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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I was wondering if the massive increase in Antarctic ice mass might create enought pressure to induce volcanism in the northern hemisphere. Isnt there a large volcani range beneath the arctic? Arent most volcaniv ranges found above the equator?
Shouldnt we nuke antarctic ice, just to be on the safe side to avoid another ice age?
Somehow, New York City was once under miles of ice. Couldnt this have been caused by Antartic ice compression causing northern hemisperic volcanism, boiling seas, and Wolly Mammoths being instantly frozen solid encased in ice?
Tell it to us straight w….we are all gonna die unless we nuke antartica!
Nah, Tom. No need to nuke Antarctica. Once the ice gets heavy enough, it will simply tip over just like Guam. 😉
If you wish to know what causes volcanoes, consult a volcanologist, a geologist who specializes in the study of volcanoes.
If you ask him if tides cause volcanic eruptions, he will probably laugh at you.
No need to do a lot of mathematical computations to know that.
Agree again with you Don Easterbrook. We are frequently on the same page.
This just in…
“I recently emailed a tree in Australia and it told me that, after careful analysis of the Pika Extinction Derivative (PED) using two data points — well, one actually — earthquakes cause the tides.”
~ Inca Dostoevsky
Most of the volcanism in the solar system is driven by tidal forces. Obviously these are much more significant and occur on geologically cold moons. So I think it is fair to assume, even if insignificant compared to tectonic forces, that tidal effects are enough (and not just those that are perceptible) to tip the balance.
This is the year to test the theory with ‘super tides’ on the way. March 21 is the next key date. The first one on the 22nd Jan doesn’t seem memorable for activity.
http://www.telegraph.co.uk/news/weather/11370901/Britain-braced-for-floods-as-supertide-strikes.html
There was a large eruption on !/21/15 at Colima Mexico. There was also further activity 2 days ago. Popocatepetl also erupted several days ago.
In an only slightly similar vein, Oklahoma has experienced over 70 quakes >mag 1.9 in the past 7 days, with only 1 such quake in past 24 hrs. Also, the entire planet has only had 17 quakes >mag 2.5 in past 24 hrs. which is only about half the daily average.
The most recent example was in the weeks leading up to the recent full moon the daily 24 hour rate was around the mid 30s. Right at the end of the full moon there was a drop to 15 quakes per 24hr period. Then there is a gradual increase. I have seen this happen many times either at the Full, or during the New.
Just out of curiosity. If these 37000 miles of volcanic ridges are erupting in the first 6 months of the year and adding lava outflows to the floor of the oceans, we should be seeing a water displacement effect. Does sea level data show any change between the first 6 months and the second six months of the year? I am not sure of the quantity of lava involved but one would imagine it might be significant enough to have an effect.
5 Tectonic ridges of speeding plates
5 Ice Ages
http://www.vukcevic.talktalk.net/Ice.jpg
Just saying..
One thing I have noticed with watching the daily quake map is that the number of quakes often drops rapidly around the full moon and the mid moon points. I have seen that happen time and again over the last 4 years. The Tohoku Quake got me interested in watching the daily activity, and I have watched ever since then. The daily average numbers of worldwide quakes at the USGS map, greater than 2.5, gradually rose after the quake in Japan in the years since then.
Thanks for the graph. That looks great.
Well, it’s actually the product of taking the timestamps from the 30 year quake listing from USGS and pulling the ephemeris data for the Sun-Earth-Moon at that point in time. The goal was to collect enough data to point the “Moon caused quake” crowd at to let them find the proof in the data. What I got, even after backing out the apparent dwell time for the moon at various portions of it’s orbit is what is in the graph. There seems to be some uptick at the New and Full sections of the lunar phase, but the signal doesn’t really stick out far enough to be something warranting additional effort (to me). It’s just enough to possibly support that article on some Berkley researchers who came up with a San Andreas – Moon connection.
As Willis (and others) have pointed out in this article, the amount of energy change that you see from the moon is not very much at all. It may be enough to cause an “already gonna happen” quake starting a few seconds before it normally would have. The differences in scale between the two forces is quite literally astronomical. (no pun intended)
Personally, I’m in the “it’s too small to be significant” camp.
