Guest Post by Willis Eschenbach [Graphs updated to include error bars]
Inspired by the paper by the charmingly-named Maya Tolstoy discussed here on WUWT, I decided to see if tidal forces affect the timing of earthquakes and volcanoes. Dr. Tolstoy’s hypothesis is that tidal forces affect the timing of the subterranean eruptions … but she has only nine “events” (either eruptions or lava flows) to test her theory. On that thread I said I thought her hypothesis was wrong, but I hadn’t looked at the data.
I figured that IF, and it’s a big if, tidal forces are affecting volcanoes, they’d also affect earthquakes. So I decided to start by seeing if there is a relationship between the tidal forces and earthquakes by looking at as many earthquakes as I could find.
For the calculation of the tidal forces, I started by going to the marvelous JPL Horizons ephemeris. I set the variables as follows for the Sun. For the Moon I just changed the “Target Body”.
Figure 1. Settings for the JPL Horizons ephemeris to obtain the instantaneous distances in the X, Y, and Z directions of the sun/moon as seen from the center of the earth.
With the X, Y, and Z variables, I calculated the individual tidal forces from the sun and moon (see “TIDAL MATH” below), and added them as vectors to give the total tidal force. I calculated the tidal force on a “per kilogram” basis. Here is a sample of the results showing recent tidal forces:
Figure 2. Daily combined sun-moon tidal forces, 2010-2014.
Some comments on Figure 2. First, on a per-kilogram basis the forces are small. One grain of sand exerts a force of about 40-50 micronewtons downwards under earth’s gravity. I weigh about 70 kg, so the tidal forces make my weight vary at the equator (the Earth’s equator, not mine) by about 3 grains of sand … however, the total tidal forces are large because the earth has a very large mass.
Next, note that as you’d expect, the peaks in Figure 2 are not aligned with the calendar year. Instead they shift slowly through the calendar year over about an eight-year cycle. This means that we should not expect to see any annual variation in earthquakes by month. And this is the case for this dataset, monthly earthquake counts only vary by ±4% (not shown). In addition, note the rapidity of the changes. These cycle every lunar month, which is about twenty-eight days.
Having calculated the tidal forces, I got a database of all large (>5) earthquakes since 1900 from the US Geological Service. To examine the distribution of the data, I took a histogram of the tidal forces on the actual dates of the earthquakes, and I compared it to the full database of daily tidal forces during the same period. Figure 3 shows the results.
Figure 3. Distribution of tidal forces during earthquakes 1900-2007 (gold) compared to distribution of all daily tidal forces during the same period (red diagonal hatched).
As you can see, the answer is clearly NO. The histogram of the tidal force at the times of the earthquakes (gold) shows the same double-peaked distribution shown by the full tidal dataset (red hatched). There is no overall relationship between earthquakes and tidal forces.
Next, I wanted to examine volcanic eruptions. So I went to the Smithsonian Global Volcanism Program website and downloaded their eruption database. Using all confirmed eruptions with known dates back to 1800, I did the same thing with the eruptions that I did with the earthquakes. Figure 4 shows the results of that analysis:
Figure 4. Distribution of tidal forces during eruptions 1800-2013 (blue) compared to distribution of all daily tidal forces during the same period (red diagonal hatched). Errors adjusted to account for number of subsamples.
Once again, there is little difference between the two datasets. Yes, there is an exaggeration of the local peak of the tidal forces in the range 0.8 to 0.9 micronewtons (bottom scale), but given 95% confidence interval, that kind of variation is not unusual. Overall, volcanoes seem unaffected by tidal forces.
Now … why should this be the case, that the quakes and eruptions are NOT affected by the tidal forces? I mean, we know that the tidal forces cause tides in the ocean and in the atmosphere. And most importantly for this question, they also cause tides in the solid earth. These tides are on the order of about half a metre (a foot and a half) at the equator. So it seems logical that they would affect earthquakes and eruptions. My speculations about the reason they don’t seem to affect quakes and eruptions are as follows:
1. The tidal forces are always there, and are always rapidly changing. Vertical tidal forces go from local extreme to zero every six hours. As a result, any stable condition of the earth’s crust must be able to withstand the worst that the tides can do.
2. The forces basically affect all of any local area equally. The diameter of the earth is on the order of 13,000 kilometres (km) (8,000 miles). The earth tides are half a meter. Not half a kilometer. Half a metre. Figure 5 shows my drawing of how the tidal force operates on the earth. It is a stretching force that applies to land, sea, and air.
