Astroblog

Two months ago I wrote a somewhat scathing critique of Mensur Omerbashich's unpublished paper “Astronomical Alignments as the Cause of ~M6+ Seismicity” http://arxiv.org/abs/1104.2036. To remind you, the paper claims to show that astronomical alignments, particularly that of comet X1 Elenin, are the proximal cause of earthquakes of magnitude 6 or stronger.

Dr. Omerbashich has recently put out a revised version of his paper, does it improve on the previous versions?

The answer is no, it raises more questions than it answers, although it answers some things (but not in a good way).

Gravitational shadowing: I now know what "gravitational shadowing" is. Mensur Omerbashich speaks of resonance patterns caused by "gravitational shadows" passing Earth. It turns out that the Good Doctor doesn't like Newton or Einstein, and has formulated a theory where gravity is a repulsive force, and that attraction between objects is due to the objects blocking the repulsive gravitational force (the explanation of "gravitational shadowing" is up the back of this paper on scale invariance).

Now, Einstein's theory has been tested to high levels of precision, and the frame dragging effect has been experimentally measured, so I'm not sure we need a repulsive theory of gravity. Still, for our purposes Omerbashich's theory reproduces the tidal effects seen with Newtonian/Einsteinian gravity, so we can use tidal force calculations in testing his theory.

The Metaphor: Dr. Omerbashich often uses the metaphor that his resonator effect to that of a group of soldiers marching in lockstep across a bridge, causing damaging resonances in the bridge. Well, imagine the Moon is a 70 Kg soldier marching along (his footfalls are the 14.7 day Full Moon-New Moon interval, see here). Adding further "soldiers" marching with the same footfall pattern and you can build up a resonance.

The problem here is the mass and periods of the other astronomical objects. Imagine marching with the soldier is an an ant. The mass of the ant is far too small to add to the resonance, and on the other critical issue, the frequency of its footfalls will not match the soldiers. AND that ant is 10 times more massive in relation to the soldier than Elenin is to the Moon. In terms of tidal force, which is what counts, Elenin is more like a bacteria, the ant is roughly the relationship between Venus and the Moon in terms of tidal force.

Now, it is just a metaphor, and we shouldn't push it too hard, but it does help think about the relative masses and periods of astronomical objects in relationship to the Earth and its alignment.

Mercury, Venus and Earth on 20 April 2010, according to Mensur Omerbashich, this constitutes an alignment.

Alignments: It's still not clear what constitutes an alignment in Omerbashich's paper. That is, how close do two objects have to be in the sky for them to significantly contribute to the resonance effect (is the ant marching with the soldiers, or behind them, and how far behind will work).

It is not explicitly stated in the paper, but looking at what he actually presents as "alignments", an "alignment" is a very large piece of territory.

For example, the "Earth-Mercury-Sun-Venus" alignment of 3 January 2010 (see table 1 of the paper), the "alignment" occurs with the planets within a circle centered on the Sun which is 4 degrees in radius. To put this in perspective, it's a chunk of sky 16 full Moons in diameter, you could cover it with your outstretched hand. This is an enormous chunk of territory to claim an alignment over (the September 3 alignment is also 4 degrees in radius).

Remember tidal force/"gravitational shadowing" falls off as the cbe of the distance, but also depends on the vector angle (this is why high tides are higher during Full/New Mooon than First/Last Quarter Moon), so angular separation is important.

Worse, Omerbashich calculates his alignments from the JPL Orbital Solution program, rather than an actual analytical astronomical program. His errors are +/- 1 degree, which is astronomically enormous (an error of +/- two full Moon diameters). So the alignments are not guaranteed to be meaningful. For example, in the April 13 "alignment", the Moon is 15 degrees from the Sun, and Mercury, Earth and Venus are over 5 degrees apart, by April 20 the "alignment" of Mercury, Earth and Venus is 12 degrees apart (see image above).

