The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Investigations => Topic started by: SteelyBob on September 07, 2021, 08:13:31 PM

I noticed that wiki is somewhat brief in its look into RLGs  the data comes from an experiment conducted in the early 20th century, a very early commercial RLG in the the early 1990s, and a MEMs gyro (like the one you would find in a phone, which work on coriolis and not lasers).
I thought people might be interested in this one: https://iopscience.iop.org/article/10.1088/17426596/723/1/012061/pdf (https://iopscience.iop.org/article/10.1088/17426596/723/1/012061/pdf), which is a large, ultra precise RLG capable of measuring tiny variations in the rotation, as well as the rotation itself.
Given that the wiki rejects the notion of a grandscale conspiracy (in favour of a smaller spacetravel one), are the scientists who wrote this paper and who worked on the device wrong?

Given that the wiki rejects the notion of a grandscale conspiracy (in favour of a smaller spacetravel one)
In favor of a smaller one that does not involve the shape of the earth.
are the scientists who wrote this paper and who worked on the device wrong?
Yes, of course  about lots of stuff. That's just the way human knowledge is, perhaps most notably in science.
Interferometery is very interesting, well worth studying, and somewhat relevant to this subject.
The presumed rotation can be measured with a simple pendulum, as well as any mechanical gyroscope (including the mems, which is not a gyroscope even in a figurative/metaphorical sense)
The rlg works, it just does not work the way the modern scientists imagine it does (they should study its invention, and its inventor) and it does not measure what they presume it does.

The rlg works, it just does not work the way the modern scientists imagine it does (they should study its invention, and its inventor) and it does not measure what they presume it does.
It appears that a fellow named Clifford Heer was the first guy to come up with the RLG concept back in 1961:
Modern Inertial Sensors and Systems
By AMITAVA BOSE, SOMNATH PURI, PARITOSH
"In Chapter 11 we defined the ring laser gyroscope (RLG) as a type of active resonator gyro. Clifford Heer conceived the RLG in 1961 [1]; he saw that the properties of the laser, recently invented by Schawlow and Townes, could be exploited to measure rotation."
How does it "...not measure what they presume it does," if not rotation as originally intended? What's your evidence for such a statement? Or is this just your opinion?

I noticed that wiki is somewhat brief in its look into RLGs  the data comes from an experiment conducted in the early 20th century, a very early commercial RLG in the the early 1990s, and a MEMs gyro (like the one you would find in a phone, which work on coriolis and not lasers).
I thought people might be interested in this one: https://iopscience.iop.org/article/10.1088/17426596/723/1/012061/pdf (https://iopscience.iop.org/article/10.1088/17426596/723/1/012061/pdf), which is a large, ultra precise RLG capable of measuring tiny variations in the rotation, as well as the rotation itself.
Given that the wiki rejects the notion of a grandscale conspiracy (in favour of a smaller spacetravel one), are the scientists who wrote this paper and who worked on the device wrong?
I don't think you've read through everything in the Wiki on this. The very paper you linked to is cited on the second Ring Laser Gyroscope page in the section 'Fluctuating Earth Rotation Rate'.
The bottom of this page:
https://wiki.tfes.org/Ring_Laser_Gyroscope
continues onto a second page:
https://wiki.tfes.org/Ring_Laser_Gyroscope__Seismology

I don't think you've read through everything in the Wiki on this. The very paper you linked to is cited on the second Ring Laser Gyroscope page in the section 'Fluctuating Earth Rotation Rate'.
The bottom of this page:
https://wiki.tfes.org/Ring_Laser_Gyroscope
continues onto a second page:
https://wiki.tfes.org/Ring_Laser_Gyroscope__Seismology
You're absolutely right  I hadn't spotted the reference to that paper in the seismology page. My apologies. That said, it doesn't really flow as a 'second page'  it's just one of several links in the article.
Reading the seismology page, and indeed the RLG main page, is a fascinating journey into the bizarre analysis that runs through most of the wiki. I'm still not clear if you have wilfully misrepresented, or just completely misunderstood what is being discussed in the various papers. That one that I linked to above, for example, is describing a new gyro with a sensitivity of below ∆Ω_{E } x 10^{8}. They aren't talking about being able to measure the earth's rotation  they are interested in parts per million of it. The earth's rotation is so ridiculously, stunningly obvious, and so easy to detect  they are way, way past that.
There's a great deal that's wrong within the wiki. Here's a few:
The Ring Laser Gyroscope (RLG) is a consumer device version of the MichelsonGalePearson Experiment (MGP)
Not really. RLG's are expensive, and accurate ones are even more so. They aren't really consumer products. MGP didn't have access to lasers, or the optical technology required for a RLG. The Canadian paper you cite in the wiki was specifically looking at a low cost model, with associated reductions in accuracy. The Honeywell GG1320AN, which seems to be the industry standard model, has far better specs  a quoted bias drift, for example, of 0.0035 deg/hr, compared to the cheaper/older model used in your paper, which had bias drifts measuring in the low single digit degrees/hr.
Essentially the tests saw wild results. There was almost no change to light's velocity in one test, and then a lot of change in another test. It is perplexing that the rotation of the earth would start and stop when tested at different times. Only through the statistics was it claimed that the experiment saw the rotation of the earth. The inconsistent results were ambiguous in nature and could offer no evidence of the shift in the phase of the light beams. As stated above, the results of the MichelsonGalePearson experiment were inconsistent and an algorithm was applied to get the desired result.
Again, not really. MGP were working with relatively primitive equipment  it is extremely hard to measure fringe distance manually like that, especially when the apparatus would have been hugely sensitive to changes in temperature and any local vibration. There is absolutely nothing wrong with taking a statistical approach  their data shows a clear normal distribution shape with the mean centred on almost precisely the fringe separation one would expect for the apparent rotation at their latitude. Taking multiple samples and applying statistical techniques to them is basic science  if you are rejecting that then there's little point in doing any science at all. If their data showed an equal chance of getting different results, that would be a very different thing. But it doesn't.
If we are to say that the Ring Laser Gyroscope is the same device, then the same criticism would apply.
But we aren't to say that, are we? Because we are nearly a century on, and we are talking about technology with accuracy that MGP could only have dreamed of.
It is further seen that, like the original MGP experiment, the raw results of the gyroscopes are inconsistent[2] and dwarf the results from rotation.
None of what follows after this sentence shows that in the context of RLGs. You've had to dig out an experiment using MEMS sensors, which are far, far less accurate than RLGs, which is why you won't find them in navigation equipment. The experiment is really interesting  they are using various statistical techniques to try to pull out the earth rate from the noise  but it is nothing to do with RLGs, although they do actually still manage to measure the earth rate nevertheless, which is very impressive.
The graphs you show from the Canadian test of the Honeywell device show absolutely no comparison of the noise with the signal caused by earth's rotation  it's not in there at all. They essentially ran a series of tests using their calibrated bench test system, some with the device orientated to remove the earth rotation component and some with it not, but the rotation rate itself isn't shown  they were only interested in the measured rate versus the accurately calibrated forced rate. None of your graphs show the actual measurement of the earth's rotation. They just show various noisy signal plots, which is hardly surprising given the nature of the device.
The seismology page takes it to whole new level of oddness.
Researchers have used these sensitive devices to detect patterns in the background microseismic noise, where certain features are interpreted to be caused by the earth's rotation. The feature of the background noise assumed to be an effect of the earth's rotation is called the "Earth line," and is admitted to be of unknown origin and cause.[2]
This is just utter nonsense, I'm afraid. Seismic activity presents itself as disturbances to the measured earth rate. The earth rate isn't extracted from the noise. The output from an accurate RLG is nothing like the MEMS graphs you showed  the noise is low ppm compared to the signal  measuring several degrees per hour (unless you are on the North Pole, or you orientate your RLG to the earth's rotation axis, you will measure < 15 / deg/hr) is trivial and accurate. High end, large installed RLGs like Grossring or GINGER are now able to resolve tiny variations in earth rate  see https://www.sciencedirect.com/science/article/pii/S1631070514001406 (https://www.sciencedirect.com/science/article/pii/S1631070514001406)
It is unclear whether those types of RLGs in airplane guidance systems claim to be able to detect the earth's rotation.
It's not unclear at all  they absolutely do, and they have to be corrected for it. As I've shown before, with you failing to respond (eg https://forum.tfes.org/index.php?topic=17396.msg227601#msg227601 (https://forum.tfes.org/index.php?topic=17396.msg227601#msg227601)), even older mechanical directional gyros have to be compensated for drift, either by a benchadjusted drift nut for short range aircraft, or via a latitude scale set in the cockpit. Something like a GG1320AN, with a bias of around 0.0035 deg/hr, will absolutely drift if earth rate isn't compensated for. It's equally true of mechanical gyro systems and laser based ones (RLGs, of course, aren't actually gyros  they are angle rate sensors). Here's one about marine systems: https://www.hydrointernational.com/content/article/howdoesinertialnavigationwork (https://www.hydrointernational.com/content/article/howdoesinertialnavigationwork))
Overall, I'm shooting for sophistry, rather than misunderstanding, but I could be wrong.