Figure 5. Tidal forces elongating a hypothetical planet and its ocean. The planet is free-falling into the sun, so there are no centripetal forces. Note that the planet is elongated as well, but this is not shown in the diagram because obviously, tides in the solid planet are much smaller than tides in the ocean. NOTE THAT THIS PLANET IS NOT THE EARTH.
Now, in Figure 5, the vertical motion due to tidal force is greatest along the line between the planet and sun. It goes to zero along the vertical plane that passes through the middle of the earth at a distance D from the sun. This is because the vertical tidal force is dependent on “r”, which varies from place to place and time to time on the actual earth (for the calculation see “TIDAL MATH” below).
As a result, any point on the earth goes from high vertical tidal displacement (for that point and time) to no vertical tidal displacement in six hours. Now, that six hours is a quarter of the circumference of the earth, which is about 10,000 km (6,200 mi). And over that distance of 10,000 km, we have a difference in elevation of half a metre. This is a vertical deflection of one part in twenty million … a very, very small amount
And that in turn means that per horizontal kilometre, the average difference in equatorial elevation due to tidal forces is five-hundredths of a millimetre, with a global maximum of about eight-hundredths of a millimetre. That small amount of deflection, one part vertical for each twenty million horizontal, means that the change in elevation is very, very gradual. And as a result, the entire local area is being affected pretty much equally.
Anyhow, that’s my explanation for the fact that although the earth is incessantly flexing from the tides, it doesn’t seem to affect the timing of earthquakes and eruptions as a whole. It’s because the flexing (by global standards) is both small and gradual.
2 AM … gotta go outside and see what the storm did. Raining all day here, and I’m happy about that …
Regards to everyone,
w.
THE USUAL REQUEST: If you disagree with someone, please quote the exact words that you disagree with. That way, we can all see exactly what you are objecting to.
UNANSWERED QUESTIONS: Is there a tidal connection to the number of very small earthquakes (microseisms)? Do big earthquakes have a tidal connection? How about big eruptions? As with any investigation, each answer brings new questions … so please, don’t bust me for not answering all of them or assume I’m not aware of them.
TIDAL MATH: The tidal force operating on a one kg mass at a point at a perpendicular distance “r” as shown in Figure 5 is given by
T = 2 G * M * r / D^3
where T is tidal force (newtons), G is the gravitational constant, D and r are as in Figure 5 (metres), and M is the mass of the sun (kg).
MY PREVIOUS POSTS ABOUT THE TIDAL FORCES
Time and the Tides Wait for Godot
I’ve been listening to lots of stuff lately about tidal cycles. These exist, to be sure. However, they are fairly complex, and they only repeat (and even then only approximately) every 54 years 34 days. They also repeat (even more approximately) every 1/3 of that 54+ year cycle, which is…
Short Post. You can skip this if you understand the tidal force. Some folks seem confused about the nature of tidal forces. Today I saw this gem: “The tide raising force acts in both directions (bulge on each side in the simplistic model)” … the author of that statement may…
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Further evidence that volcanism isn’t periodic related to the year… astrology.
If it was true then someone in some civilization at sometime would have already made the claim. People notice volcanoes and earthquakes.
It’s a dog that doesn’t bark, If there was a hint of truth in this claim then it would have been discussed for thousands of years,
Suggest you Google “cyclicity in earthquakes and volcanism” for a sample of the voluminous literature on periodic behavior of these two phenomena.
Thanks, David, but I’ll pass. My custom is to let a man do his own googling. If you have a specific citation, please bring it forwards, and I’m more than happy to discuss it.
Regards,
w.
David
“[V]oluminous literature” does not necessarily translate to scientific analysis.
Half the fun of reading Willis’ posts is watching him respond to cogent stated disagreements about his analysis.
Please cogently state your disagreement so we can all watch…
David, I did, since my MO on this stuff (not other stuff where I am primary inventor) is to just see what is what. Most of the cyclicality papers you refer to are for specific volcanos or earthquake zones, and refer to cyclicality on geologic scales. For example, the 2011 Tohoku quake/tsunami was preceded by the 869 Sanriku quake/ tsunami in the same basic place, for which warning stones about the tsunami height reached still stand at Aneyoshi. So, can Japan relax for another 1150 years? Or, when might the next 1906 SF quake along the San Andreas fault occur, based on sediment core evidence of several previous quakes along the same fault in the same area at roughly equal intervals? ( which makes sense if slip/strike strain buildup is roughly linear with respect to roughly constant local tectonic movement.)