Quite a while back, I ran across a commenter who was adamant that the oceanic tides had an influence on the quakes occurring at El Hierro. In my opinion, that had a better argument since the island was inflated due to magmatic intrusion. However, the tide data for a port there didn’t show any correlation that I could find to the quake activity.
[Thank you for checking, for replying. .mod]
Thanks Geo.
One thing that I really should have mentioned on that graph, the energy is in Joules.
Hi,
Everytime I see a post by you, Willis, I read it as I know it will be very informative and interesting. I am amazed at the breadth of your posts and knowledge. I believe I will start referring to you as ‘Marvin’ with “a brain the size of a planet.” (Hitchhikers Guide to the Galaxy).
Perihelion was on Jan. 4 (UTC) this year. During December the distance gets smaller and during January (after perihelion) the distance increases. Maybe the timing ought to be mid-Nov to mid-Feb for investigation. If closeness has anything to do with volcanism then what do May and June have to offer that Nov/Dec do not?
I’ve updated the graphs to include 95% confidence interval error bars.
w.
Some active volcanoes do follow a rough cyclical pattern from less to more to less activity. It has nothing to do with tidal forces; it has to do with fluids, gasses, and pressures. Think about a geyser such as Old Faithful, it has a cyclical pattern (that changes over time) but has to do with how fast the reservoir is refreshed and how fast the water takes on heat. Volcanoes sometimes have a similar mechanism to their activity.
Earthquakes might be able to trigger a volcano – they release a large amount of energy in a small amount of time.
I see no mechanism where a tidal force could act with enough force in a small amount of time to trigger much of anything. To see such a relationship would take a large amount of data over a geologic time period (i.e. millions, tens of millions, or hundred of millions of years) if it exists at all.
How are atmospheric tidal effects calculated in climate modeled hypothesis.
Here is 16 minute Youtube of Maya Tolstoy explaining her hypothesis. There is also mention made of a confirming study of Sumatra earthquake tidal triggering by Sachiko Tanaka. That paper is here.
Discussing how she discovered a tidal signal in the quaking of a subsea volcano, she makes an excellent point all “true believers” should note: “As a recent graduate … I didn’t know it wasn’t supposed to be there.” That is, follow the data, not the dogma. Hopefully, she will maintain that open-mindedness throughout her career.
A very interesting topic and still lively since the work of Love in 1909.
http://en.wikipedia.org/wiki/Earth_tide
Nice plots on the Wiki page of the Lunar (larger) tide rising and body tide forces.
With regard to effects of tidal stress on volcanic activity is a link to a paper on Mt. Etna from 2007.
Here is well written article on Wired from 2012, revised from original published in 2011, http://www.wired.com/2012/05/on-earthquakes-eruptions-and-the-moon-eruptions-revisited/
Of course we need more measurements of much better spatial coverage and time-resolution to help get to the real answer. Not this year from looking at the Obama budget. Pity.
“The thin seafloor lithosphere in this extensional environment
70
would make seafloor volcanism much more sensitive to deformation due to eccentricity
71
compared to terrestrial settings.”
———————–
This statement lifted from Tolstoy’s paper, helps put her findings in perspective. It also becomes apparent that her forcings scenarios are not applicable in terrestrial or thicker seafloor crustal comparisons. Her speculations about volcanic response to glaciation are a reach, but nevertheless interesting.
For me, this paper concludes: “we think we have observed something interesting which may become significant as we gain the ability to study it further.”
Good point Alan,
Comparing thin sea floor crust with thick continental crust is like comparing a twig to a tree. They have very different intrusive/extrusive settings. Furthermore, most known volcanic eruptions are continental, on land, and related to crustal thickening. Oceanic sea floor ridge volcanism is generally related to crustal thinning and extension.
Sea floor volcanic eruptions are seldom observed and many active sea floor volcanoes have yet to be located let alone explored. How would we know what they correlate with?