As well, there are a couple of errors in listing alignments that make them look better than they are. For example, the Full Moon is shown as occurring on February 27, at the same time as the Magnitude 8.8 Earthquake in Chile, but the Full Moon (and closest Earth-Sun-Moon alignment) was on February 28 at 16:38 UT, while the Chilean Earthquake was at 6:34 UT on February 27. Other errors that I noted in my first post have not been fixed.

This is the alignment of June 12 (Earth-Sun-Moon, Earth-Uranus-Jupiter) as noted by Dr. Omerbashich, it makes no sense from Omerbashich's own hypothesis.

Furthermore, in terms of the metaphor of soldiers marching in lockstep, some of the alignments are at cross purposes.

Any three (or more) bodies in more or less a straight line constitute an alignment, but many times one alignment is at a significant angle to the other.

For example, in the June 12 alignment, the Earth, Jupiter, Uranus alignment is almost at 90 degrees to the Earth, Sun, Moon alignment.

Now we know that the highest high tides occur when the Moon and Sun are in alignment, and the lowest high tides occur when the Moon and Sun are 90 degrees from each other. The same principle should occur here. In terms of the soldier metaphor, it's like the soldiers are marching 90 out of phase, breaking the lockstep.

What's still missing: Dr. Omerbashich ignored lot of solar system territory in his alignments. It was unclear in his initial paper why the focus was the tiny comet Elenin, rather the the other comets of 2010, like the spectacular Hartley, or the plethora of much bigger asteroids. His reasoning is that anything with an inclination of greater than 1 degree to the plane of the ecliptic can't form long alignments (3 days plus) with other planets.

However, by this criteria, there are 11, 903 known objects in the solar system capable of doing just that, like 24 Themis, a 193 Km diameter asteroid far more hefty than wimpy Elenin. It forms a nice long alignment with Venus and Earth centered on September 15, and a Saturn-Sun-Earth-Themis alignment centered on September 30. Yet these are not considered despite Themis producing a larger "gravitational shadow" than Elenin.

As well, He's still claiming that Elinin is dragging around a mass of gravitationally locked particles, but this is the coma, a feature of all comets that approach the Sun closely, (comet 81P Wild had a coma of 50,000 Km and 103P Hartley had a coma of 150,000 Km). The coma is not gravitationally locked, but is dynamic, being continually renewed as particals are lost to space.

Testing the hypothesis: Dr. Omerbashich doesn't test his hypothesis beyond showing there are alignments with earthquakes at roughly the same time (he claims that the numbers are too small for statistics, which immediately raises a red flag).

But the null hypothesis is not "there will be no earthquakes in the absence of alignments" but "earthquakes will occur randomly with respect to alignments". After all, geologists and geophysicists have their own explanations for earthquakes (plate slipping and plate subduction), for which there is some degree of evidence.

Now, some of the alignments do coincide with earthquakes, but is it more than you would expect by chance alone? Our intuitive sense is a very poor guide to answering statistical questions, so we have to be a bit rigorous here.


One of these graphs represents real data from a year of earthquakes, and one is simulated through random number generation. Can you tell which is which (click to embiggen, answer below at [*]).

In my original post I showed that the frequency of earthquakes during Full/New Moon alignments were no different than you would expect by chance, and that the Full/New Moon alignments had no more earthquakes than the First/Last Quarter Moons, which is not what would be expected under Omerbashich's hypothesis.

For this post I generated a random distribution with the frequency of 6+, 7+ and 8+ earthquakes based on the 10 year average for these earthquakes.

Remember, in any given year there are 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 +/- 1 days of that (the window used by Dr. Omerbashich) you will almost certainly, on average have at least one quake of magnitude 6-6.9 in that date range and a roughly 13% chance of having a larger magnitude quake in that time slice.

The resonance patter seen as a gravitational shadow transverses Earth. Or is it?

I generated random "earthquakes" for 365 days then dropped the dates of Omerbashich's alignments on them.