The rlg works, it just does not work the way the modern scientists imagine it does (they should study its invention, and its inventor) and it does not measure what they presume it does.
I would echo Stack's comment. Don't be so mysterious...if not rotation, what then does a RLG measure? Bear in mind you can put them in a test rig and measure their accuracy very easily (see the Canadian paper in the wiki). So if you've got a system that is proven to be accurate when you rotate it at a known rate, and then it measures a rate of (15 deg / h) x (sin latitude) when you put it flat on a table, what exactly is it measuring, if not the rotation of the table, and therefore the earth?

There's a great deal that's wrong within the wiki. Here's a few:
Quote
The Ring Laser Gyroscope (RLG) is a consumer device version of the MichelsonGalePearson Experiment (MGP)
Not really. RLG's are expensive, and accurate ones are even more so. They aren't really consumer products.
Incorrect. Businesses are consumers.
(https://i.imgur.com/29IcLXG.png)
The Canadian paper you cite in the wiki was specifically looking at a low cost model, with associated reductions in accuracy.
Incorrect:
"The gyroscope demonstrated excellent highrate
performance although significant scale factor deviations
were noted during temperature variations."
"Results of the testing showed that instrument
performance at high angular rates was better than
specifications although significant scale factor deviations
were noted during temperature variations. "
(https://i.imgur.com/I49BDmc.png)
Again, not really. MGP were working with relatively primitive equipment  it is extremely hard to measure fringe distance manually like that, especially when the apparatus would have been hugely sensitive to changes in temperature and any local vibration. There is absolutely nothing wrong with taking a statistical approach  their data shows a clear normal distribution shape with the mean centred on almost precisely the fringe separation one would expect for the apparent rotation at their latitude.
If it's measuring variation it is not directly measuring the phenomenon. They are measuring some sort of variation and are using statistics to make indirect conclusion. There are multiple phenomena involved, which muddies the conclusions.
But we aren't to say that, are we? Because we are nearly a century on, and we are talking about technology with accuracy that MGP could only have dreamed of.
It appears that the raw results from the Honeywell Gyro are also inconsistent.
The graphs you show from the Canadian test of the Honeywell device show absolutely no comparison of the noise with the signal caused by earth's rotation  it's not in there at all. They essentially ran a series of tests using their calibrated bench test system, some with the device orientated to remove the earth rotation component and some with it not, but the rotation rate itself isn't shown
The raw tests with the earth's rotation from the Honeywell Gyro shows that the signal is inconsistent and noisy.
The output from an accurate RLG is nothing like the MEMS graphs you showed
Citation needed. The raw tests from the Honeywell gyro looks very noisy.
measuring several degrees per hour (unless you are on the North Pole, or you orientate your RLG to the earth's rotation axis, you will measure < 15 / deg/hr) is trivial and accurate.
Citation needed. Where are the raw results showing this?
High end, large installed RLGs like Grossring or GINGER are now able to resolve tiny variations in earth rate  see https://www.sciencedirect.com/science/article/pii/S1631070514001406
Irrelevant if you can't demonstrate what the earth rate actually is in these studies. These studies seem to imply that it's a seismic phenomenon, as seen on the Ring Laser Gyroscope seismology page in the Wiki.
It's not unclear at all  they absolutely do, and they have to be corrected for it. As I've shown before, with you failing to respond (eg https://forum.tfes.org/index.php?topic=17396.msg227601#msg227601), even older mechanical directional gyros have to be compensated for drift, either by a benchadjusted drift nut for short range aircraft, or via a latitude scale set in the cockpit. Something like a GG1320AN, with a bias of around 0.0035 deg/hr, will absolutely drift if earth rate isn't compensated for. It's equally true of mechanical gyro systems and laser based ones (RLGs, of course, aren't actually gyros  they are angle rate sensors). Here's one about marine systems: https://www.hydrointernational.com/content/article/howdoesinertialnavigationwork)
Citation needed for the adjustment for Ring Laser Gyroscopes. Your links are talking about mechanical gyroscopes.
About the latitude nut:
From a video demonstrating the Latitude Nut: https://www.youtube.com/watch?v=xNYW8JWMVOY&ab_channel=fromjesse (https://www.youtube.com/watch?v=xNYW8JWMVOY&ab_channel=fromjesse)
04:22 "over here on the other side this is your latitude nut right there that can induce you can move that in or out and you can induce some a drift clockwise or counter clockwise on the you know east or west on the whatever you want to call it the scale here"
If you can induce the rotation by rotating a nut, how do you know if you're introducing it or removing it by adjusting the nut?
14:22 "the earth's rotation would then be added or subtracted from the existing drift of the gyroscope"
Oh, so now there is "existing drift" that the earth's rotation is added or subtracted from to get the "true drift".
Very scientific evidence there for the validity of this nut.
Clearly, more evidence is needed on this beyond these assumptions and appeals.

A test was done with a mechanical gyroscope in a terrestrial environment and no "latitude nut" was needed. The earth didn't move.
https://www.youtube.com/watch?v=_AD6xk6jyDQ&feature=emb_title&ab_channel=JohnSavage
An airplane gyro and other gyros are tested here, showing that there is no drift:
https://www.youtube.com/watch?v=nUFMZkxochs&ab_channel=RobDurham
On the Latitude Nut:
To know how much you need to adjust it you need to know multiple variables.
https://books.google.com/books?id=6VTzCQAAQBAJ&pg=SA2PA37&lpg=SA2PA37&source=bl&ots=rUQ9gIz_q5&sig=ACfU3U0_8LNHps7CCyyOkxNGsEmz643Rw&hl=en&sa=X&ved=2ahUKEwjgvOOlkvDyAhXSElkFHe7nD14Q6AF6BAg8EAM#v=onepage&q&f=false
(https://i.imgur.com/A0qN9lK.png)
Alternatively, you know, the earth was not rotating and this complex compensation is not needed and there was simply a wander of some particular amount during a particular journey.
Can you see how uncontrolled wander invalidates this latitude nut proof of yours?

Incorrect. Businesses are consumers.
I can't get too excited about this one. My point was that your phrase suggested that RLGs are cheap. They aren't. Hence my point about your MEMS example  you find that kind of tech in all sorts of everyday items, not least our phones, for example. The closest most people get to an RLG is the cockpit of the aircraft that takes them holiday.
The Canadian paper you cite in the wiki was specifically looking at a low cost model, with associated reductions in accuracy.
Incorrect:
"The gyroscope demonstrated excellent highrate
performance although significant scale factor deviations
were noted during temperature variations."
"Results of the testing showed that instrument
performance at high angular rates was better than
specifications although significant scale factor deviations
were noted during temperature variations. "
That doesn't change the fact that the whole point of the model in question is to make it cheap. The materials used and other specs are way lower than their normal products. Yes, the device performed well, but the bias, amongst other stats, is way, way worse than, say, a GG1320.
Again, not really. MGP were working with relatively primitive equipment  it is extremely hard to measure fringe distance manually like that, especially when the apparatus would have been hugely sensitive to changes in temperature and any local vibration. There is absolutely nothing wrong with taking a statistical approach  their data shows a clear normal distribution shape with the mean centred on almost precisely the fringe separation one would expect for the apparent rotation at their latitude.
If it's measuring variation it is not directly measuring the phenomenon. They are measuring some sort of variation and are using statistics to make indirect conclusion. There are multiple phenomena involved, which muddies the conclusions.
Are you contesting that fringe separation is a function of rotation rate? Or not? MGP were trying to measure fringe separation. It's not easy. But they did it. And the shape of the stats proves that it is highly unlikely to be a fluke, because far more results occurred around the mean than around the extremes.
It appears that the raw results from the Honeywell Gyro are also inconsistent.
Really? I thought you said it performed well? If you're confused by the noise on the graphs then you clearly don't understand electronics, or indeed how RLGs work.
The raw tests with the earth's rotation from the Honeywell Gyro shows that the signal is inconsistent and noisy.
All of the tests show similar noise levels. If you think the earth is flat, then you presumably don't think the change of angle used to eliminate the earth's rotation from the test would have had any effect, though, right?
The output from an accurate RLG is nothing like the MEMS graphs you showed
Citation needed. The raw tests from the Honeywell gyro looks very noisy.
'Looks very noisy'...how much noise would it take for you to say that it wasn't noisy? Do you even understand what the noisy signal is? Do you understand the relative amount of noise in the MEMS example, versus the Honeywell gyro in the experiment, versus a more advanced Honeywell gyro, versus something like the large, fixed devices mentioned in the other papers...the ones that can measure changes in rotation rate down to 10^{8}? Citation needed? The one you've cited works nicely  https://iopscience.iop.org/article/10.1088/17426596/723/1/012061/pdf (https://iopscience.iop.org/article/10.1088/17426596/723/1/012061/pdf)
measuring several degrees per hour (unless you are on the North Pole, or you orientate your RLG to the earth's rotation axis, you will measure < 15 / deg/hr) is trivial and accurate.
Citation needed. Where are the raw results showing this?
Bob Knodel did quite a nice job, didn't he?!
About the latitude nut:
Lattitude Nut
https://www.youtube.com/watch?v=xNYW8JWMVOY&ab_channel=fromjesse
04:22 "over here on the other side this is your latitude nut right there that can induce you can move that in or out and you can induce some a drift clockwise or counter clockwise on the you know east or west on the whatever you want to call it the scale here"
“This is your latitude nut. You can move it in or out and induce some drift clockwise or counterclockwise, east or west”
If you can induce the rotation by rotating a nut, how do you know if you're introducing it or removing it by adjusting the nut?
Because when you build the device you design so that, without the gyro spinning, the device is balanced with the nut in the neutral position. All the nut does is move in and out, tipping the scales as it were, and via precession inducing a clockwise or anticlockwise rotation to oppose the drift.
The test was done with a mechanical gyroscope in a terrestrial environment and no "latitude nut" was needed. The earth didn't move.
https://www.youtube.com/watch?v=_AD6xk6jyDQ&feature=emb_title&ab_channel=JohnSavage
Clearly, more evidence is needed on this beyond these assumptions and sourceless appeals.
That video is more fakeable than anything NASA might put out. There's no actual way of figuring out if the gyro is spinning while the video runs, nor is there any way of knowing whether or not he's simply constrained the gyro. If anything, it's too perfect, as most gyros have some inherent drift due to friction and other intolerances.

