How can I measure the terrestrial tide on my place?

[berkeman]

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.

I know, I was just giving the OP a bit of a hard time for saying that the prediction software blows up during eclipses...

 

[Baluncore]

I know, I was just giving the OP a bit of a hard time for saying that the prediction software blows up during eclipses.

And there I was trying to imagine what could make our universe non-linear with respect to gravity. It would certainly make the universe more interesting.

 

[gNat]

In my work with the North Carolina Division of Water Resources our measurements of water levels in monitoring wells (especially those in basement rock) commonly reveal Earth tides (https://www.ncwater.org/?page=20).

The data is collected hourly (using a pressure transducer) which is frequent enough to capture the curve shape and show the similarity to ocean tides, although at a much reduced amplitude. Water levels from our well called Troutman (L67U2) are displayed in the attached image.

The upper graph illustrates the complete record for this well and the water level responses due to evapotranspiration and rainfall. The lower graph shows a recent week of data and captures Earth tidal responses. This well is 354 feet deep and about 180 miles from the ocean.

We only give the public access to daily measurements from our wells, but we can honor special requests for hourly data. I've weighed into suggest that the original question might be answered by a locally monitored well with at least hourly water level measurements.

 

[anorlunda]

In my work with the North Carolina Division of Water Resources our measurements of water levels in monitoring wells (especially those in basement rock) commonly reveal Earth tides

Wow. Very interesting. Thank you for sharing.

There are several periods visible in the data. The 12 hour cycle shows roughly 4.5cm peak-to-peak deviation. I can't say if that is reasonable for an Earth tide. I can also speculate that tides change the stresses in the rocks that cause water in the cracks to move and thus force water into the wells. That would make a very sensitive instrument for tidal forces, but the water level would not directly indicate changes in elevation of the Earth's crust.

That data sounds ripe for a grad student to take on as a thesis project.

 

[Baluncore]

I am surprised that Earth Tide can be seen in the record. I would expect the Earth to rise and fall with the ground water. I am going to take some convincing.

In the bottom graph there is a minimum at midnight and noon every day. There seems to be no daily phase shift like a tide, so I would hazard a guess that it was due to the rate of discharge from the well, which might be driven by local water demand.
Are the wells pumped on local demand, or are there two cycles of pumping per day, 12 hours apart ?

 

[gNat]

No pumping from this well, nor are there any nearby pumping wells. Please explain your phase shift comment. The hydrograph (time-series plot of water level) is impacted by rainfall events which might be hiding a phase shift?

 

[Baluncore]

My answer should be more complex, but I will keep it short until more information is available.
It is a fascinating observation and deserves a full analysis and explanation.

The lunar tide is the greater component and should appear 54 minutes later each day. I do not see that distinctive signature in your record. Instead your record is dominated by a very regular solar 12 hour component. Where is the lunar component?

Your graph of data from one week, 21–28 march shows a clear semidiurnal component, but of what? The new moon was on 24 March so we expect a greater tide with both Moon and Sun tides summing in phase. But on that day at midnight and midday, your record shows low water, which is the exact opposite of what is expected for land, or for water surface in the middle of an ocean.
That says the land must be rising and the water is somehow being left behind. But how could that be? Is the hydrostatic load on the lithosphere being reduced by the Earth tide so the low density water will fall back down the hole?

 

[gNat]

Thank you for explaining the two components of tides and I see that we're missing something. I've attached another picture of hydrographs of the same time period from two wells. I've selected a longer time period (one month) for display in the lower graphs. With this webpage, a plot of data over too long a time period obscures the smaller wiggles. I wonder if you might be interested in looking at more of the data through our web service. I'd like to send you that link offline if possible so as to keep the load off our server, but I'd really appreciate your input on a feature of the data we collect which I've always attributed to Earth tides. The water level data can get very complex with discharge and recharge effects, so it's sometimes hard to sort through it all. I've tried to pick a period of time with less of that noise. Thanks.

 

[anorlunda]

Thank you for explaining the two components of tides and I see that we're missing something.

I think @Baluncore and I are saying the same thing. There can be many factors that influence the well levels. Only careful and detailed data analysis could confirm those factors and determine their relative magnitude. That's a big project. As I said, a graduate thesis size project. I think it would be interesting and perhaps worth doing, because after analysis it may be possible that the elevations are a very sensitive indicator of underground effects, if (the big if) signal can be separated from noise.