The Tanaka Sumatra Tidal triggering link, which got kerrupted: http://onlinelibrary.wiley.com/doi/10.1029/2009GL041581/abstract
http://onlinelibrary.wiley.com/store/10.1029/2009GL041581/asset/image_n/grl26693-fig-0002.png?v=1&t=i5vpcwx8&s=bc87a355a0a1378d4754bae5658ced486cc3c038
Sorry to be a nitpicker, but it should be “farthest” not “furthest”.
Jerry,
Referring to what, exactly? Is it in the article? Where? You don’t say. ☹
Figure 5.
Willis, I may have this totally wrong -but to me it seems that Maya Tolstoy’s whole idea is both correct and incorrect and that a very important result is overlooked. It just looks to me as though she is looking at a correct process but at the wrong end results.
Firstly: The idea of the paper must surely be correct in small form : Volcanism ( a large scale moving process) must be affected by tidal effects (a secondary large scale process that is operating within the same physical system of processes). Basic science makes this unavoidable – Vulcanism cannot NOT be affected because it is in direct contact with tidal forces – although the effect may be too small to be relevant to the main thrust of her paper. Making the paper incorrect in its current form.
However, within vulcanism there are further processes that must be affected to a much greater degree by tidal forces… vulcanism is the movement of large more or less solid materials – within which there are associated movements of lighter more mobile elements – liquids and gases – especially water and hydrocarbons.
If volcanic hydrocarbons and water can be shown to be moved by tidal forces – so that effusion occurs in greater quantities in associated cycles with these forces then the writer would have a real subject worthy of research. The time scales are also something needed to be looked at on a much greater timescale: multi-decadal and multi-centennial level, as any movements would be more likely to be produced over long time periods rather than shorter due to the repeat harmonics of tides.
If it could be shown that lighter materials did move in quantities then those quantities might even indeed produce the odd vulcanic eruption every now and then too!. In which case the writer might prove her original paper in the long term although by result of forces not included in her original paper.
I’m probably talking rubbish -but it does seem to me that she has missed the most likely process that could occur between vulcanism and tidal forces: The resultant long period, large scale tidal movement of light elements (liquids and gases) like water and hydrocarbons in volcanic zones.
Willis writes “Now … why should this be the case, that the quakes and eruptions are NOT affected by the tidal forces?”
Expansion in one direction is compression in another and vice versa. Perhaps to be more sure, you need to take location into account too.
I’m sorry, but upon a third reading of this post, I still don’t get it. The earthquake and volcanic eruption data overlay the tidal force data to an amazingly close extent, yet you cite this as evidence that they are unrelated. It’s a non sequitur to me. What am I missing?
The comparison is between tidal forces on all days and tidal forces on days with earthquakes.
No significant difference
MfK February 7, 2015 at 9:51 pm
MfK, if the earthquakes were related to the tides, we’d see more earthquakes (or perhaps less) when the tidal forces were strongest or weakest. And if that were the case, the eruption data would NOT overlay the tidal force data. If there were a relationship we’d see a peak or a valley in the eruption tides that would not exist in the general tide data.
w.
Thanks for including madam Tolstoy’s CERN presentation, Vuc. It shows that she isn’t studying underground earthquakes as such. No, she is studying underground acoustic noise – low frequency sound sources. And, of course, she records the sounds of fluids moving around down there. To me, this has to do with seafloor hydraulic processes within a local area. Because madam Tolstoy chose a very unique location for her studies, with lots of compressible gases down there, in the cracks and crannies, she picks up a lot of noise, as that portion of the ocean floor is “hydraulically active”. So, we all know that small gas bubbles are compressible, and will therefore shrink their volume under higher pressure (read high tide), and expand their volume during low confining pressure (read low tide), it is very natural that she finds the tidal cycle.
The same actually occurs in the large Gullfaks hydrocarbon field In the North Sea. -Also that reservoir expands and contracts in concert with the tidal wave.
Agreed, thanks vuk and thanks to you, Martin Hovland for the insights.
Willis
The mechanism for this process is to have an Earth facing coronal hole. The partial stream from the “hole” is enhanced from solar flares, regardless of their location.