Alternatively, you know, the earth was not rotating and this complex compensation is not needed and there was simply a wander of some particular amount during a particular journey.
Can you see how uncontrolled wander invalidates this latitude nut proof of yours?
So every avionics manufacturer is wrong? Every single flight manual, ATPL ground school exam, every military and civilian training course the world over is wrong? Look at this video: https://www.youtube.com/watch?v=t2yzsc3y1R8 (https://www.youtube.com/watch?v=t2yzsc3y1R8)
Earth rotation is a fundamental part of the align process. These people do this for a living, but they are wrong? The align process takes longer at extreme latitudes than at the equator because....why exactly?
If it's RLG testing you want...this guy is all over it. https://www.repairfaq.org/sam/laserlia.htm#liarlghr (https://www.repairfaq.org/sam/laserlia.htm#liarlghr)
Scroll down to the bit where he tests the GG1320AN: If the GG1320 were sitting on a table at the North pole, the Sagnac frequency δf due to the Earth's rotation would be around 3.38 Hz. At the latitude here of 39.95°, δf drops to 2.17 Hz. Multiplying by 4 for the GG1320 X4 resolution results in 8.68 counts/second, which is consistent with the observed count rate. It's comforting to know that the Earth is still spinning correctly as advertised. ;) The larger than expected change from 9 to 10 seconds when the GG1320 is supposed to be stationary is almost certainly because I was touching it. And as further confirmation that the slow counting is indeed due to the Earth's rotation, with the GG1320 tipped at around 40 degrees away from true North, the counting slows to a virtual standstill with just some randomness in the LSB due to vibrations, and reverses direction when tipped beyond 40 degrees. When tipped the other way up to 50 degrees towards North, the counting is most rapid. Isn't Physics wonderful? ;)
And if you want another example of drift correction due to latitude, how's about the AHRS system on a Hawk T1 training jet? This is a mech gyro based system, with a cockpit selectable latitude scale that is used to ensure the correct earth rate correction is applied. This simulator manual has quite a good overview: https://cdn.cloudflare.steamstatic.com/steam/apps/1478120/manuals/aerofly_fs_2_just_flight_hawk_t1a_manual.pdf?t=1605888346 (https://cdn.cloudflare.steamstatic.com/steam/apps/1478120/manuals/aerofly_fs_2_just_flight_hawk_t1a_manual.pdf?t=1605888346)
See page 15 for the control panel (note the 'LAT' control) and page 48/49 for the description.

Here's another interesting system, with measuring earth rate used as a specific test:
https://www.nature.com/articles/s415660200588y.epdf?sharing_token=8NhBRjx0KBddEuYa3GD6ydRgN0jAjWel9jnR3ZoTv0OX15JTFosKvFbDq1JK4EvG4QOgBd2ItHe3lP4RP7X9NXl4TBW4ckvuEEZ8zqrpxlpshE4AqhQbG4yIS2nho7BHQLAchvEAZo_Obub82qwMpLjPGPVroId3MHoKjoIsNsw2vuj1fSNaAN0m7d1w1YTr_M155Afcrae8zEf7uyyFDygAoD7zkT4gNXE7eUktXFtoXXPzw5CZMGA_HSFJV4WUrzfRfNtHtNfguJ0fX_QnGnYfWopGLDx_SJKg%3D&tracking_referrer=physicsworld.com (https://www.nature.com/articles/s415660200588y.epdf?sharing_token=8NhBRjx0KBddEuYa3GD6ydRgN0jAjWel9jnR3ZoTv0OX15JTFosKvFbDq1JK4EvG4QOgBd2ItHe3lP4RP7X9NXl4TBW4ckvuEEZ8zqrpxlpshE4AqhQbG4yIS2nho7BHQLAchvEAZo_Obub82qwMpLjPGPVroId3MHoKjoIsNsw2vuj1fSNaAN0m7d1w1YTr_M155Afcrae8zEf7uyyFDygAoD7zkT4gNXE7eUktXFtoXXPzw5CZMGA_HSFJV4WUrzfRfNtHtNfguJ0fX_QnGnYfWopGLDx_SJKg%3D&tracking_referrer=physicsworld.com)

I can't get too excited about this one. My point was that your phrase suggested that RLGs are cheap.
Does it? Consumer device means that a company is making it for sale. It doesn't mean that it's cheap.
Rich people are also consumers and have industries tailored around selling expensive things to them. They are called consumers, FYI. Same with businesses.
That doesn't change the fact that the whole point of the model in question is to make it cheap. The materials used and other specs are way lower than their normal products. Yes, the device performed well, but the bias, amongst other stats, is way, way worse than, say, a GG1320.
You haven't provided raw results from that gyro.
You are ignoring that the specs show that the resolution on this Honeywell gyro is above that necessary for the 15 deg/hr.
(https://i.imgur.com/I49BDmc.png)
Really? I thought you said it performed well? If you're confused by the noise on the graphs then you clearly don't understand electronics, or indeed how RLGs work.
Then you should explain to us how it works. Where is the Earth's rotation in the raw output of the Honeywell gyro:
https://apps.dtic.mil/dtic/tr/fulltext/u2/a266418.pdf
2.3 GRAPHICAL REPRESENTATION
“ Figure 22 shows graphical representations of typical raw gyro outputs. The family of graphs (a) thru (e) illustrate the RLG counts and analog parameters for a bias drift test that includes local Earth rate with strobing at a nominal 10 seconds.”
(https://wiki.tfes.org/images/7/73/Honeywell_RLG1.png)
All of the tests show similar noise levels. If you think the earth is flat, then you presumably don't think the change of angle used to eliminate the earth's rotation from the test would have had any effect, though, right?
What are you talking about? If the earth is rotating then it should appear somewhere in the raw output. So show us where it is.
'Looks very noisy'...how much noise would it take for you to say that it wasn't noisy? Do you even understand what the noisy signal is? Do you understand the relative amount of noise in the MEMS example, versus the Honeywell gyro in the experiment, versus a more advanced Honeywell gyro, versus something like the large, fixed devices mentioned in the other papers...the ones that can measure changes in rotation rate down to 108? Citation needed? The one you've cited works nicely  https://iopscience.iop.org/article/10.1088/17426596/723/1/012061/pdf
I just see a bunch of seismic related stuff in that link:
(https://i.imgur.com/4ogXSYH.png)
So is this stuff in black the rotation of the earth? It says that it's the rotational signal.
With the rotational signal in black I see that the time other than the earthquake the Earth is wobbling, + and , sort of like the Honeywell gyro.
Here is a definition of rad/s:
(https://i.imgur.com/B0MdubD.png)

(https://i.imgur.com/I49BDmc.png)
Really? I thought you said it performed well? If you're confused by the noise on the graphs then you clearly don't understand electronics, or indeed how RLGs work.
Then you should explain to us how it works. Where is the Earth's rotation in the raw output of the Honeywell gyro:
https://apps.dtic.mil/dtic/tr/fulltext/u2/a266418.pdf
It's staring you in the face, if you understand what you're looking at.
The RLG counts for the graphs you've shown there are strobed at 10 seconds, so the line at roughly 10 counts means around 1 count per second. As per the specs you've quoted, the scale factor is 116000 counts per revolution, so the gyro is indicating a rotation of 1 / 116000 = 8.62 x 10^{6} revs / sec
Convert that into degrees per hour and you get 11.2. I don't see a lat/long or address for the lab in the paper, but I'm guessing it's southern Canada, around 49 degrees North. 11.2 / sin 49 = 14.8 degrees per hour.
Pretty good, although clearly you'd need to average out the line with a bit more precision, and to locate the lab better than my rough guess.
So yes, the device can and does detect earth rate, and your graphs show it quite clearly. Thanks for sharing.
Worth pointing out that the specs on RLGs can be a bit misleading  early / cheaper ones struggled with slow rotation rates due to 'locking', which prompted the use of dither  this adds to the noise but improves low rotation rate performance.
I just see a bunch of seismic related stuff in that link:
(https://i.imgur.com/4ogXSYH.png)
So is this stuff in black the rotation of the earth?
In black I see that the time other than the earthquake the Earth is wobbling forward and backward, + and , sort of like the Honeywell gyro.
Here is a definition of rad/s:
(https://i.imgur.com/B0MdubD.png)
I'm well aware of what a radian is, thanks. No, the stuff in black isn't earth rotation. You wouldn't see it on that scale  earth rate is 0.000072 rad/s.