Perhaps you can show the data to UNC and offer to cooperate with them if a student wants to do a research project using your data.

 

[gNat]

I appreciate your time and thoughtful insights. I'll see if our Triangle's universities are up to the task.

 

[jrmichler]

The data in Post #38 has similarities to inland lake water level data that we gathered last summer. This was from a research project studying evaporation and seepage in an inland seepage lake. Seepage lakes do not have streams entering or leaving. We were seeing a cyclic daily water level variation on the order of 2 to 5 mm. We know that variation was a false reading.

Water level was measured using a pressure sensor mounted to a pipe driven into the bottom of the lake. Measuring water level with a pressure sensor requires atmospheric pressure compensation because normal variation of atmospheric pressure is more than a foot of water. There are two ways to compensate for atmospheric pressure. One way is a differential pressure sensor with one side in air. That requires shielding, filtering, and a desiccant to keep the air end dry and not plugged by spiders. The other way is with two pressure sensors, one under water, and one to measure atmospheric pressure. Software subtracts one from the other to get water depth.

This was a low cost pressure sensing system that used the second method. The instrumentation had a temperature correction built in, but that temperature correction was less than perfect, and was the cause of the daily cyclic variation. We were able to get useful information by taking readings at 30 minute intervals, then calculating daily averages from the 30 minute data.

More expensive instrumentation using the differential pressure method was used in a similar project in 2018:
https://rdcu.be/bNGpD

 

[gNat]

We also use two pressure sensors, one below water and the other dangling in the well above water, but below land surface to avoid temperature effects (we've documented them in the past) and resorted to moving the barometer into the well as a result. I've attached another image of the Troutman well water levels vs. the NOAA tidal gauge at Wrightsville Beach 8658163 both keyed to EST. Any thoughts?

 

[Baluncore]

I've attached another picture of hydrographs of the same time period from two wells. I've selected a longer time period (one month) for display in the lower graphs.

When I compare the two wells for 14 April 2019 to 14 May 2019 I see a good correlation.

Lunar phases during the period were approximately as follows.
First quarter 13 April 2019 minimum amplitude
Full moon 19 April 2019 max
Last quarter 27 April 2019 min
New moon 05 May 2019 max
First quarter 12 May 2019 min
Full moon 19 May 2019 max

When the moon is full or new the tidal amplitude should be greatest.
A quarter moon should have lower tidal amplitude.

The three minimum amplitudes in the record appear to correlate with the quarters.
The pattern appears to repeat with the expected 14.75 day period. For example, there are four broad daily peaks before the minimum on 27 April, last quarter. There are then four broad daily peaks before the minimum on 12 May, first quarter.
So it is actually looking more tidal.

It would be interesting to see atmospheric pressure over the same period. Maybe the roughly weekly cycles of highest water correspond to narrow low pressure troughs, between wider, more stable, high pressure systems.
The longer 3 week decline can be explained by steady aquifer discharge.

It would be easy to get sucked into this research and analysis.
My hypothesis would be that the hydrostatic pressure in the aquifer is relieved by the Earth Tide.

 

[Baluncore]

I've attached another image of the Troutman well water levels vs. the NOAA tidal gauge at Wrightsville Beach 8658163 both keyed to EST. Any thoughts?

The two correlate remarkably well.
Earth tides are not delayed by water wave propagation or oscillation as are ocean tides. Coastal tides are period selective filters so the waveforms will be different but the period will match.
It would be interesting to look at the model for Earth tide over the same period. Unfortunately my Earth Tide code is bent at the moment and needs some “end of leap seconds” therapy.

 

[gNat]

The two correlate remarkably well.
Earth tides are not delayed by water wave propagation or oscillation as are ocean tides. Coastal tides are period selective filters so the waveforms will be different but the period will match.
It would be interesting to look at the model for Earth tide over the same period. Unfortunately my Earth Tide code is bent at the moment and needs some “end of leap seconds” therapy.

I'm not quite sure what therapy is necessary, but good luck. So, if it was unbent, you can model Earth tides at a particular location?

 

[Baluncore]

So, if it was unbent, you can model Earth tides at a particular location?