Re January-June what about Surtsey? According to Wikipedia this started in November.
http://en.wikipedia.org/wiki/Surtsey
or this Japanese one?
http://www.bbc.co.uk/news/world-asia-25032329
Or did the eruptions begin in the Jan-July time frame and are not reported in these articles?
We are missing the significance/ the logical implications of the observations. The undersea lava that is produced is not affected by changes in the amount of water in the oceans and is not affected by minor gravitation changes on the planet.
1) The entire ocean floor system is moving year by year over geological time (37,000 miles of volcanoes are produce as the ocean floor crust moves apart.) Why does the ocean floor move? What is the source of the force that moves the ocean floor? Why does the force that moves the ocean floor crust increase during the first six months of each year? Why did the force that moves the ocean floor increase during the glacial phase?
The ocean floor lava occurs because something is pushing the ocean floor apart. The lava occurs due to the rate that something is pushing the ocean floor under the continents. The force (there must be a constant force to move the ocean floor crust) that is pushing the ocean floor apart is deep CH4 that is released as the core solidifies.
The super high pressure liquid CH4 breaks a path through the mantel. As I noted in the previous thread the super high pressure liquid CH4 picks up heavy metals as moves through the mantel which explains why Uranium, Thorium, Gold, and so forth are found concentrated up to a million times in the upper crust and why there are heavy metals in crude oil and black coal. The path the super high pressure CH4 creates explains why the only commercial source of helium is from oil deposits. The helium is produced as the radioactive uranium and thorium that the liquid CH4 concentrated, decays.
The helium that is produced by radioactive decay then moves up through the paths in the mantel created by the movement of the high pressure CH4. The biological theory for the origin oil cannot explain why helium is found in oil deposits. The helium gas cannot break the mantel. There are no natural pathways through the mantel. There needs to be both a mechanism to concentrate the uranium and thorium and to a mechanism to create the path way to enable the helium to move up into the oil deposit. The super high pressure liquid CH4 that is released when the core solidifies appears to be the only physical explanation for the observations.
2) The undersea volcanoes produced 8 times more lava (the sea floor moved faster under the continents) during the glacial period. The question is how large are the sources and sinks of CO2?
The undersea volcanoes produced 8 times more lava as more liquid CH4 is moving the ocean floor. As I noted it is the rate that the ocean floor is spreading apart that determines how much lava is produced.
The 8 times more lava produced means there is 8 times more CO2 emitted, yet atmospheric CO2 drops during the glacial phase rather than increases. There must be a super sink of CO2 to maintain equilibrium. As Salby notes atmospheric CO2 tracks in lagging manner planetary temperature.
There are massive amounts of CH4 moving through the mantel which is required to move the ocean floor crust under the continents. The oldest ocean floor crust is 200 million years old.
The warmists assumed that the natural sources of CO2 are small and hence assumed that the biosphere re-cycles a small input of new CO2. That assumption is not correct. There are very large natural inputs of CO2 into the biosphere from the deep liquid CH4 that is produced when the core solidifies. Salby is correct the majority of the increase in atmospheric to natural CO2 that is released not due anthropogenic CO2. I believe can definitive prove Salby is correct (I will do some work for a new thread.)
http://www.sciencedaily.com/releases/2015/02/150205142921.htm
I find Tolstoy’s hypothesis regarding frequency intriguing but the hypothesis of a resulting connection to climate change (or even atmospheric CO2 levels) seems to have been gratuitous. Carbon dioxide released more than a few hundred feet below the surface should go into solution. Even if a cyclical mid-ocean ridge CO2 signal was being swamped by other undersea sites of CO2 release, if subsea CO2 was reaching the surface, it should have been detected by recent GOSAT measurements (which I believe has a “resolution” of a few ppm).
Some of the GOSAT images I have seen could be interpreted to show a very minor increase of CO2 (relative to the ocean’s CO2 sink effect elsewhere) along a N-S axis in the Atlantic. While this might be used to justify future research, in the absence of a notable CO2 spike over the ocean, I think the climate connection is without merit. Perhaps the GOSAT data releases will shed further light on the subject.