I'm well aware of what a radian is, thanks. No, the stuff in black isn't earth rotation. You wouldn't see it on that scale  earth rate is 0.000072 rad/s.
So there is noise that is dominating the results, and the earth rate is interpreted indirectly. I see. Well, isn't that a downer for your argument.
So yes, the device can and does detect earth rate, and your graphs show it quite clearly. Thanks for sharing.
Really, where in the wiggly line graph is the rotation of the earth? Can you point it out to us in a photo editor please?

I'm well aware of what a radian is, thanks. No, the stuff in black isn't earth rotation. You wouldn't see it on that scale  earth rate is 0.000072 rad/s.
So there is noise that is dominating the results, and the earth rate is interpreted indirectly. I see. Well, isn't that a downer for your argument.
Errrr....not really. That's an earthquake you're looking at there, so yes, the noise (ie the earthquake) is dominating the results, which is as you'd expect. When it's not earthquaking, it measures the earth rate very well, indeed far better than the Honeywell one...
Really, where in the wiggly line graph is the rotation of the earth? Can you point it out to us in a photo editor please?
On all three of the graphs you've shown the left hand yaxis is 'RLG CNTS'  the line averages around 10 after the warm up. As I've shown, that works out pretty much bang on what you'd expect for earth rate. It's not hugely precise, but then it's not really intended for that purpose and it is, as I explained earlier, relatively cheap compared to the far more precise GG1320  a similar trace from a 1320 would have far less 'wiggle'.

Oh, so the only diagram of raw results in the article you posted is flawed because there's an earthquake.
Here is another paper on GINGERRINO which has some angular rotation rate graphs. Nothing about an earthquake appears to be mentioned here:
https://www.frontiersin.org/articles/10.3389/fspas.2020.00049/full
(https://www.frontiersin.org/files/Articles/501250/fspas0700049HTML/image_m/fspas0700049g008.jpg)
Figure 8. (A) The data utilized in the present analysis (30 days from June 15, 2018), ωs0 with mean subtracted, and the data after around day 20 have been removed since GINGERINO was in split mode. (B) ωs, mean subtracted, evaluated with the model of the laser systematic. The data have been decimated down to 1,800 s. Since GINGERINO is a singlering gyroscope, with an ~45° inclination with the Earth axis, it is impossible to distinguish rotations and inclinations. On the right, the sensitivity is expressed in change of the relative angle with the Earth rotation axis, showing that the orientation of the apparatus of GINGERINO is stable at the level of a few μ rad.
The units are nrads and μrads now. Maybe the rotation of the earth is in this graph somewhere? Can you point it out to us?
On all three of the graphs you've shown the left hand yaxis is 'RLG CNTS'  the line averages around 10 after the warm up. As I've shown, that works out pretty much bang on what you'd expect for earth rate. It's not hugely precise, but then it's not really intended for that purpose and it is, as I explained earlier, relatively cheap compared to the far more precise GG1320  a similar trace from a 1320 would have far less 'wiggle'.
I'm not sure I can see what you're talking about without an image. Can you use an image editor to point out the earth's rotation in one of the graphs?

Oh, so the only diagram of raw results in the article you posted is flawed because there's an earthquake.
I wasn't really referring to the diagram, more the text itself. The whole point is the incredible accuracy of the system  down to 10^{8}. If it's a diagram you want, then there's the ∆Ω/Ω graph just above the one you posted. You seem to be demanding that these papers have a section called 'we measured the earth rate and here's what we found it to be'  they aren't going to do that, as they are way, way past that and Ω_{E} itself isn't really of interest  they are interested in tiny, tiny variations in it, hence the article.
Here is another paper on GINGERRINO which has some angular rotation rate graphs. Nothing about an earthquake appears to be mentioned here:
https://www.frontiersin.org/articles/10.3389/fspas.2020.00049/full
(https://www.frontiersin.org/files/Articles/501250/fspas0700049HTML/image_m/fspas0700049g008.jpg)
Figure 8. (A) The data utilized in the present analysis (30 days from June 15, 2018), ωs0 with mean subtracted, and the data after around day 20 have been removed since GINGERINO was in split mode. (B) ωs, mean subtracted, evaluated with the model of the laser systematic. The data have been decimated down to 1,800 s. Since GINGERINO is a singlering gyroscope, with an ~45° inclination with the Earth axis, it is impossible to distinguish rotations and inclinations. On the right, the sensitivity is expressed in change of the relative angle with the Earth rotation axis, showing that the orientation of the apparatus of GINGERINO is stable at the level of a few μ rad.
The units are nrads and μrads now. Maybe the rotation of the earth is in this graph somewhere? Can you point it out to us?
No, I can't because if you read the text you've quoted it clearly says 'with mean subtracted'  they aren't interested in the absolute figure, they are interested in the delta. And the delta being measured is absolutely tiny  nano rad/s, or 10^{9}.
I'm not sure I can see what you're talking about without an image. Can you use a photo editor to point out the earth's rotation in one of the graphs?
How's this? The average RLG counts are just under 10, I'd say. That's your earth rate, as I showed in the earlier calculations.
(https://i.postimg.cc/DzpMSxQX/twrtsfwe.png)

I wasn't really referring to the diagram, more the text itself. The whole point is the incredible accuracy of the system  down to 108. If it's a diagram you want, then there's the ∆Ω/Ω graph just above the one you posted. You seem to be demanding that these papers have a section called 'we measured the earth rate and here's what we found it to be'  they aren't going to do that, as they are way, way past that and ΩE itself isn't really of interest  they are interested in tiny, tiny variations in it, hence the article.
So now you are arguing that the papers aren't about showing the earth rotation and are just about a series of higher level assumptions. They are "way way past that". Why are you posting these papers of higher level assumptions as proof if it's not about that then?
No, I can't because if you read the text you've quoted it clearly says 'with mean subtracted'  they aren't interested in the absolute figure, they are interested in the delta. And the delta being measured is absolutely tiny  nano rad/s, or 109.
I'm not interested in the mean of the figures, I'm interested in the Earth's rotation. I don't see it.
(https://i.postimg.cc/DzpMSxQX/twrtsfwe.png)
Looks pretty questionable. If that's the Earth's rotation then something is increasing and decreasing it's speed by 30%. Maybe circle back when you figure out why light's speed is constantly increasing and decreasing and which phenomena it's related to and whether it is affecting your assumptions.
Maybe something better than presenting a bunch of noisy garbage and pretending that you know which phenomena is caused by which and why.

So now you are arguing that the papers aren't about showing the earth rotation and are just about a series of higher level assumptions. They are "way way past that". Why are you posting these papers of higher level assumptions as proof if it's not about that then?
Your inability to comprehend this stuff is not my problem.
No, I can't because if you read the text you've quoted it clearly says 'with mean subtracted'  they aren't interested in the absolute figure, they are interested in the delta. And the delta being measured is absolutely tiny  nano rad/s, or 109.
I'm not interested in the mean of the figures, I'm interested in the Earth's rotation. I don't see it.
And you won't see it. It isn't there to be seen. You posted it, not me.
(https://i.postimg.cc/DzpMSxQX/twrtsfwe.png)
Looks pretty questionable.
Based on what? You asked where the rotation was, presumably because you don't understand the data, and now when I show it to you where it is in the data it's too noisy for you? At the start of this I pointed out that this was a cheaper model  it is less accurate, and more noisy  that's the whole point. Measuring earth rate  15 deg/hour  using a device that's designed for measuring up to 1000 deg / sec is always going to be tricky. If they used a more precise one, it would be less noisy and more precise
If that's the Earth's rotation then something is increasing and decreasing it's speed by 30%.
If that's how you interpret scientific measurement data then it's no wonder your understanding of the planet is so hopelessly at odds with reality. The data has noise in it, but the trend is clear  it's just shy of 10 counts every 10 seconds, which is exactly what we would expect the earth rate measurement to be at the latitude in question. The noise level is significant, yes  but then the rotation rate is tiny, so it's not surprising. When you put roughly the same noise level on a more substantial rotation rate, like the 100 deg/ sec tests shown in graph (f) you get deviations at the 4th or 5th significant figure. Significant noise:signal ratio at low rotation rates is exactly what you would expect to see in a cheaper device like this one.
Maybe circle back when you figure out why light's speed is constantly increasing and decreasing and which phenomena it's related to and whether it is affecting your assumptions.
Maybe something better than presenting a bunch of noisy garbage and pretending that you know which phenomena is caused by which and why.
The measured earth rate is bang on what we would expect, and the noise level is exactly what we would expect for the device in question. You didn't understand the data, and are now flailing around for another explanation that might give you an 'out' now you've been shown what it is. The data shows the measurement of earth rate. All of the data aligns perfectly with RE expectations.

