How can I measure the terrestrial tide on my place?

[rtx22]

How can I measure the terrestrial tide on my place?

Since i don't have a MEMS gravimeter or a laser spectometer what will be the simplest method to measure the local Earth tide variations?

 

[anorlunda]

Clarify please. You want to measure the tidal movement of the Earth's crust, not the movement of the sea surface, correct?

 

[rtx22]

Clarify please. You want to measure the tidal movement of the Earth's crust, not the movement of the sea surface, correct?

Yes, the tidal movement of the Earth's crust.

 

[berkeman]

Yes, the tidal movement of the Earth's crust.

Sorry, what do you mean by "tidal"? Do you mean variations due to tidal forces of the moon on the Earth's crust, or do you really mean the movements of the crust due to plate tectonics?

In either case, it would seem that you need very precise position sensors spread over a fairly significant area (unless I'm misunderstanding your question). Paging @davenn

 

[Baluncore]

When performing gravity surveys the Earth Tide amplitude with time is computed from a model that employs Love Numbers, that is then applied as a correction to the gravity survey measurements. Station altitude and nearby topography is also applied as a local correction for gravity surveys.
https://en.wikipedia.org/wiki/Love_number

By measuring air temperature and pressure you can predict the rate of a free running pendulum clock with reference to GPS time. The amplitude must also be regulated or modeled. Once you have identified the correction coefficients and apply them to the pendulum, you will be left with an error function that is mostly the Earth Tide. You will know you have solved the pendulum calibration when you see the tidal pattern.
Start here; http://www.leapsecond.com/hsn2006/

 

[rtx22]

It seems that it is not so easy to measure the terrestrial tide "at home".
Berkeman, I know that there are a lot of movements of the Earth's crust, such as: tectonic plate expansion, day / night variation, earthquakes and other geological transformations of the crust, but the measurement of the Earth's terrestrial tide caused by the Moon ( and Sun) is what interests me.
Baluncore, by the pendulum method the tidal variation is an indirect and not a direct result: "you will be left with an error function that is mostly the Earth Tide", the result is not even a sure one and can be composed of several factors. What about using inclinometer or clinometer , is it possible to measure the variation of the terrestrial tide? Wouldn't it be simpler? Thank you both for your answers.

 

[Baluncore]

Baluncore, by the pendulum method the tidal variation is an indirect and not a direct result: "you will be left with an error function that is mostly the Earth Tide", the result is not even a sure one and can be composed of several factors.

You need to identify why you want to make the tidal measurements and how accurate they need to be. Will it be an automatic station or manually operated?

Everything will be indirect. It may be the period of a pendulum, the current through a mass balance, or the length of a temperature compensated Pyrex coil spring. 20 years ago, the most accurate gravity meters threw a steel ball up in an evacuated tube, then timed the trajectory over many trials.

Do you have a good station location that is screened from the elements and clear of local movements of mass? If you are near the sea it may be difficult to predict Earth Tides since Ocean Tides are more complex coastal water resonances that influence the Earth Tides by delayed mass movement of water.

You should first learn how to calculate the gravitational variation expected. Work out the Earth tilt expected in arc seconds. You will need that information to verify your measurements.

Only then should you look for an instrument, or try to work out how to measure such a small gradient. You could look for a used gravity meter. If you float a steel ball in a magnetic field you can measure the current needed to keep the ball in a fixed position, but you must screen that from all external magnetic fields. How accurately can you measure a current?

 

[rtx22]

You need to identify why you want to make the tidal measurements and how accurate they need to be. Will it be an automatic station or manually operated?

Everything will be indirect. It may be the period of a pendulum, the current through a mass balance, or the length of a temperature compensated Pyrex coil spring. 20 years ago, the most accurate gravity meters threw a steel ball up in an evacuated tube, then timed the trajectory over many trials.

Do you have a good station location that is screened from the elements and clear of local movements of mass? If you are near the sea it may be difficult to predict Earth Tides since Ocean Tides are more complex coastal water resonances that influence the Earth Tides by delayed mass movement of water.

You should first learn how to calculate the gravitational variation expected. Work out the Earth tilt expected in arc seconds. You will need that information to verify your measurements.

Only then should you look for an instrument, or try to work out how to measure such a small gradient. You could look for a used gravity meter. If you float a steel ball in a magnetic field you can measure the current needed to keep the ball in a fixed position, but you must screen that from all external magnetic fields. How accurately can you measure a current?