Not the same thing at all as Willis is investigating based on Tolstoy’s paper concerning tidal forces. Naming things can be tricky, deserving a whole chapter in The Arts of Truth, about critical thinking. Regards.
Guys you all have it wrong. Earthquakes are caused by immodestly dressed women!!
I have it from the highest authority:
Women to blame for earthquakes, says Iran cleric | World news | The …
http://www.theguardian.com › World › Iran
Apr 19, 2010 – Women behaving promiscuously are causing the earth to shake, … We cannot invent a system that prevents earthquakes, but God has created …
The Earth moved for me. Just saying’.
Well humans see the ocean tidal bulge on a regular basis, but we generally are comparing the water level movement relative to the land movement, which is considerable.
But stresses in the ground that might conceivably help in a slippage for an earthquake, or unplugging some volcanic magma “tube”, would be differential forces between one piece of rock and some spot nearby.
If the global ground tide difference is a half a metre over the entire diameter of the earth, then clearly the differential force between two spots in the rock that are a meter or even a 100 meters apart, is going to be totally miniscule.
We don’t see tides in a swimming pool or a small lake or reservoir, because the differential tidal force over the size of the lake is quite negligible.
The 500 mm movement of the ground over the diameter of the earth, would be microns over a rock of 1 km size.
g
Plate tectonics has a large input into volcanicity and earthquake frequency because they are connected geologically. But tidal forces on the earth between the sun and moon are too small, if your calculations are correct, to add any more heat to the tectonic mix. Tectonics works on heat and that heat is supplied by the radioactive decay of potassium, thorium and uranium in that order of heat supplied due to the quantities of each element not its radioactive content.
Earth’s tectonic plates are also resting on the very low-strength asthenosphere (http://www.geosci.usyd.edu.au/users/prey/ENG-1/HTML.Lect1/sld017.htm), which effectively decouples them from the vastly greater inertial mass of Earth’s subjacent spheres, thereby making them particularly susceptible to small, cyclical variations in tidal forces. Resonance effects could also be in play here.
My first response is why? The tidal forces are still miniscule relative to Earth’s lithosphere tectonic plates.
Consider that most if not all of the plates are well anchored along their convergent boundaries.
What is the effect of the huge amount of water (sitting on top of 70% of the tectonic plates) that does react to tidal forces? In other words, since tectonic plates are slip-slidin’ around, albeit s-l-o-w-l-y, and they are on top of earth’s waterbed, the asthenosphere, can these tectonic plates be assumed to be not affected by the weight of the water on top of them, water that does react like clockwork even in relatively infinitesimal distances to the forces of the moon, but react nonetheless? Has anyone measured this anywhere?
Ah. Just sawATheoK’s statement: “Consider that most if not all of the plates are well anchored along their convergent boundaries.” Not so anchored that they don’t produce ridges with lava from below. And I thought the Indian plate moved 2mm NE every year, pushing up the Himalayas.
I believe that is the low end estimate of India’s progress northward.
Consider, the entire subcontinent India is ramming the Eurasian continent, uplifting massive mountain ranges and definitively changing the climate. I would consider that boundary extremely well anchored. If you prefer, consider it intensively engaged.
Now splash it with a slow half meter of water current; a current that flows both ways almost equally in an East-West directions. How far do you think India has moved because water is flowing back and forth at right angles to India’s movement?
@ATheoK,
Yes, I can see that. But the Indian plate ‘anchor’ is destructive, isn’t it? And active, or at least more active, as a result.
and @Rud Istvan,
But what if they aren’t, Rud? Is that possible?
I mean, I’m asking dumb questions because I am dumb about this stuff. What if the earth doesn’t absorb these changes? What if they accumulate in off phases and trigger something? I’m almost embarrassed to hit the Post Comment button. Not almost, I am. But if I don’t ask, I’ll never learn.
Not only heat. For example, most quakes arise when the elastic strain exceeds the ‘friction’ along a fault. And volcanos when the buildup of magma pressure exceeds the (usually) preexisting rock plug force in the vents. The question is whether tidal forces can provide a ‘trigger’ to such events. Willis’ analysis says no. In hindsight, there may be two obvious reasons why. Most faults and plugs (and rift zones and subduction zones) are not roughly aligned with ‘stretching’ tidal force. So hardly even feel them. And, Earth spins pretty fast so the small tidal forces are just tiny periodic transients to most geologic features enabling quakes and volcanoes.