You claim that there are more accurate devices, but refuse to provide raw graphs, data, and provide only claims and assumptions. Maybe the 'more accurate' devices create bigger spikes compared to the baseline like the last GINGERRINO graphs did.
You think that a trend is proof, yet refuse to acknowledge that there are many diurnal phenomena above and around us beyond the supposed rotation of the earth.
You see that the data is tainted with phenomena which are not the rotation of the earth, yet refuse to acknowledge that the presence of unmitigated effects invalidates the assumptions involved.
How often are inconsistent experiments with unknown effects and a series of assumptions accepted in hard sciences like chemistry or biology? I'll answer for you: Hardly ever. We can test and control and address most of the elements those sciences, but not when measuring something large and outside of our control like in this experiment. The quality is better there. In this case it's basically a dilapidated road with potholes that need to be filled with assumption.
You post various papers and then later dismiss them as being "way, way" beyond what we're talking about and position them as higher level assumptions.
Are we done here? This is just a load of assumptions and very little in the way of tangible evidence. You might think that this is asking for too much, but in other sciences mystery inconsistencies and experiments tainted with unknown effects and 'oh well, let's just assume' just doesn't cut it. The presence of other things affecting the experiment pretty much invalidates it all. The affecting elements have not been properly removed from the experiment by the experimenter to allow for a determinable conclusion.

You claim that there are more accurate devices, but refuse to provide raw graphs, data, and provide only claims and assumptions.
Well, I pointed you to the 1320AN, and quoted the bias stability...if you really want me to walk you by the hand to the data here's the spec sheet: https://aerospace.honeywell.com/content/dam/aerobt/en/documents/learn/products/sensors/brochures/GG1320ANDigitalLaserGyrobro.pdf (https://aerospace.honeywell.com/content/dam/aerobt/en/documents/learn/products/sensors/brochures/GG1320ANDigitalLaserGyrobro.pdf)
Furthermore, I linked to several papers showing the specs of far more sensitive RLGs  you are using the lack of raw data from those devices as evidence of something, although quite what that is I'm not really clear. But when raw data is shown to you, you haven't the faintest idea how to interpret it, hence your inability to understand counts versus rotation rate, or the difference between rate and rate with mean subtracted.
I've also linked to some interesting experimental data measuring earth rate, which you ignored, and to an aircraft nav system instructional video that clearly indicates a strong link to latitude and earth rotation, which you again ignored.
You think that a trend is proof, yet refuse to acknowledge that there are many diurnal phenomena beyond the supposed rotation of the earth.
No, I think the data is data, not proof in and of itself. In the case of RLGs, the easiest way to prove you are measuring earth rate and not some anomaly in the system to is to rotate the axis of the gyro in and out of alignment with the spin axis of the earth, just as indicated in the quote I shared with you, which you ignored:
And as further confirmation that the slow counting is indeed due to the Earth's rotation, with the GG1320 tipped at around 40 degrees away from true North, the counting slows to a virtual standstill with just some randomness in the LSB due to vibrations, and reverses direction when tipped beyond 40 degrees. When tipped the other way up to 50 degrees towards North, the counting is most rapid.
If that Canadian paper had a graph of test BD11991A, for example, we would see a good example of this  this was one of the trial runs with earth rate removed via rotation  I expect we would see a noisy line close to the origin (although not necessarily zero, remember the device has a significant bias of around 1 deg / hour)
You see that the data is tainted with phenomena which are not the rotation of the earth, yet refuse to acknowledge that the presence of unmitigated effects invalidates the assumptions involved.
Pretty much all experimental data is in some way 'tainted' with other data that you don't want  it's a question of degrees. Even a simple task like measuring the length of something is actually difficult to do on a very precise level  both the thing being measured and the thing doing the measuring will expand and contract with temperature, for example, introducing noise to the data. The issue is whether that noise invalidates the experiment.
How often are inconsistent experiment with unknown effects and a series of assumptions accepted in hard sciences like chemistry, biology, etc.?
Vague, desperate stuff, Tom.
You post various papers and then later dismiss them as being "way, way" beyond what we're talking about.
I quoted those papers to point out that far, far more accurate devices exist than the ones you used in your article on RLGs, one of which, incredibly, wasn't even a RLG. Compare the signal:noise ratio of the MEMS experiment to the data from the Canadian paper, and then look at the 1320AN spec sheet, and then the various fixed Gseries papers. As I said in the original post, it seems very odd that you've chosen two relatively inaccurate devices when so many more advanced ones are out there. Using inaccurate devices and then pointing triumphantly at noisy data is a bit silly, really.
Are we done here? This is just a load of assumptions and very little in the way of tangible evidence.
I think you're done here. I'm quite happy, thanks.

I'm asking you for data from these 'accurate' gyroscopes which the shows smoother results you claim. You again refuse to provide it and instead choose to keep arguing why you should not.
Earth rotation rate from the underground G ring laser research gyroscope over 30 days:
https://www.researchgate.net/figure/TherotationrateoftheEarthmeasuredwiththeGringlaserasafunctionoftime_fig4_45928679
(https://i.imgur.com/pE6LgO3.png)
FIG. 4: The rotation rate of the Earth measured with the G ring laser as a function of time. Averaging over 2 hours was applied
to a corrected dataset, where all known geophysical signals have been removed.
For the detection of fundamental physics signals one has to remove all known perturbation signals of the Earth from
the ring laser timeseries. Furthermore we have applied 2 hours of averaging of the data in order to reduce the effect
from short period perturbations. Figure 4 shows an example. In order to reduce the local orientation uncertainties,
which remain after local tilts measured with the high resolution tiltmeters have been removed, averaging as indicated
above was applied to a series of 30 days of data collection, including the period shown in fig. 3.
It appears fairly questionable as to what this is.
If you are going to argue that they can't yet take out all geophysical phenomena affecting the device, then you have invalidated your argument entirely. You are agreeing that they are measuring a mess of noise and interpreting the results indirectly.

I'm asking you for data from these 'accurate' gyroscopes which the shows smoother results you claim. You again refuse to provide it and instead choose to keep arguing why you should not.
Earth rotation rate from the underground G ring laser research gyroscope over 30 days:
https://www.researchgate.net/figure/TherotationrateoftheEarthmeasuredwiththeGringlaserasafunctionoftime_fig4_45928679
(https://i.imgur.com/pE6LgO3.png)
FIG. 4: The rotation rate of the Earth measured with the G ring laser as a function of time. Averaging over 2 hours was applied
to a corrected dataset, where all known geophysical signals have been removed.
For the detection of fundamental physics signals one has to remove all known perturbation signals of the Earth from
the ring laser timeseries. Furthermore we have applied 2 hours of averaging of the data in order to reduce the effect
from short period perturbations. Figure 4 shows an example. In order to reduce the local orientation uncertainties,
which remain after local tilts measured with the high resolution tiltmeters have been removed, averaging as indicated
above was applied to a series of 30 days of data collection, including the period shown in fig. 3.
It fairly questionable as to what this is, to me.
If you are going to argue that they can't yet take out all geophysical phenomena affecting the device, then you have invalidated your argument entirely. You are agreeing that they are measuring a mess of noise and interpreting the results indirectly.
Do you understand the difference between Ω and ∆Ω? That graph isn’t what you claim it to be, which is kind of embarrassing.

Do you understand the difference between Ω and ∆Ω? That graph isn’t what you claim it to be, which is kind of embarrassing.
It clearly says that it's the "rotation rate of the Earth" in the caption and text, and not some kind of offset or variation.
"FIG. 4: The rotation rate of the Earth measured with the G ring laser as a function of time."
Do you know how to read? Embarrassing. Please do continue to tell us why words don't mean what they say, and how it's all wrong and misinterpreted, but there is this better data on this from better devices that you continuously refuse to share.