Very good your answer. At the moment I want to try manually and then connect the measurements to a laptop. The location is isolated from lakes, seas or electromagnetic sources.
I also thought about using a https://www.amazon.com/dp/B07YC3493S/?tag=pfamazon01-20 with Hall sensor, but there you depend on the saturation of the electronic components and the accuracy and filtering of the power supply, if you measure the compensation currents.
Again I thought it would be better to measure the capacitance (as a capacitor) between two objects in levitation (or between floating ball and the levitation kit) and not the current in the electrical circuit, what do you say? How or with what could I compare the results?

 

[Georgeros]

What you both say is already done:
Seismometers sensors are using capacitor measurement;
The floating fields are used in gravimeters;
But no one can actually record Earth terrestrial tide variations, the gravimeters use standard tidal calculation and not measure it (see http://seismologie.be/en/gravimetry/observations/real-time-g ) and the seismometers or geophones I don’t believe can senses the tidal movements that can reach 22cm on Africa...

 

[Baluncore]

What you both say is already done:

Welcome to PF.
Yes. I have been involved with it, but that was between 20 and 40 years ago.

I believe the problem here is finding a low-technology technique that can be applied by a practical person without too much trouble. Accurate time and frequency is available from GPS.

Capacitance measurements can be applied to static balances, but static levitation does not have the resolution of instruments employing a dynamic trajectory in a vacuum. If the position of a free falling tossed object was measured using laser interferometry, most of the variables might be eliminated.

The reason I suggest an amplitude maintained free running pendulum clock is that it can be compared with GPS time and will produce a long term time difference record. You could record every crossing time to the microsecond, while monitoring pendulum amplitude, temperature and atmospheric pressure.

Over time the recorded data can be analysed to identify and extract the influence functions. The residue will contain the Lunar and Solar cycles that you want to extract, with seismic event phase shifts, noise and a long term base line slope due to ageing. Anyone with your data record can try their hand at the signal processing game.

Should a pendulum swing in the NS or EW plane, or in both as a circle?
What effects will Earth's rotation have? Coriolis effect? and the Foucault Pendulum?

No matter how you measure the gravity, you will still need to remove the local atmospheric load on the Earth's surface from the gravity measurements. That simply becomes part of the pendulum signal post-processing.

 

[chemisttree]

I would have thought you could measure something like that with a gps signal?

 

[Baluncore]

The problem with GPS height is that the vertical error is significantly affected by the ionosphere. The daily ionospheric error is both variable, and greater than the Earth Tide, which makes it a bit hard to separate out the tidal signal.

Differential GPS has the accuracy, but requires a nearby known station, which unfortunately also has a very similar tide. There are now networks of geodetic stations with GPS, so it is possible to find the tidal signal, if you first model what you are looking for.

GPS time and frequency can still be used to accurately measure the period of a pendulum because the ionospheric delay drift is so much slower than the pendulum period.

 

[Phizicist]

I did my masters thesis on microgravity to detect caves many years ago. it worked, successfully. i used a gravity meter supplied by the school that was manufactured by lacoste and romberg (google it). I'm a retired geophysicist and geologist with mostly seismic and oil company experience. i am on linkedin for those interested. I'm obviously not a forum expert, very few postings anywhere. retirement stirs the mind.The following posting caught my eyes, see my response, I'm not sure how to post in the correct forum. Please advise.
How-can-i-measure-the-terrestrial-tide-on-my-place? the tidal movement of the Earth's crust?

You can but the simplest is to rent a gravity meter. As I recall the cost around $10,000 so the cost to rent shouldn't be that high.

the tidal movement in terms of actual elevation change of the Earth's crust is insignificant. however, it's very different for tidal forces (gravity), of course, the sun and the moon being the main causes. the tidal forces are significant and can be readily measured and in fact are required to be measured and recorded throughout the day at around 1 hour increments in any regional gravity survey since they usually are considered noise. and thus need to be removed.