Interesting. The Earth is not a solid but has the crust, mantle (rigid and viscous), core (liquid and solid). The crust is 7 to 20+ miles thick. Earthquakes seem to be mostly crustal movements. What would a probability distribution of just the movement of the crust or can a model not be constructed how tidal forces effect the crust. Perhaps using CA seismic data stations?
Also, earthquakes and volcanos occur at the weakest (thinnest) part of that crust. Think about the Pacific ring of fire and subduction zones. Global averaging and normalizing does not consider these differences.
Except maybe for Bárðarbunga, Grímsvötn, and friends, who sit on about 40 to 45 km of crust (above the Moho)…
As a guess, tidal changes would have little effect on a strike-slip fault as compared to a subduction zone.
…. charmingly-named Anna Tolstoy …
Maya Tolstoy
Thanks, Vuk. Either Anthony or one of the mods fixed it for me as I slept, my continual thanks to them for the great work they all do for us here.
w.
+1!
I know a tick on a dog who really likes the moon.
He’s a lunar tick.
He will be ropable if someone delves into tides and neglects to mention the moon.
…paper by the charmingly-named Anna Tolstoy…
It’s Maya Tolstoy. (Perhaps you were thinking of “Anna Karenina”, a fictional character created by Count Leo Tolstoy.
This is an interesting, and counter-intuitive approach. I guess both the frequency and amplitude of the tidal input are too small to effect a couple with the forces which produce the majority of quakes. Such forces being related to plate tectonic drivers, as correctly noted above. I had always assumed there had to be some kind of connection, and we know what “assume” spells. I suppose 97% of scientist made the same assumption. BTW, such a triggering effect, if real, would apply equally to fault movement of all orientations, in reply to the comment directly above. Bloke must be in a different pub, or I would explain, with diagrams!
Really enjoyed this Willis, thanks.
I just hope Mr. Eschenbach takes more care with his analyses than he did with Maya Tolstoy’s name.
[fixed -thanks -mod]
Since you have not found any faults with my analysis, you resort to snark? Sorry, David, not impressed.
w.
David
As I said in an earlier response to one of your not very effective posts to Willis, keep picking away at him so the rest of us can watch…
I just hope you have more substance than simply correcting first names.
My first thought was that your methodology was invariant to time and location. There may be offsetting locations where earthquakes occur less often and others where there are more earthquakes.
So I googled “time of day earthquakes” and came up with this link: http://www.researchpipeline.com/wordpress/2012/10/08/earthquakes-vs-time-of-day/
He seems to have a mistaken idea on how tides work so he ends up over-binning his data and comes up with what I believe to be an incorrect conclusion. But it was an interesting alternative hypothesis.
I do not agree with some of the conclusions of Dr. Tolstoy (January-June, CO2 factor etc.), however in her earthquake presentation she talks of those in the deep oceanic trenches (specifically Marianna trench). Using a globally distributed earthquakes data base it may mask some of specifics of the ‘outliers’. Having looked trough various data bases related to tectonics I found that area of the north Atlantic is unique in that respect. This is also case for the Earth’s magnetic field in the area. When analysis is expanded to the N. Hemisphere-wide data sets (for both tectonics and magnetic field) the specific information is lost.
‘Zooming in’ on a specific area may reveal otherwise invisible
http://www.vukcevic.talktalk.net/GMEC-AMO.gif
Shouldn’t the tidal bulges in Figure 5 be aligned with the position of the moon rather than the sun? (Except when the moon and sun are themselves aligned, of course)
Apparently, Willis’ planet has no large moon, unlike the Earth.
D Cohen
That is my thought as well. Reading through the article I can’t see anything that Willis doesn’t see, but the tidal forces are the sum of the positions of the moon, Earth and Sun. The Earth really has to be treated as a double planet with a barycentre about 1000 miles below the surface.
http://www.astronomycafe.net/qadir/q665.html says 1700 km so close enough and shows the calculation.
Thus the stresses on a particular place change far more than the rotation of the face towards or away from the sun. When the moon is on the sun-side, the face of the earth looking towards the moon is quite close to the barycentre. The far side of the earth is being flung out not by the radius of the earth but by about 7000 miles radius from the barycentre.
Whatever the distance is, the effect is not only from rotation and the pull of the sun at two radii, one astronomical unit minus D/2 and the other one astronomical unit plus D/2. It is much greater at minus D/8 and plus 7*D/8.
