319 quakes between magnitudes 5-5.9, 134 earthquakes of magnitude 6-6.9 (this includes the earthquake that demolished Christchurch), 15 earthquakes of magnitude 7-7.9 and 1 earthquake of 8 or greater. So, choose any random date and within +/- 3 days of that (the window used by Mr Nolle) you will almost certainly, on average have two-three quakes of magnitude 6-6.9 in that date range and a roughly 25% chance of having a larger magnitude quake in that time slice. So just having one magnitude 6 or greater earthquake near a supermoon is not particularly surprising. Indeed, in 2010 there are 4 “supermoons” and 1 “extreme supermoon” (Perigee of 356592 Km 2 h after full Moon), none of which are associate with any earthquakes more than we would expect by chance (see chart above). The complete lack of any significant activity associated with the January 30 “extreme supermoon” is telling.

Mr. Nolle has a number of examples of Full Moons near earthquakes, but again this is just cherry picking, we expect some to turn up by pure chance alone. Mr. Nolle emphasises that the Christchurch magnitude 6.3 earthquake is in his time range around a "supermoon", but you would expect at least 2-3 magnitude 6 or greater quakes in that time frame (and there 3 in this range, exactly what you would expect by chance). By ignoring all the Full/New Moons that are not associated with earthquakes you can make it look as if there is an associate where there isn’t one.

I’ve plotted the frequency of all earthquakes of 5 or greater in 2011, showing the times of New and Full Moon, and apogee and perigee (see diagram at the top of the post, the yellow symbols are full/New Moon, blue symbols times of Perigee/apogee). If Mr. Nolle is right, we should expect more earthquakes around aligned Moons near perigee, if fact you can see there is no association at all. The big earthquake that devastated Japan occurred just off apogee, during first quarter, when the tidal force was quite low.

We might also expect that earthquake magnitude would correlate with perigee closeness (when the tidal field is strongest), so I plotted the magnitude of all quakes in 2011 (up to the first Japanese quake, after that he subsequent quakes are aftershocks from the main quake, and not independent) against the lunar distance at the time of the quake (to the nearest minute).

I have shown the regression line and its 95% confidence limits. The line slope is not statistically significantly different from zero, ie there is no relationship between earthquake magnitude and lunar distance. To do this properly, you need to calculate the total Sun-Moon tidal force and use more data points (I leave that as an exercise for my readers, times of perigee and full/new Moon from Inconstant Moon, Distance at UT time from SkyMap, Earthquake data here), but any association as obvious as Mr. Nolle claims would stand out).

The distribution of days +/- 1 and +/-2 days from Full and New Moon. By chance alone we would expect 3-4 out of 10 super-earthquakes to occur within +/- 2 days of a Full or New Moon.

Our statistical sense confounds us sometimes. One of the Bad astronomer’s commenter’s pointed out that of the 10 most severe earthquakes 3 occured within +/- 1 day of the full/new Moon, and 2 more within +/- 2 days of the full/new Moon, as if this indicated an association.

But assume mega-earthquakes fall randomly anywhere in a given month. In any given month there are two Full/New Moons, +/- 1 day gives you 6 days possible days where it could fall, a 20% chance of a random quake being +/- 1 day near a Full/New Moon. There are 10 days within +/- 2 days of Full/New Moon, giving a 33% chance of a random Earthquake being within +/- 2 days of Full/New Moon. Thus the observed frequency of mega-quakes near Full/New Moons is pretty much what we would expect by chance.

So, the “supermoon” was beautiful, but not baleful, despite Mr. Nolles dire predictions.


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