probably the easiest way to at visualize the amount of theoretical gravitational forces differences on land, as you ask, is to simply look at the high and low tides in the sea or large lake, hopefully nearby to you. i hope this simple explanation is not insulting. to get the actual amount, you'd need to rent a gravity meter and record away, probably over the period of a month. or just look at a local tidal chart (there can be local sea level changes not due to tides such as topography or wind direction).
on some of your comments and questions:
- movements of the crust due to plate tectonics? no effect at all, 5 cm/year max, 2 cm/year more typical.
- tectonic plate expansion, day / night variation, earthquakes and other geological transformations of the crust? insignificant over the course of days, or weeks, or years.
- inclinometer or clinometer , is it possible to measure the terrestrial tide?
- But no one can actually record Earth terrestrial tide variations, the gravimeters use standard tidal calculation and not measure it. no really. we can measure. standard tidal calculations not accurate enough since there could be all kinds of errors, like large topographic differences, ore bodies, caves, etc.
- Earth surface vertical elevation changing movement due to tides? insignificant, unmeasurable over the course of days, or weeks, or years.
- my comment- Earth surface elevation differences must be accounted for, they can be detected down to .1 foot differences (the accuracy I needed to be able to detect caves).
- my comment- the gravity meter has to be perfectly level for every measurement.

hopes this helps,
cheers

 

[Baluncore]

I'm not sure how to post in the correct forum. Please advise.

Welcome to PF.
You will get the hang of it.

I think the idea in this thread is to actually measure the Earth's tide, at a fixed base station, over a long period of time. That is certainly a challenge, but it is possible. When we measure gravity at a fixed station, we are effectively measuring the changing distance from the centre of the Earth underfoot, and so to detect the changing elliptical equatorial profile, which is the Earth tide.

The Earth's orbital plane about the Sun is not parallel with the Earth's Equatorial plane, which is different again to the Moon's orbital plane about the Earth. So the Earth tide is the sum of Solar and Lunar terms, with asynchronous periods, and varying magnitudes. It is certainly easier to compute the Earth tide than it is to measure it. At least we can predict the pattern to look for in the data.

I don't think there is a budget to buy or rent a gravimeter, so it is a case of trying to identify a gravimeter that can be built on a budget by a practical person. By automating and logging data continuously at a fixed station it should be possible extract the Earth Tide from the recorded data.
As technology changes, different possibilities will rise and fall.

There is an article here from 2012 on the historical advances in gravimeters.
https://www.hindawi.com/journals/ijge/2012/687813/

I believe the three options, in order of complexity, are a pendulum, a spring balance, or a thrown mass. I don't think superconductive or atomic rubidium sensors are realistic for skilled amateurs on a budget, but I am open to suggestions.

Typical MEMS accelerometers do not have anywhere near the resolution needed to measure tides. But there is this article small-and-inexpensive-mems-gravimeter. See the comments: “The Nature abstract and the summary here neglect to mention that the accelerometer, to function to the precision needed, must be in high vacuum and temperature controlled to within 1 milliKelvin. Do-able, but it’s not quite as simple as just a thin slab of silicon.”

The slope of the Earth's surface changes due to Earth tide, but by how much? Around the Earth's equator, there are two Earth tide highs, and two Earth tide lows. Those points at 90°, are about 10,000 km apart. The peak to peak change due to Earth Tide is about half a metre, which makes the amplitude of the elliptical deformation ±0.25 m. The slope is then 0.25 in 20e6/2Pi = 7.85e-8 radian = 0.016 arc sec. But the best theodolites and levels can only measure 0.2 arc sec.
Astronomical VLBI with 15 m precision dishes is only now being used to establish the base lines of continent-wide geodetic networks to a resolution of about 2 mm. That is now being used to correct GPS networks.

So, what other practical possibilities are there?

 

[anorlunda]

earth surface vertical elevation changing movement due to tides? insignificant, unmeasurable over the course of days, or weeks, or years.

That seems to be the number the OP is looking for. You say insignificant. Is there a reference?

If tidal, then days/weeks/months are not relevant, but diurnal variations are. I would think that satellite based radar altimeters would pick it up. They measure the height of waves at sea. If the OP could access the raw satellite data, he might be able to find the answer there.

 

[Baluncore]

If tidal, then days/weeks/months are not relevant, but diurnal variations are.

Since the solar and the phase-sliding lunar components are summed, and the tidal ellipse has a dominant second harmonic variation, the amplitude of the resultant vector sum will vary significantly over the fortnight.

I would think that satellite based radar altimeters would pick it up. They measure the height of waves at sea.

That has the same problem as GPS. The ionosphere and tropospheric delays vary on a daily cycle, confounding the much smaller Earth tide that shares the same part of the spectrum. Satellite high resolution radar mapping must be corrected to defined geodetic reference points on the ground.
Simply put, satellites are on the wrong side of the atmosphere, they do not remain on station or return often enough.

Ocean waves have a distinctive radar scattering spectral response that contains wave period and amplitude information. The fine structure of the wave systems present is known with much greater resolution than is the distance to the surface and back with the variable travel time.