That doesn’t make the forces large, but certainly larger.
As for the tidal effects of the moon on the tectonic plates, the ‘push’ which is a travelling wave, is always in one direction. If there were no oceans the effect would still be substantial as a force, With the oceans sloshing around, there is a greater effect. The net effect is to lift and drop the earth a little to the side each rotation.
None of that says there is a relationship with volcanoes however. It is possible there are electrical forces involved from pulses. A few million amps can release pre-stressed plates but cyclically? Seems unlikely.
Thanks for that, Crispin, but I’ve taken all of that into account in my calculations. Because I used the XYZ distances from the center of the earth, the fact that the earth-moon system rotates around its own barycenter is included in those distances. And the same is true for the fact that the earth-moon-sun system rotates around its own barycenter. All of that is reflected in the XYZ distances.
w.
Is this just awkwardly written, as a centripetal force , well according to one source “The force of gravity in keeping an object in circular motion is an example of centripetal force”.?
The earth and all orbiting bodies are free falling into the sun at all times. They just happen to be moving sideways fast enough so as not to get any closer (Circular orbits). Centripetal force never comes into play. It’s not really even a force.
unsatisfactory answer Kirk.
garymount
Willis had a post last spring (April maybe?) on the topic of gravitation forces and the concept of free falling bodies as Kirk above notes. I had a difficult time with it as did many others. Willis is correct as well as Kirk. If you can locate the post and follow the thread perhaps that will help. I had to do a little thought experiment to grasp the concept. It was an eye opener. Hope this helps.
garymount,
This is the thread I was referring to with regards to the above discussion. It was Feb 2014
http://wattsupwiththat.com/2014/02/14/canute-ponders-the-tides/
Gary.M
How so? I would elaborate but don’t know in which direction. Willis states “this is not the earth” and I’m not sure why he makes the distinction. It is in fact the earth. It is a body in free fall with no centripedal force. Centripedal is a false force in my opinion. It’s a lazy name for the real thing. “Acceleration” is what it should be called – or gravity. It is an inward force not an outward one.
Nice stuff. A few questions;
What is the effect on the hydrostatic pressure at the bottom of the ocean, at the hydrostatic vents?
What about the energy exchange? A very small deflection of a huge mass represents a lot of potential energy.
What is the peristaltic effect on the oceans, and on the magma. Could it contribute to the rotational velocity of both?
And yet, despite the tiny forces involved, the tide produces a 50 ft change in water height in the Bay of Fundy twice a day.
Isn’t that due to the geography of the area, a funneling of the water?
Tidal heights cannot be predicted by first principles directly from tidal forces. They are a harmonic resonance determined by the size and shape of the ocean basin, and the orbital parameters of the sun, earth, and moon. As a result some locations have very small tides, some very large, and these vary over time
As a result you cannot calculate the water pressure from the tides directly from tidal forces, because water flows. As it flows it magnifies the effects of the tidal forces in a non uniform, non-linear fashion.
So its been going on for ever and nobody noticed.
There is no such thing as continental drift.
There is no way a frequency resonance could cause an effect.
Saturn does not cause heating in one of its moons through gravitational affects.
No I will not look through you telescope.
Some times I am just wrong.
Sorry.
Jupiter’s tidal forces are cause of volcanic eruptions on its moon Io.
In juxtaposition with the other Galilean Moons. Io is the inner most of the 4 Galilean moons.
Twobob February 7, 2015 at 5:24 am
Say what? I made none of those claims. Are you sure you are on the right thread? I did something simple. I compared the times of earthquakes and eruptions to the tidal force on the day they occurred. How on earth you get from that to continental drift is a mystery.
w.
Willis Eschenbach, I think he’s replying to my comment (the first one under your article) not your post. The position of my comment may have led to some confusion.
My comment suggested an alternative approach to reaching the same conclusion as your post – that the effect may exist but it is too small to be noticed.
Twobob points out that my approach is not 100% conclusive. And my response is, “What is?”
Wills,
Seafloor eruption rates, and mantle melting fueling eruptions, may be influenced by sea-level and crustal loading cycles at scales from fortnightly to 100 kyr. Recent mid-ocean ridge eruptions occur primarily during neap tides and the first 6 months of the year, suggesting sensitivity to minor changes in tidal forcing and orbital eccentricity. An ~100 kyr periodicity in fast-spreading seafloor bathymetry, and relatively low present-day eruption rates, at a time of high sea-level and decreasing orbital eccentricity suggest a longer term sensitivity to sea-level and orbital variations associated with Milankovitch cycles.