Not surprisingly, a lot of the alignments had "earthquakes" associated with them. The image to the left is for a typical association. It looks as if the earthquake magnitude rises with time, just like in the (badly flawed) figure 1 of Omerbashich's paper. But of course we are just seeing a random association with simulated data.

This rather graphically establishes that Dr. Omerbashich's results are no more than chance associations. You can do Chi Squared tests as well, to show that the distributions are just what we expect by chance alone, but those are kind of dry. Is there another way to demonstrate that Omerbashich's results are just chance?

Fourier Analysis: We can use Fourier Analysis. I reported the results in my previous post but didn't show the graph. I do so now. Fourier analysis is the standard way to extract signals of cyclical phenomena from noisy data. Usefully, it can pull out multiple periods from a single data set.

The canonical astronomical example is Fourier analysis on Sunspot data to find the periodicity of sunspots (see http://linuxgazette.net/115/andreasen.html and scroll down to example 2).

Another use which is even more relevant here is extracting the orbital period of exoplanets from doppler shift data (heck, it was even used back in 1805 by Gauss to find the periods of the Orbits of Pallas and Juno).

So what we are trying to find in the earthquake data is the periodicity associated with the Earth- Moon-Sun alignments, Earth-Mercury-Sun alignments , Earth-Venus-Sun alignments and so on. Long period alignments won't turn up in Fourier analysis with the amount of data we have, but the short period ones will. Importantly, I'm talking about the periodicity of the alignments, not the length of the alignments. Mercury and Venus produce long alignments as per Omerbashich, but occur quite frequently.

Now, again I emphasize that the data will be noisy, we don't expect a M6+ earthquake every alignment, nor do we expect the earthquakes will occur precisely at times of maximal tidal force/"gravitational shadowing". But again, that's the point of Fourier Analysis, it can pull out patterns out of noisy data.

In the 11 year data set from 2000 to 2010 there are 264 Earth-Moon-Sun alignments, 69 Earth-Sun-Mercury alignments, 14 Earth-Venus-Sun alignments and 20 Sun-Earth-Jupiter alignments (alignments calculated using SkyMap, earthquake magnitude data from here).

If these alignments play any significant role, as Dr. Omerbashich claims, then we should recover these periodicities in an 11 year data set (for example, I can recover the 11 year sunspot cycle from a 32 year data set - this is short data set compared to the signal).

Even if the Moon signal is relatively weak, with 264 alignments the peak should stand out (I can recover this peak in a single years tidal records using Fourier Analysis). Mercury should stand out like a sore thumb. And Earth Moon Sun signal should be particularly strong if Omerbashich is correct. Dr. Omerbashich himself picked up the Moon periodicity in superconducting gravimeter data (see this paper, figures 4 and 5), so if this translates to earthqukes, as he claims, it should show up.

Left image, Fourier analysis plot of 11 years of daily earthquake data (2000-2010). Right image Fourier analysis of one year of tidal data (click to embiggen).

As you can see, there are no peaks in the earthquake data. In contrast the 14.7 day Moon periodicity is readily recovered in the one year tidal dataset.

Impotantly, in the tidal data set, even though there is always a highest high tide, its timing and magnitude are variable. The fact that we can pick up the Moon peak out of a short, noisy data set is a positive control for the Earthquake dataset.

If, as Dr. Omerbashich claims, the majority of M6+ is due to astronmical alignments, we should recover some of these patterns from a 11 year data set. We don't, we can't even see the Moon. suggesting any influence of astronomical alignments on earth quakes is very small.

Summary: Analysis of earthquake data stes show that the apparent corrleation between earthquakes and astronomical alignments is by chance alone. The effect of comet Elenin on earthquakes is non-existant, whihc is only to be expected, you would hardly expect a bacterium marching in lockstep with a soldier to break a bridge, would you?


[*]Which distribution is real and which is random? Data 1 is the earthquake record for the year 2000, and data 2 is the randomly generated data.

Labels: comets, Pseudoscience