Yes, it is used to eliminate the Earth tide from geological gravity surveys.
There is one here; https://geodesyworld.github.io/SOFTS/solid.htm#link2

 

[gNat]

It would be interesting to see atmospheric pressure over the same period. Maybe the roughly weekly cycles of highest water correspond to narrow low pressure troughs, between wider, more stable, high pressure systems.
The longer 3 week decline can be explained by steady aquifer discharge.

It would be easy to get sucked into this research and analysis.
My hypothesis would be that the hydrostatic pressure in the aquifer is relieved by the Earth Tide.

First, you're right about how fascinating the data can be. My job is analyzing the bigger wrinkles in the data which are associated with measuring aquifer conditions (drought and availability) -- more important to the citizens of NC.

We do have the barometer readings for the same time period which are part of the attached graphic. I definitely see correlation, but it isn't as in sync as the tide vs water level plot. I expect to see correlation with atmospheric pressure as this is a water table well (surficial aquifer).

 

[Baluncore]

We do have the barometer readings for the same time period which are part of the attached graphic. I definitely see correlation, but it isn't as in sync as the tide vs water level plot. I expect to see correlation with atmospheric pressure as this is a water table well (surficial aquifer).

Thanks for that atmospheric pressure graph. My atmospheric hunch paid off way better than I expected. I am surprised at how much the record can be cleaned up by subtracting an atmospheric component.

Where the water depth is measured with a pressure sensor, and the barometric correction applied, it is hard to separate out the source of the atmospheric component. Is it more or less reference tracking/calibration, or is it water level in the bore? But it does not really matter once a coefficient for the well/instrumentation has been determined.

For any water well I would compute two coefficients.
1. Atmospheric pressure correction. Recorded barometer.
2. Tidal correction. As predicted by Solid, Earth Tide.

When those terms are removed from the data you will be left with the long term discharge-recharge process, plus the noise floor. The frequency components of the signals are identifiable, or well separated.

I am surprised that Earth Tide can be seen in the record. I would expect the Earth to rise and fall with the ground water. I am going to take some convincing.

I do take a lot of convincing, but I now believe that Earth Tides can be detected in water well levels.

As a model/mechanism, I see the weight of the rock changing with the tidal variation of little g. That changes the compression in deeper rock which is detected by the displacement of interstitial water from the rock volume.

It would be interested to see how the tidal coefficient for different wells correlated with different geological environments. There may also be some interesting delays in the response.

I would expect different coefficients for different rock types/structures. A granite would have few horizontal fractures (unloading) that communicate with the well. A deep porous sandstone might give a greater tidal signal. Regional fracture zones would complicate the correlation.

Now back to the OP. Is there enough variation in NC well geology to indicate what rock type or structure is best for detecting the Earth Tide?

 

[gNat]

We have a bunch of wells, NC has diverse geology, and we don't always see the ripples we associate with Earth tides, so I'm guessing that some of those questions can be answered with enough effort. For example many of our wells are in coastal plain sediments (rarely lithified) and we don't see evidence of Earth tides, although (if memory serves) I've seen them sometimes in very deep coastal plain wells (1,000+ feet).

Yes, it is used to eliminate the Earth tide from geological gravity surveys.
There is one here; https://geodesyworld.github.io/SOFTS/solid.htm#link2

I used Solid with the link you sent and a bit of manipulation to get a month's time and subtracted 5 hours to make the results in EST and produced the attached graphic. I see that Earth tides have the same period as ocean tides, but there are interesting inflections based on the phase shifts associated with the lunar and solar components. I've plotted the Up component (meters) against the Troutman (L67U2) hydrograph (elevation in feet above msl). Similar to atmospheric pressure, it is negatively correlated with the water level changes (higher Up component means lower water level). Does that make sense?

I hope to incorporate Solid results in a future web page to allow more comparisons and an analysis of how rock type may influence Earth tides measured in our water levels.

 

[Baluncore]

Seeing the same signatures in both records as the solar and lunar components slide past each other over the month is very convincing. The tides are reinforcing and cancelling as expected in both records.

Similar to atmospheric pressure, it is negatively correlated with the water level changes (higher Up component means lower water level). Does that make sense?

Yes. That is correct.
Understanding why the graph is inverted requires a simplified hydro-geological model. There are two different scenarios, both result in the water level in the well moving with a reversed phase when compared to the solid Earth or the ocean tide.
I am working on a clearer explanation of the model.