… does not take into account sea-level, crustal loading cycles etc. See again “scales from fortnightly to 100 kyr”. Like you, I’m inclined to be dubious of the fortnightly scale of things, but the 100 kyr eccentricity-driven is tougher to dismiss. Impossible to dismiss when the histogram bins are daily, don’t take into account other factors Tolstoy considered, and only cover a century’s worth of data.
Indeed, I have not examined parts of Dr. Tolstoy’s claims, nor did I say that I had. I said I was inspired by her claims.
w.
Willis, thank you for making it clear that your present analysis isn’t a commentary on Tolstoy’s cited work. That obviously wasn’t immediately apparent to me.
This quote is from the original article Willis referenced in WUWT From The Earth Institute at Columbia University:
I believe this is the relationship that is worth investigating. Clearly this timing rules out the lunar orbit as a factor, so it doesn’t make sense to include it in the analysis. If the lunar orbit isn’t a factor, then the tidal force is unlikely to be the cause.
It it simply coincidence, of is “Something Unknown” causing these eruptions to synchronize with the earth’s annual cycle?
Others showed in the first thread, that at least a few submarine volcanoes occur outside Tolstoy’s time frame.
Which doesn’t break the hypothesis.
It does break the statement “…all known modern eruptions…” and assumptions based on that statement.
Were the submarine volcanoes in Tolstoy study area? If so, then the article must have sensationalized the results of the actual paper. If not, then the quote remains.
In either case, Willis is try to show statistical significance, not 100% certainty.
if eruptions are statistically more likely to January through June, then that is significant and worthy of study, because it suggests eruptions are predictable to some degree.
ATheoK,
Echoing ferdberple somewhat, I don’t know where the “all modern eruptions” statement comes from. I don’t find it in Tolstoy’s paper, so from my POV, observing that eruptions happen year round doesn’t break her hypothesis. Her argument, right or wrong, is one of relative frequency influenced by tidal forces and orbital parameters, NOT that those things are the main causal mechanism.
Must be the reading comprehension.
From the “Earth Institute at Columbia University press release:”
From Maya’s paper: (my bolding)
While the University issued the press release, I assume that they had Maya proof read it to ensure they had her research right.
Or the press office simply muffed it as they so often do. I resolve such disputes by reading the primary document.
I, with colleagues of mine, had a privilege to observe pictures and sound from many important UK and world events as they are unfolding, then see later on in the media what journalists made out of it; my advice is that one should always allow for a minimum + or – 30% error bar on whatever journalists write.
Hole Earth as a body as well as its individual parts are subject of the tidal forces. Hydrosphere is (almost) free to move into atmosphere, that is not the case for the mantle, outer liquid or the metallic inner core. Since none of these are ‘compressable’ I suspect some kind of ‘shunting’ effect, however small, is propagating in a spiral from the centre towards periphery.
typo : Whole Earth
Todays funniest typo, though. It nearly makes sense…in a way..
August 24, 79 AD is geologically modern. And that was no small puppy.
And, replying to myself, August 27, 1883, when Krakatoa went pop, is decidedly modern.
I don’t think that theory “all known modern eruptions occur from January through June” holds much water.
Toldtoy’s study is of submarine volcanoes, not subaerial.
Tolstoy. Sorry. Typing with cold fingers on an iPhone 4S on a boat.
ferdberple,
The January-June relationship, if real, is almost certainly driven by eccentricity of Earth’s orbit around the Sun, which means tidal force. This is counter-intuitive because the Moon’s tidal force is always stronger, so yes, “something else” is going on. I’d start with noting that perihelion is on January 4, the eruptions are happening more often AFTER the closest approach. Orbit around the Sun is obviously longer-period than Moon around the Earth, so the sustained weaker tidal force becomes a detectable signal statistically over the higher frequency stronger tidal force. What else. Oh, axial tilt. After perihelion in January, approaching equinox in March the Sun’s tidal force is moving into the same plane as the Earth’s rotation. The Moon not being in the same orbital plane. Etc.
Who knows. But those are the kinds of things I’d be thinking about before ruling tidal force out of the picture completely. And yes it could be a statistical error due to small sample size.
once could imagine that the earth’s mantle/crust has a natural frequency of approximately 1 year in length that is in resonance with our orbit around the sun, and this leads to peaks and troughs in the mantle, which synchronizes the period of eruptions.
as such, the earths rotation as well as the orbit of the moon, being much higher frequency would have much less effective power to excite the mantle/crust, thus the much lower response of eruptions to the moon.