Do you understand the difference between Ω and ∆Ω? That graph isn’t what you claim it to be, which is kind of embarrassing.
It clearly says that it's the "rotation rate of the Earth" in the caption and text, and not some kind of offset or variation.
"FIG. 4: The rotation rate of the Earth measured with the G ring laser as a function of time."
Do you know how to read? Embarrassing. Please do continue to tell us why words don't mean what they say, and how it's all wrong and misinterpreted, but there is this secretive smooth and stable data from better devices that you continuously refuse to find and share.
I’m assuming you don’t understand then.
Yep, the caption text says that, but it’s not well written  an error, I guess. The graph clearly says ∆Ω on the axis, and the units are pico radians / sec, which is absolutely tiny. It clearly isn’t Ω, but ∆Ω.
If that was the presented the same way as the graphs from the Canadian paper that you didn’t understand, you’d be looking at a flat line. But of course that would be pointless, because the purpose of the analysis isn’t to measure Ω, but to look at tiny variations in it for other purposes.

So you have resorted to arguing that the captions are mislabeled, but you know better than the scientists, and continue to insist that there is this better data out there that supports your case. Give us a break.
Maybe the data you are trying to argue for doesn't exist and they can't really measure the earth's rotation with this device and only make various inferences and you are the one in error. You have a hard time showing it it, after all. You have argued that they're not showing the Earth's rotation rate in full because they are "way, way" beyond that. Alternatively, you don't have the data so you're "way, way" wrong.

So you have resorted to arguing that the captions are mislabeled, but you know better than the scientists, and continue to insist that there is this better data out there that supports your case. Give us a break.
Maybe the data you are trying to argue for doesn't exist and they can't really measure the earth's rotation with this device and only make various inferences and you are the one in error. You have a hard time showing it it, after all. You have argued that they're not showing the Earth's rotation rate in full because they are "way, way" beyond that. Alternatively, you don't have the data so you're "way, way" wrong.
Do you accept that it can’t be Ω if it’s measured in picorads/sec?
Either the axis or the caption is wrong  they can’t both be correct.
You seem to be obsessed with a desire to see a flat line, but you don’t seem to understand the data. That graph is effectively a zoomed in look at the flat line  the ‘noise’ in the rotation data. If you don’t believe it, I can’t really help you, but everybody reading this can see it for themselves.
You don’t need better data  it’s staring you in the face, once again. You keep saying the rotation signal is ‘dominated’ by other factors  they are showing you a graph with the other factors down in the 10^{12} region. Given that Ω is 0.26 x 10^{5} rad/s, that’s a phenomenal level of precision.

Delta and Phi can mean a lot of things. I see a zero there on the axis for the Delta baseline, for example.
Nothing in the text in the document says that "here are the variations of the earth's rotation". Nor does the text around the graph. It says that it the line represents the "rotation rate of the Earth". They must not have explained what they were showing in the document, except for when your brain created an unsaid interpretation apparently.
If you are going to argue your imagined version of things I would suggest citing someone other than yourself. You appear to have a rich imagination where the scientists are writing down wrong things, the data you want to exist is there but hidden and unexplained, and misexplained, but you have special knowledge to correct them based on your special personal logic. ::)

This paper has some interesting graphs on the super precise GINGERINO Ring Laser Gyroscope.
https://iopscience.iop.org/article/10.1088/17426596/1342/1/012084/pdf
(https://i.imgur.com/KnoBKmM.png)
The lefthand axis ranges from 6 to +6 x 10^10 rad/s
https://www.calculatorsoup.com/calculators/math/scientificnotationconverter.php
Converting 4 x 10^10 to a real number = 0.00000000004 (real number)
The 4 on the chart is 0.00000000004 rads/sec
http://www.kylesconverter.com/frequency/degreesperhourtoradianspersecond
For the earth's rotation, 15 deg/hour = 0.000072722 rads/sec
(https://i.imgur.com/mFraaD0.png)
Where's the rotation of the earth? This chart doesn't go that high. The rotation of the earth is several magnitudes higher.
Perhaps it has something to do with this quote about the GINGERRINO in bold here:
https://www.frontiersin.org/articles/10.3389/fspas.2020.00049/full
(https://www.frontiersin.org/files/Articles/501250/fspas0700049HTML/image_m/fspas0700049g008.jpg)
Figure 8. (A) The data utilized in the present analysis (30 days from June 15, 2018), ωs0 with mean subtracted, and the data after around day 20 have been removed since GINGERINO was in split mode. (B) ωs, mean subtracted, evaluated with the model of the laser systematic. The data have been decimated down to 1,800 s. Since GINGERINO is a singlering gyroscope, with an ~45° inclination with the Earth axis, it is impossible to distinguish rotations and inclinations. On the right, the sensitivity is expressed in change of the relative angle with the Earth rotation axis, showing that the orientation of the apparatus of GINGERINO is stable at the level of a few μ rad.
This appears to suggest that they can't distinguish the rotation of the earth directly and they may be making indirect inferences.

This paper has some interesting graphs on the super precise GINGERINO Ring Laser Gyroscope.
https://iopscience.iop.org/article/10.1088/17426596/1342/1/012084/pdf
The lefthand axis ranges from 6 to +6 x 10^10 rad/s
Converting 4 x 10^10 to a real number = 0.00000000004 (real number)
The 4 on the chart is 0.00000000004 rads/sec
For the earth's rotation, 15 deg/hour = 0.000072722 rads/sec
Where's the rotation of the earth? This chart doesn't go that high. The rotation of the earth is several magnitudes higher.
You're absolutely right, that paper does have some interesting graphs  you just don't understand them, or are wilfully misrepresenting them. It would help if you read the totality of things, instead of scrabbling around for cherries to pick, especially when you don't understand them. If you actually read the detail around that graph, it clearly says 'residual'.
Fortunately for our discussion, if you just look above that graph, you'll see this one, which I guess is the kind of thing you've been after, or have been pretending to be after:
(https://i.postimg.cc/jqXQjhRz/cvbnm.png)
This shows the raw rotation data over a couple of months, with an earthquake visible as an obvious spike. Look at the yaxis  the line is showing around 4.925 x 10^{5} rad/s, which if you correct for the latitude of Gran Sasso, around 42.47 degrees N, comes in at 7.29 rad/s, which is bang on earth rate.
That graph is exactly what I said you'd see if you measure earth rate using a more precise system  thank's for drawing my attention to it, as I'd obviously not noticed it when we spoke previously. When discussing the Canadian test of the Honeywell RLG you said the data:
Looks pretty questionable. If that's the Earth's rotation then something is increasing and decreasing it's speed by 30%.
Now you've got a graph showing earth rate with noise levels that are barely readable, outside of the obvious seismic event. Are you now satisfied with the evidence, or are you going to move the goalposts? I'd say that graph should have pride of place in the wiki  what do you think? It is, after all, raw data from a highly accurate RLG showing earth rate to a remarkable degree of precision.
Perhaps it has something to do with this quote about the GINGERRINO in bold here:
https://www.frontiersin.org/articles/10.3389/fspas.2020.00049/full
Figure 8. (A) The data utilized in the present analysis (30 days from June 15, 2018), ωs0 with mean subtracted, and the data after around day 20 have been removed since GINGERINO was in split mode. (B) ωs, mean subtracted, evaluated with the model of the laser systematic. The data have been decimated down to 1,800 s. Since GINGERINO is a singlering gyroscope, with an ~45° inclination with the Earth axis, it is impossible to distinguish rotations and inclinations. On the right, the sensitivity is expressed in change of the relative angle with the Earth rotation axis, showing that the orientation of the apparatus of GINGERINO is stable at the level of a few μ rad.
This appears to suggest that they can't distinguish the rotation of the earth directly and they are making indirect inferences.
It's not that they are hiding it in these various graphs, like you are arguing. They can't see it directly and have an excuse for that.
If you don't understand stuff, it's best not to go public with it. The point they are making is the GINGERINO is a single axis system  there is just one ring laser, orientated horizontally with respect to the earth's surface, and therefore at an angle to the earth's rotation axis equal to it's latitude in Italy. This is as opposed to, say, an aircraft INS where you would typically have three, arranged orthogonally. This means it can only measure rotation around one axis, meaning any disturbances in the steady rotation rate could be either rotations or inclinations of the earth, but you wouldn't know which.

This shows the raw rotation data over a couple of months, with an earthquake visible as an obvious spike. Look at the yaxis  the line is showing around 4.925 x 105 rad/s, which if you correct for the latitude of Gran Sasso, around 42.47 degrees N, comes in at 7.29 rad/s, which is bang on earth rate.
7.29 rad/s is 1503670 degrees per hour. You apparently do not know what you're talking about.
(https://i.imgur.com/j3apzyd.png)
The line should be at ~7.27 x 10^5 rad/s, which is 15 degrees per hour. This one is closer and has it about right in this link:
https://indico.cern.ch/event/736594/contributions/3184374/attachments/1741872/2819336/DiVirgilio_COSMO2018.pdf
(https://i.imgur.com/ScjVBMN.png)
The Earth rotation rate in blue is pretty funky there. Not too consistent.
Another image:
(https://i.imgur.com/DZuMslA.png)
And see how it says seismology at the top?
https://iopscience.iop.org/article/10.1088/17426596/1342/1/012084/pdf
GINGERINO is shown in Fig. 2 . It is located inside the deep underground INFN laboratory of the Gran Sasso (LNGS) [7]; its aim was to characterise the underground rotational seismic disturbances.
GINGERINO is a "rotational seismic observetory":
https://publishing.aip.org/publications/latestcontent/goingdeeptomeasureearthsrotationaleffects/
GINGERino is now operating, along with seismic equipment provided by the Italian Institute of Geophysics and Volcanology, as a rotational seismic observatory.
So no, I don't see how these other types of graphs are clearly the 'rotation of the earth' either. Rotating seismic disturbances can also exist on a FE.