 

[Dr. Courtney]

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.

Why not get the height vs time for many, many days and then recover the amplitudes of the tidal components with a Fourier transform? I've used Fourier transforms to recover regular water tide magnitudes even though individual readings were swamped with noise from wind and other effects. If one knows the frequency, the Fourier transform is the right tool to recover the amplitudes in spite of lots of noise.

 

[Baluncore]

Why not get the height vs time for many, many days and then recover the amplitudes of the tidal components with a Fourier transform?

You can do that if you have the time.

You could record GPS height for a year and then extract many lunar and many solar frequency components, but those sinusoidal components have complex varying astronomically dependent amplitudes.
You are looking for a couple of dozen sinusoids, with mutually irrational periods, in a massive data set of noise. Rather than an FFT you would do better writing a bank of numerical correlators. You will find what you are looking for, if you look at noise for long enough. I expect the solar components will be very difficult to separate from the harmonics of the daily ionospheric delay.

The open source software mentioned earlier, SOLID written by D. Milbert, models the solid Earth tide. By computing the Earth relative position of the observer, Moon, and Sun, it implicitly handles the sum of the variation in component amplitudes with time and observer position. You could correlate the GPS height record with the SOLID model for your location, then subtract the tidal component to get the much greater variation in GPS delay.

 

[Dr. Courtney]

You can do that if you have the time.

You could record GPS height for a year and then extract many lunar and many solar frequency components, but those sinusoidal components have complex varying astronomically dependent amplitudes.
You are looking for a couple of dozen sinusoids, with mutually irrational periods, in a massive data set of noise. Rather than an FFT you would do better writing a bank of numerical correlators. You will find what you are looking for, if you look at noise for long enough. I expect the solar components will be very difficult to separate from the harmonics of the daily ionospheric delay.

The figure below shows that the Fourier transform works very well at finding nearly all the expected water tide peaks at low frequencies with a year's worth of data. Sure, with the Earth tide data, the solar peaks may be difficult to separate from the systematic noise from the ionosphere. But the larger lunar peaks (O1, K1, M2) should be fairly easy to find, identify with confidence, and determine amplitude estimates. In any case, nothing against numerical correlators, but with a year's worth of raw data, one can do a lot with freely available code. https://sourceforge.net/projects/amoreaccuratefouriertransform/

Note however, that I recommended a Fourier transform rather than an FFT. The code used for the graph below is a standard Fourier transform using explicit integration rather than an FFT.

 

[Baluncore]

The figure below shows that the Fourier transform works very well at finding nearly all the expected water tide peaks at low frequencies with a year's worth of data.

That is expected for ocean tides measured against a shore reference. It has been analysed that way for over 150 years.

This thread is about the solid Earth tide. Measuring the GPS height at a fixed land station for one year will not produce such a clean analysis of solid Earth tide. On land, where there can be no possibility of a differential reference, I would expect to see GPS ionospheric delay variation noise swamping K1 and S2. I expect you will see an M2 sinewave, but without any detail necessary to identify the solar component of the solid Earth tide.

 

[gNat]

Sorry to be slow to post again. I was busy brushing up on my Python skills and building better access to the hourly ground water level data and SOLID.

I've attached eight pictures (sorry) of graphs which combine ground water levels from various stations in our network (across NC) and SOLID results from those locations over the specified time periods. Each graph is set up to show the same range of distance (in feet) on the two Y axes, so amplitudes of both Earth tides and water level fluctuations can be compared. I've identified the rock type associated with each well in the file names.

A couple of things are becoming clear. Well-foliated metamorphic rocks seem to show the strongest amplitudes and more massive or less indurated formations yield weaker to no Earth tide influences. In a few of the graphs I had to pick my timeframe carefully so as to show Earth tide fluctuations because recharge events swamped out that signal.

The two wells at Pink Hill are Cretaceous sand aquifers. The deeper, likely more indurated, shows Earth tides and the other doesn't (nothing recognizable).

I hope this is helpful to others. I know it's fascinating to me to get a better grasp of the forces influencing water levels in our wells. An Earth tide compression causes increased pressure on ground water which shows up as a water level peak. Larger openings in the rock, yield higher peaks. As the Earth tide de-compresses, ground water pressure decreases which causes a valley in the water level. Water level responses vary from non-existent to about 1/8 the amplitude of Earth tides (rough estimate).