People think that the earth’s tide are simply water moving up and down, but they are not. the tides result from a complex wave-train traveling around the world as the earth rotates.
Clearly if the oceans are affected, so is the rest of the earth. We see peaks and valleys in the tides at resonance points such as the Bay of Fundy. Why not something similar acting on much longer frequency resonance points in the mid-ocean ridges?
Brandon Gates February 7, 2015 at 6:25 am
As I said in the head post, for earthquakes and for terrestrial volcanoes, there is absolutely no “January-June relationship”. The distribution of both across the calendar year is random and regular, with approximately the same number occurring every month.
w.
Willis, the January-June relationship comes from Tolstoy’s paper. I’m only talking about it down here because ferdberple brought it up.
ferdberple,
That’s more or less where I was going with this. Tolstoy devotes several paragraphs to it in her paper, quick excerpt:
This may reflect a long-wavelength sensitivity of melting at depth, melt transport and/or dike formation, due to lithospheric/asthenopheric extension and unloading. The thin seafloor lithosphere in this extensional environment would make seafloor volcanism much more sensitive to deformation due to eccentricity compared to terrestrial settings. The apparent sensitivity of mid-ocean ridge magmatism to this relatively minor yearly orbital perturbation implies that it may also be sensitive to long-term orbital perturbations, thus linking seafloor volcanism to the Milankovitch cycles observed so strongly in climate data.
Cross-checking all that against her cited references exceeds my time and brainpower at the moment. What I do know is that she goes from that to possible CO2 release which provides part of the srong 100 year glaciation cycle signals. Or in translation: “Hey, there is some CO2 leading T at work here,” which I think is what’s being contested on the original thread where this paper was discussed (I haven’t tracked that post very closely, being more occupied elsewhere).
… make that “strong 100 kyr glaciation cycles … “
January is perihelion and the maximum solar tidal force, as well as southern hemisphere summer. One can think of all sorts of reasons that either one could be contributing, but I agree with Willis that the statistical evidence is weak and somewhat anecdotal.
From the way earthquakes happen (building up stresses until a stress-relieving event is “suddenly” triggered by some sort of nucleating shake) it does make sense that the threshold for a triggering event is lowest at times of greatest tidal stress, but again, one needs a lot more data turned into evidence to convincingly support the hypothesis empirically. At the moment it is at best anecdotal.
rgb
Number of recent earthquakes were preceded by strong geomagnetic storms. NASAs Goddard Space Flight Center looked into this phenomenon some years ago.
I suggested a simple mechanism
http://www.vukcevic.talktalk.net/TF.jpg
Started a daily survey ( geomagneti storms, lunar phases and M>4.5 ) for more than a year, even posted a warning on the WUWT 6 -7 hours before Japan’s mega-quake.
More details about it all (with links) here
Got swamped by the data, after all people die in the earthquakes, it is not subject that idle cranks should mess about, and I went off to more benign pseudoscience. Case against half a dozen Italian seismologists was also of some interest.
I’ll comment on vukcevic’s excellent graph. When a tidal force pulls in a left-right direction, there is less load on the fault and maybe an increased possibility of an earthquake. It can be tested on a subset of earthquakes on mainly north-south oriented faults (which get pulled by tidal forces most) and a tidal force at the moment of an earthquake, not a daily tidal force.
Yeah, but there are various problems right there. Yes, tidal “forces” are tensorial in the rotating, revolving frame of the Earth, but what you are looking at (or for) are differences in tidal forces across the fault, and these are almost nonexistent. How can I put this? The difference in tidal pseudoforce in the maximum direction is order of:
is the solar-radial distance between a sphere of center-of-mass orbital radius 
centered on the sun and the point in question (and where 
is the usual surface acceleration of gravity). This is an upper bound — there are further geometric corrections as well or corrections of the same order due to the earth’s rotation on its own axis and bulge and of course this is typically small compared to the related lunar tidal pseudoforce (because even though the mass of the sun is much larger than the mass of the moon, the ratio of the radius of the earth to the radius of the moon’s orbit is much, much larger and this ratio is cubed!). Also, this force vanishes completely when the location in question is at right angles where the angular projection would be maximum, so you are looking at a maximum “left-right” force that occurs only at certain very specific angles relative to the radial axis where the sun is directly overhead (where the force is strictly vertical).