7.29 rad/s is 1503670 degrees per hour. You apparently do not know what you're talking about.
Well, hey, we all make mistakes. I have obviously missed off the 'x 10^{5}'. I suspect you know that. I won't edit it, since you've pointed it out, but I will clarify here for anybody reading this.
The line on the graph is roughly 4.92 x 10^{5} rad/s. The latitude of the equipment is around 42.47 degrees N. So 4.92 x 10^{5} / (sin 42.47) = 7.29 x 10^{5} rad/s.
7.29 x 10^{5} rad/s x 3600 x 360 / (2 x pi) = 15.04 degrees / hour
(https://i.imgur.com/j3apzyd.png)
The line should be at ~7.27 x 10^5 rad/s, which is 15 degrees per hour. This one is closer and has it right in this link:
https://indico.cern.ch/event/736594/contributions/3184374/attachments/1741872/2819336/DiVirgilio_COSMO2018.pdf
(https://i.imgur.com/ScjVBMN.png)
Well, yes, that's earth rate right there. Thanks for sharing.
The Earth rotation rate in blue is pretty funky there. Not too consistent.
Well, hang on a minute. Look at the noise level in your MEMS example (noise bigger than the earth rate), then the Canadian Honeywell paper (noise around 2030% of earth rate  which you said was too much), then the graph we discussed above, and also this graph, which shows several different sources. The blue one (the old 1Hz data) is clearly the noisiest, but even that has fluctuations less than 1% of the earth rate. Then compare with the green and red lines and you're into a whole order of magnitude less noise. It goes back to my earlier question  if the noise is making you doubt the veracity of the figures, what level of noise would you require to change your mind?
Another image:
(https://i.imgur.com/DZuMslA.png)
And see how it says seismology at the top?
That graph is fantastic  another one for the wiki, I would suggest. It shows earth rate beautifully, and clearly shows how tiny the noise is compared to the magnitude of the underlying rate. Yes, of course  it says seismology at the top. It is showing another earthquake effect. How does that invalidate the clear line showing earth rate, outside of the earthquake section?
https://iopscience.iop.org/article/10.1088/17426596/1342/1/012084/pdf
GINGERINO is shown in Fig. 2 . It is located inside the deep underground INFN laboratory
of the Gran Sasso (LNGS) [7]; its aim was to characterise the underground rotational seismic
disturbances.
So no, I don't see how these other types of graphs are clearly the 'rotation of the earth' either. Rotating seismic disturbances can also exist on a FE.
If the that RLG was on a flat, not rotating earth, then yes, it would show seismic disturbances too. But if the FE wasn't rotating, then the fluctuations would be around zero, and not 7.29 x 10^{5} rad/s, wouldn't they? What is the RLG measuring at 7.29 x 10^{5} rad/s, if not earth rate? And why do these different RLGs at different locations measure earth rate differently, but when corrected for the sine of their latitude find it to be the same? That is clear, brilliant evidence for a rotating globe shaped earth.

Sines also exist in flat circles, not just globes. I am sure you know this since you are using a circle to get that result:
https://courses.lumenlearning.com/precalctwo/chapter/unitcirclesineandcosinefunctions/
Defining Sine and Cosine Functions
Now that we have our unit circle labeled, we can learn how the (x,y) coordinates relate to the arc length and angle. The sine function relates a real number to the ycoordinate of the point where the corresponding angle intercepts the unit circle.
(https://i.imgur.com/puNQHcZ.png)
If the that RLG was on a flat, not rotating earth, then yes, it would show seismic disturbances too. But if the FE wasn't rotating, then the fluctuations would be around zero, and not 7.29 x 105 rad/s, wouldn't they?
According to you it's not at 7.29 x 10^5. You just told me that at 42 degrees they are going slower at 4.92 x 10^5 rad/s. You are saying that they get slower as you near the pole.
The Gingerino is an underground "rotational seismic observatory". If the seismic fluctuations are rotating around the earth with the celestial bodies on a FE it is clear why seismic signals would pass over the device faster at 42 degrees than at the North Pole.
Likewise, on an RE the earth is moving at a different rate at the North Pole and at 42 degrees.
And why do these different RLGs at different locations measure earth rate differently, but when corrected for the sine of their latitude find it to be the same?
What are you talking about? You only have a single data point.
And on an FE the result of such data would be only be useful in determining whether the Flat Earth is a Monopole or BiPolar model.

Sines also exist in flat circles, not just globes. I am sure you know this since you are using a circle to get that result:
If the that RLG was on a flat, not rotating earth, then yes, it would show seismic disturbances too. But if the FE wasn't rotating, then the fluctuations would be around zero, and not 7.29 x 105 rad/s, wouldn't they?
According to you it's not at 7.29 x 10^5. You just told me that at 42 degrees they are going slower at 4.92 x 10^5 rad/s. You are saying that they get slower as you near the pole.
No  the other way round. If you try to measure the earth rate using a gyro with its spin axis vertical to the earth's surface then the measured rate of rotation will be earth rate multiplied by the sine of the latitude. Sin 0 is 0, sin 90 degrees is 1, so the measured rate increases the further away you go from the equator, reaching earth rate at the poles.
The Gingerino is an underground "rotational seismic observatory". If the seismic fluctuations are rotating around the earth with the celestial bodies on a FE it is clear why seismic signals would pass over the device faster at 42 degrees than at the North Pole.
Likewise, on an RE the earth is moving at a different rate at the North Pole and at 42 degrees.
And why do these different RLGs at different locations measure earth rate differently, but when corrected for the sine of their latitude find it to be the same?
What are you talking about? You only have a single data point.
And on an FE the result of such data would be only be useful in determining whether the Flat Earth is a Monopole or BiPolar model.
You seem to be completely muddling the seismic data, which shows as oscillatory signals, with the steady state rotation. Look at the Gingerino graph:
(https://i.imgur.com/DZuMslA.png)
If the earth wasn't rotating, then you wouldn't have the steady state line at 7.29 on the yaxis  it would be showing zero, and the seismic activity would show as vibrations above and below zero. That graph shows earth rotation perfectly. If the world is flat, and it's not rotating, then why is the RLG showing a constant rotation?

If the earth wasn't rotating, then you wouldn't have the steady state line at 7.29 on the yaxis  it would be showing zero, and the seismic activity would show as vibrations above and below zero. That graph shows earth rotation perfectly. If the world is flat, and it's not rotating, then why is the RLG showing a constant rotation?
Sure the graph shows rotation. So, based on the results of the RLGs experiments (we might also mention the MGX) you are saying that it is the Earth which is rotating around its own axis? Is that your last word? You still have time to retract your statement.

Sure the graph shows rotation. So, based on the results of the RLGs experiments (we might also mention the MGX) you are saying that it is the Earth which is rotating around its own axis? Is that your last word? You still have time to retract your statement.
Not sure it's my last word on the matter, but yes, the graph clearly shows the output from a ring laser gyro measuring the earth's rotation around the polar axis. What is your point?

What is your point?
You must be joking, of course.
Here is the point: you are using the wrong formula for the RLGs and the MGX. To detect rotation, you need the SAGNAC EFFECT formula. Your formula (the one that you are endorsing) is the CORIOLIS EFFECT formula. Then, you have two possibilities: either the Earth is rotating, OR, you have a rotational ether drift above the surface of the Earth. The deciding factor is the SAGNAC EFFECT.
Each RLG has TWO FORMULAS: one for the Coriolis effect, and one for the Sagnac effect.
One is a mechanical effect, the slight deflection of the light beams (Coriolis), it is proportional to the area/angular velocity. The other one is an electromagnetic effect (Sagnac), it is proportional to the velocity of the light beams.