 

[Baluncore]

Interesting.
I was wondering how much rock there was above the water table, but since you don't give the surface RL of the well I thought I would try Google Earth. You appear to be giving station Lat/Long coordinates for wells in a regional mapping grid rather than in WGS84 = GPS, as used by Google Earth and SOLID. What grid are you using?

My SOLID is now working and seems to agree close enough with yours, give or take the couple of miles possible error in location.

 

[gNat]

No, those are WGS84 coordinates in decimal degrees. I've attached the Google map of Pink Hill station using the coordinates given on the previous image. The wells are the three dots to the east of the location symbol.

Land surface elevations (feet above MSL):
Pink Hill 126
Gibsonville 648
Marble 1,711
Troutman 816
Tater Hill 4,060
Oxford 462
Olivers Crossroad 45

 

[anorlunda]

I'm having trouble visualizing the definition of Earth tide.

1. Are we saying that the entire continental shelf is rising and falling relative to the center of the Earth? What happens with the mantle underneath the continent?
2. Or is it stretching/shrinking near the surface more than being displaced up/down. I would think that stretching/shrinking would cause interstitial water to move from the rock to the cracks and voids, thus changing water level in wells relative to the surface instruments, thus making water level a sensitive indicator.
3. Or is is that the entire globe from Earth's core to the surface is distorted in the ellipsoid direction due to tides?

Wikipedia says #3, citing a magnitude of about 1 meter.
https://en.wikipedia.org/wiki/Earth_tide

But if the whole globe is distorted, the distance between the top and the bottom of a well hole would remain nearly constant. #3 also makes me think of Jupiter's moon Io, which is heated to the extreme by frictional heating by tidal motions. Is Earth's internal heating due to friction significant relative to radioactive decay?

 

[Baluncore]

3, Or is is that the entire globe from Earth's core to the surface is distorted in the ellipsoid direction due to tides?

That is the case.
The Earth appears to be elastic with an average rigidity somewhere between glass and steel. The globe has an immediate elliptical tidal distortion with a maximum trough to peak radial range of 51.5 cm, when everything acts in the same direction.

But if the whole globe is distorted, the distance between the top and the bottom of a well hole would remain nearly constant.

Yes. It remains almost constant. But:
The mass of rock near the surface is fixed. The tide results in a minute change of local little g, so the weight of the rock and it's downward force changes with the tide. The elasticity or compressibility of porous rock is greater than solid rock, so the volume of more porous rock changes more under compression. The water is squeezed out of the deep rocks and must move a few millimetres up in the formation. The percentage pore volume at the water table sets the vertical range sensitivity of the inverted tide in the well.

In effect, the rock of the aquifer is a compression spring supporting the weight of all the rock above. The space around that spring is filled by non-structural fluid, which is ground water. (The wet rock has weight reduced by buoyancy in that hydrostatic fluid). As the rock spring changes length, water is displaced in the vertical direction. The reduction in rock column length is small, but it is added, to differentially raise the water level in the well.

 

[rtx22]

Yes, it is used to eliminate the Earth tide from geological gravity surveys.
There is one here; https://geodesyworld.github.io/SOFTS/solid.htm#link2

Has anyone compared the software data with the data from the gravimeter or the pendulum in reality and not with data from the internet? The superconducting gravimeter gives me other data, data that do not coincide with those of the program, not always.
There are also other tidal components like M2 S2 Ssa Sa MmN2 K2 KI OI PI that induce major variations in reality that the software does not have implemented.
Test yourself if you have a gravimeter.

 

[Baluncore]

Has anyone compared the software data with the data from the gravimeter or the pendulum in reality and not with data from the internet?

Can you please give a link to the tidal data on the internet.

The Earth tide computed by the “Solid” software correlates remarkably well with the borehole data observed. "Solid" is used to reliably remove tidal changes from gravity surveys.

For ocean tides, the coastal profile geometry selects and amplifies many different components. Those resonances are insignificant in the solid Earth tide, so those components can be ignored.
Land-based measurement of little g near the coast, requires allowance for the tidal movement of the mass of nearby ocean water.

The superconducting gravimeter gives me other data, data that do not coincide with those of the program, not always.

Which superconducting gravimeter are you referring to, and where is it located ?