, to something like the fifth power (it’s a second or even third order correction to the average tidal force at the fault location). I’d say that is way down in the noise compared to the direct tidal bulge and all stretching associated with it.
where
Next you have to integrate the differential tangential force components on both sides of the fault over some “suitable” surface slab to determine the lateral force differential, assuming that the two plates are basically “free”, to try to determine the tensorial stress and likely strain. Yuk. But in the end, I suspect that the stretching and contraction of the surface in association with the bulge wave itself, which is the result of plastic deformation due to mere differential buoyant forces acting on the entire interior volume of the Earth that are going to be orders of magnitude more important than transverse strain due to the difference in tidal forces exerted on the masses on either side of a fault. That force scales like projection of a projection of the distance between them, divided by
rgb
rgb – thank you for considering my comment. However, you would only be correct if the Earth were liquid. With a solid crust, the tensions tend to concentrate at points of weakness.
Is it wrong to assume:
Tectonic plates are large solid bodies, part of the plate experiencing strongest tidal pull might be thousands of miles away from the ‘fault line’, but mechanical force would be transferred all the way to the stress point, while the opposite plate may be affected by much smaller force, creating significant delta across very small distance.
Robert, regarding your post above, I fixed the error in your Latex so the main equation would display properly.
In addition, I resized it by adding the size instruction “&s=3” to the very end of the latex code, just before the “$”. The size codes range from -4 to 5, with the default of 0 being a pretty small font.
I use &s=3 for fractions and main equations, and &s=1 for variable names in text, so I resized yours accordingly.
Regards,
w.
ferdberple referenced the statement, as appearing in the Earth Institute’s write- up about Tolstoy’s findings.
http://www.earth.columbia.edu/articles/view/3231
The orbital parameter seems to dominate, closest distance 04 january and 04 july widest
re …Tolstoy found that all known modern eruptions occur from January through June…
Krakatoa in the Dutch East Indies (now Indonesia) began on August 26, 1883
Willis,
You picked “large” earthquakes for part of your analysis. What about microseismicity? There are a vastly greater number of events that facilitates statistical analysis and the forces involved with triggering the small events are at a more proportional scale to the tidal forces you are considering.
C’mon “Willis”, how many people are there writing articles under the name “Willis”? I can’t believe that they are all the work one person, who also has a job, a wife and who goes on holidays.
Willis doesn’t spend time around here smartin’ off, like so many of us who never publish anything.
OT: The dimensioning on that sketch reminded me of this article about squiggly lines on drawings.
Nice work again, Willis. Given the fact that earthquakes are a release of stress that builds up over time, my first thought was to ask what you thought of a lagged response due to “fatigue” from the oscillatory vibration for big earthquakes, but of course, with the exceedingly small movement involved, in the range (perhaps) of thermal expansion movements in which there is no permanent strain, this seems a dead issue. It might be interesting to see if there is any “bunching up” of earthquake frequencies and/or volcanic occurrences to see if there is some other operator at work.
Hydrologists looking after millions of piezometers around the world get an oscillation in the depth to the water table caused by earth tides (separate from the hydraulic push from rising tides in sea water in coastal regions). In this case, at earth high tide, the well water level drops because the lifting of the overlying mass increases the porosity of the aquifer. It is confounded by barometric pressure which also effects water levels. If you subtract the effect of barometric, then you get the the 12hr variation that is tide induced.
How wonderful to be living on a little round ball!
I could imagine a situation silmilar to Yuri Geller spoon bending where the tidal forces from the moon, sun and other large celestrial bodies might ‘flex’ sensitive points on the planet but not cause earthquake or volcanic activity in sequence with the force applied. However, the number of medium to large earthquakes over the past century appear to have been somewhat less than the previous century. That being the case it is unlikely that the day to day terrestial tide have a significant influence.
Hydrologists looking after millions of piezometers around the world get an oscillation in the depth to the water table caused by earth tides
This is the reason given by my fellow french gardeners for planting and sowing with the lunar cycle.
???
A six hour plus/minus cycle constrained by shallow strata of rock, clay, detritus, gravel, sand, marl, swamp… and someone claims that people notice the tides in their holes down to the water table?
I’ve never noticed much difference in my water table and we use well water. Nor for that matter have I ever noticed changing water levels in swamps I’ve visited.
So do the Chinese.