 

[Vanadium 50]

A gravimeter measures the force; the OP is apparently looking for the response to the force. Different things.

Earth tides are a few centimeters. The requirement is to measure this relative to the Earth's center, so ~10^-8. GPS is typically 100x worse. You can look at velocities, which will be of order ~10^-6 m/s, or accelerations, maybe a few ~10^-11 m/s². (a few nanogals)

None of these are big numbers.

 

[Baluncore]

A gravimeter measures the force; the OP is apparently looking for the response to the force. Different things.

Yes.

The solid Earth suffers an elliptical distortion wave due to the tide. That cyclically changes the observer's distance r, from the centre of mass of the Earth. The gravimeter is affected by that change of 1/radius². It is a small number.
It is slightly bigger than the drift in a portable survey gravimeter.

I am looking for suggestions here. What alternative are there?
Maybe a laser ring gyro? to measure the local surface tilt of the tidal ellipse in milli·arc·seconds, as a cyclic phase shift of the continuous Earth rotation about it's axis?

 

[Vanadium 50]

But the direct gravity from the moon will be a few thousand times larger.

 

[Baluncore]

But the direct gravity from the moon will be a few thousand times larger.

Can you please show how you calculate that factor of 1000 ?

I would expect the tidal yield of the Earth to compensate for about half of the potential equilibrium between Earth and Moon attraction to the gravimeter test mass.

 

[Vanadium 50]

Moon's direct gravity is 1/6 the Earth and 60 Earth radii away. So ballpark it's down by 1/6*1/60². Compare that to the 10^-8 from being an inch or two farther from the earth.

 

[Baluncore]

For an observer on surface of Earth; Me= 5.9722e24 kg; Re = 6378137 m;
For the Moon in orbit; Mm = 7.342e22 kg; Rm = 385e6 m;
As a free fluid, Earth would yield k metres to balance the Moon attraction.
At equilibrium; Mm/Rm^2 = Me/(Re–k)^2 – Me/(Re+k)^2
∴ k = 5.38 m.

The amplitude of the most significant lunar term, M2 is about 385mm.
The amplitude of the Earth body tide exceeds 0.5 m; Not an inch or two.
There may be a factor of 10, but there is not a factor of 1000.

But still, what alternatives are there to measure about 0.5 m of Earth deformation over a period of 12 hours or more?

 

[anorlunda]

But still, what alternatives are there to measure about 0.5 m of Earth deformation over a period of 12 hours or more?

That's a better way to express the question. Forget tides. Forget gravity. How would one measure 0.5 m of Earth deformation over a period of 12 hours regardless of the cause?

 

[Vanadium 50]

How would one measure 0.5 m of Earth deformation over a period of 12 hours regardless of the cause?

The problem is "motion relative to what?" It's with respect to a point 4000 miles away. An inaccessible point 4000 miles away. An inaccessible point 4000 miles away, where nearby points are subject to the same motion as the point you want to measure.

The problem is quasi-solved by the lunar ranging experiments. They do this by looking at the moon for a very long time and removing the 24h 50m component to the motion.

 

[jim mcnamara]

This seems to be a detailed investigation and results for obtaining a value for Earth tides for points and larger areas. Author is Duncan Agnew, UCSD Geosciences.

I read the first few pages and then skimmed around. The discussion is based on a large number of references but I cannot tell if the white paper was ever published. Most parts, except the the introduction, of it are clearly referenced to journal articles.

It is meant for coursework. For https://www.unavco.org/

https://www.unavco.org/education/pr...005-strainmeter-course-materials/tidenote.pdf

Not a short read.

 

[Baluncore]

Interferometry has possibilities as part of a local tilt-meter.
1. An open long channel of liquid is a local lake. It has density variations due to temperature. Wind causes local atmospheric pressure differences.
2. A long liquid filled tube must be level, with temperature stabilised vertical ends, along with a parallel air tube to equilibrate the air pressure at the ends.
3. A free hanging pendulum on a long wire. Free pendulums start swinging of their own accord, due to the random noise, including tides. Unfortunately it is also a seismometer, that then becomes a Foucault pendulum. It will need to be damped.
4. I think the Ring Laser Gyroscope or Fiber Optic Gyroscope, has possibilities. They are competing well for inertial navigation systems at the moment. Each has it's own advantages, and problems. Optical gyros employ two counter-rotating paths. When away from the poles, triaxial optical gyros take a few minutes to detect Earth rotation and so determine true North for an inertial navigation system.
An optical gyro mounted parallel to the equatorial plane will produce a continuous signal due to Earth rotation. That will have a diurnal phase shift due to the tidal surface tilt of the mountings, with a magnitude of about 15 milli_arc_sec at the equator. If that phase shift can be detected against a clock with low phase noise, such as a GPS stabilised clock, then there are possibilities. Increasing the length of the optical path increases gyro resolution.
I cannot see any way to operate a 4 path system to cancel rotation while detecting tilt, except a crossed pair at the pole, where the tidal signal is minimum, so there is no signal to detect.

 

[anorlunda]

Thanks @jim mcnamara , that link was very helpful. The passage below from that paper highlights difficulties in interpreting actual measurements if we had them.

A large part of the difficulty in using Earth tides to make inferences about the Earth lies in the signals caused by the ocean tides: a good example of one scientist’s signals being another one’s noise. The mass fluctuations associated with the ocean tides would cause changes in the potential even on a rigid Earth, from the attraction of the water; on the real Earth they also cause the Earth to distort, which causes more change in the potential, plus displacements. All these make up the load tides, which are combined with the body tide to make up the total theoretical tide.

 

[Baluncore]

I am happy to correct for local ocean tides as they are reasonably well known. At a coastal gravity station they could be measured, which would reduce the atmospheric pressure, storm surge and wind influence. But that would certainly make it difficult for a beginner living on the coast.

Which is why I asked these questions...

Do you have a good station location that is screened from the elements and clear of local movements of mass? If you are near the sea it may be difficult to predict Earth Tides since Ocean Tides are more complex coastal water resonances that influence the Earth Tides by delayed mass movement of water.

The reply told me it would not be a problem...

The location is isolated from lakes, seas or electromagnetic sources.

But I do agree that identifying the structure of the Earth through the study of Earth body tides would be particularly difficult, if not impossible. Seismic records do a better job, they also work under the oceans. Gravimeters have been used successfully in submarines.

A.E.H. Love identified the key coefficients for predicting Earth tides. There are several computer programs now available to predict Earth tide corrections for gravity surveys. The same type of software is now used also with GPS baseline VLBI.

We can predict Earth body tides better than we can measure them.
Anyone who wants to give it a try might take a look here.
https://geodesyworld.github.io/SOFTS/solid.htm

 

[MRBlizzard]

I want to remind all of you about the Inertial Guidance System in the fighter { I think it was the F-15). The technicians installed the GPS in the plane parked in the hanger, and left it running. The next morning the engineers arrived and looked at the data. They spent the better part of a week before they realized that the plus / minus six inch variation was the Earth tides.

Even GPS, if you average over 30 minutes or so, should give you the altitude accurate to about 4 inches. I remember the grassland ecologists were using a unit like that for an ecology study on the Great Plains.

 

[rtx22]

We can predict Earth body tides better than we can measure them.
Anyone who wants to give it a try might take a look here.
https://geodesyworld.github.io/SOFTS/solid.htm

Predictions? I'm not interested in predictions. Solid tidal variations may depend on several factors that are not taken into account in that software. Do you know how the tidal force is distributed on an ellipsoid considering that it comes from 2 main objects? Can there be intersecting areas of the reverse polarity tidal forces? However, the software cannot predict the tide when an astronomical event of eclipse occurs.
I am now working on testing the methods provided by you:
- pendulum method + gps
- floating force field method
It is not easy or easy but I will let you know if I succeed. Thanks for the guidance.

 

[berkeman]

However, the software cannot predict the tide when an astronomical event of eclipse occurs.

Why not? Because of a few minutes of darkness?

 

[rtx22]

Why not? Because of a few minutes of darkness?

Considering that no studies have been published on this issue it is possible for you to be right. We will see.

 

[berkeman]

Considering that no studies have been published on this issue it is possible for you to be right. We will see.

Most likely there are no peer-reviewed papers published on this because it is not an effect. What makes you think it might be? Is there anything special about an eclipse other than a variation in illumination?

 

[Baluncore]

@rtx22. I encourage you to repeat the experiments.
Ask more questions.

Physics becomes a religion when it demands blind faith.

 

[anorlunda]

Is there anything special about an eclipse other than a variation in illumination?

During an eclipse, Earth-Moon-Sun are on a common line. E-M-S for a solar eclipse and M-E-S for a lunar eclipse.

But that should pose no problem for software models that include both Lunar and Solar tidal forces.