What is your point?
You must be joking, of course.
Here is the point: you are using the wrong formula for the RLGs and the MGX. To detect rotation, you need the SAGNAC EFFECT formula. Your formula (the one that you are endorsing) is the CORIOLIS EFFECT formula. Then, you have two possibilities: either the Earth is rotating, OR, you have a rotational ether drift above the surface of the Earth. The deciding factor is the SAGNAC EFFECT.
Each RLG has TWO FORMULAS: one for the Coriolis effect, and one for the Sagnac effect.
One is a mechanical effect, the slight deflection of the light beams (Coriolis), it is proportional to the area/angular velocity. The other one is an electromagnetic effect (Sagnac), it is proportional to the velocity of the light beams.
All of the graphs have come from papers and briefings made by other people. The specific graph we are discussing came from this slide pack: https://indico.cern.ch/event/736594/contributions/3184374/attachments/1741872/2819336/DiVirgilio_COSMO2018.pdf (https://indico.cern.ch/event/736594/contributions/3184374/attachments/1741872/2819336/DiVirgilio_COSMO2018.pdf)
It clearly explains the use of the sagnac effect to derive the rotation rate. That graph is derived from the sagnac effect.
[edited to fix link]

What is your point?
You must be joking, of course.
Here is the point: you are using the wrong formula for the RLGs and the MGX.
What's the wrong formula you're referring to and who is using it?

Show me your formula. Is it by any chance, dt = 4Aω/c^{2}? That's the CORIOLIS EFFECT formula.
Here is the SAGNAC EFFECT formula:
2(V_{1}L_{1} + V_{2}L_{2})/c^{2}
A huge difference.

Note to everyone who is following this discussion: without the correct Sagnac effect formula, the RE can claim immediately that the Earth is rotating around its own axis, and there's nothing the FE/UAFE can do about it (see the Bob Knodel episode).
This is one of the main reasons why the other FES forum has been hijacked by the RE (admin + mods), in order to cause as much mayhem as possible, so that there could be no meaningful debate about the MGX/RLGs in the upper forums.

Show me your formula. Is it by any chance, dt = 4Aω/c^{2}? That's the CORIOLIS EFFECT formula.
Here is the SAGNAC EFFECT formula:
2(V_{1}L_{1} + V_{2}L_{2})/c^{2}
A huge difference.
Where did you get those formulae from? It would be helpful if you could both explain what the various terms are, and to complete the formulae. The first one doesn't look right at all  the Coriolis effect is simply a function of motion in a noninertial, rotating frame  the speed of light, c, wouldn't normally come into it. Also that one starts with 'dt = ', but there is no corresponding derivative on the other side of the formula, which means it is essentially meaningless, as dt on its own is zero. I wonder if you've got that from vibrating Coriolis gyro systems? Hard to tell.
Likewise your Sagnac formula bears no resemblance to the Sagnac formula described in several of the papers we've been discussing, Wikipedia, as well as the slide deck I linked to, which is:
(https://wikimedia.org/api/rest_v1/media/math/render/svg/1fca22b83bfdd767eab6a619945053d2d289e800)
where Δφ is the phase difference measured by the interferometer, λ is the wavelength of the light, and ω is the rotation rate (sometimes presented as the capital letter Ω in the context of earth rate).
Your formula for the Sagnac effect has only one side of the equation, so it's not clear what the term actually represents, and it seems to bear no resemblance at all to Sagnac's original formula. It may well be that it is in some way related, but without your source, or some context, it's just meaningless I'm afraid.
You appear to be claiming that RLGs are in fact measuring the rotation of some 'ether', presumably rotating above the FE surface. If that's the case, then you need to explain what the mechanism is by which this mysterious rotation is being detected, and why it is related to the latitude of the sensor. Why would the measured rotation be zero at the equator, and a maximum at the North Pole and southern pole / ice wall / whatever it is ?

dt is not the derivative, it is the delta t, difference in time, time shift formula. The notation for the derivative is d/dt (dt is the differential notation).
The ether drift is latitude dependent.
http://www.orgonelab.org/miller.htm
The Coriolis effect is SUBLUMINAL.
The Sagnac effect is SUPERLUMINAL.
That is, if you want the Sagnac effect, the formula must reflect the superluminal velocity. No superluminal velocity, no Sagnac formula.
Coriolis and Sagnac effect formulas for a square ring laser interferometer:
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2153966#msg2153966
Derivation of the Sagnac effect formula:
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2117351#msg2117351
KASSNER EFFECT
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2234871#msg2234871 (part I)
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2235136#msg2235136 (part II)
Dr. Gianfranco Spavieri
In both the outward and return paths, the oneway speed is c (in agreement with Einstein’s second postulate) if the length L of the outward path covered by the signal is reduced to L(1  2v/c) < L in Eq. (3).
CORIOLIS EFFECT = a path measuring L(1  2v/c), a comparison of two separate/different segments
SAGNAC EFFECT = a path measuring L, a comparison of two continuous loops
Therefore, Michelson and Gale, Silberstein, Langevin, Post, Bilger, Anderson, Steadman, Rizzi, Targaglia, Ruggiero, have been measuring ONLY the CORIOLIS EFFECT formula (area and angular velocity), nothing else. The formulas features on the wikipedia and mathpages websites are the CORIOLIS EFFECT equations, not the correct SAGNAC EFFECT formulas.
Here is the crown jewel of all the SAGNAC EFFECT formulas:
Δt = (l_{1} + l_{2})/(c  v_{1}  v_{2})  (l_{1} + l_{2})/(c + v_{1} + v_{2})
The velocity terms are immediately identified: c  v_{1}  v_{2} and c + v_{1} + v_{2}.
Δt = (l_{1} + l_{2})/(c  v_{1}  v_{2})  (l_{1} + l_{2})/(c + v_{1} + v_{2}) = 2[(l_{1}v_{1} + l_{2}v_{2})]/c^{2}

dt is not the derivative, it is the delta t, difference in time, time shift formula. The notation for the derivative is d/dt (dt is the differential notation).
The ether drift is latitude dependent.
http://www.orgonelab.org/miller.htm
The Coriolis effect is SUBLUMINAL.
The Sagnac effect is SUPERLUMINAL.
That is, if you want the Sagnac effect, the formula must reflect the superluminal velocity. No superluminal velocity, no Sagnac formula.
Coriolis and Sagnac effect formulas for a square ring laser interferometer:
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2153966#msg2153966
Derivation of the Sagnac effect formula:
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2117351#msg2117351
KASSNER EFFECT
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2234871#msg2234871 (part I)
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2235136#msg2235136 (part II)
Dr. Gianfranco Spavieri
In both the outward and return paths, the oneway speed is c (in agreement with Einstein’s second postulate) if the length L of the outward path covered by the signal is reduced to L(1  2v/c) < L in Eq. (3).
CORIOLIS EFFECT = a path measuring L(1  2v/c), a comparison of two separate/different segments
SAGNAC EFFECT = a path measuring L, a comparison of two continuous loops
Therefore, Michelson and Gale, Silberstein, Langevin, Post, Bilger, Anderson, Steadman, Rizzi, Targaglia, Ruggiero, have been measuring ONLY the CORIOLIS EFFECT formula (area and angular velocity), nothing else. The formulas features on the wikipedia and mathpages websites are the CORIOLIS EFFECT equations, not the correct SAGNAC EFFECT formulas.
Here is the crown jewel of all the SAGNAC EFFECT formulas:
Δt = (l_{1} + l_{2})/(c  v_{1}  v_{2})  (l_{1} + l_{2})/(c + v_{1} + v_{2})
The velocity terms are immediately identified: c  v_{1}  v_{2} and c + v_{1} + v_{2}.
Δt = (l_{1} + l_{2})/(c  v_{1}  v_{2})  (l_{1} + l_{2})/(c + v_{1} + v_{2}) = 2[(l_{1}v_{1} + l_{2}v_{2})]/c^{2}
So, using your 'crown jewel' formula, if I have a RLG system, with an interferometer, and I measure some phase shift Δφ, how do I calculate the rotation rate, ω? Your formula has neither of those terms in it.

v = ωr
But that is nothing compared to the main issue. Why didn't Michelson and Gale detect the much larger Sagnac effect on the light beams?

v = ωr
Ok...so v = ωr and
Δt = (l1 + l2)/(c  v1  v2)  (l1 + l2)/(c + v1 + v2) = 2[(l1v1 + l2v2)]/c2
So my interferometer detects a phase shift of Δφ radians between the two light beams...how do I calculate rotation rate from that? Where does t come into it? And r? And which v are we talking about?

So my interferometer detects a phase shift of Δφ radians between the two light beams
Yes, that's the Coriolis effect phase shift. But you won't detect the Sagnac effect.
Each interferometer has two phenomena to deal with: a mechanical effect (Coriolis effect) and an electromagnetic effect (Sagnac effect). Two separate formulas.

So my interferometer detects a phase shift of Δφ radians between the two light beams
Yes, that's the Coriolis effect phase shift. But you won't detect the Sagnac effect.
Each interferometer has two phenomena to deal with: a mechanical effect (Coriolis effect) and an electromagnetic effect (Sagnac effect). Two separate formulas.
So are you suggesting that every RLG that measures rotation via an interferometer is in fact wrong?

Let us imagine the Earth as a very large scale turntable. To detect the rotation of the turntable itself, you need the Sagnac effect. With the Coriolis effect, you have either of two possibilities: either the turntable is rotating or the ether drift is rotating above its surface.
What Michelson did is to substitute the Coriolis effect formula for the Sagnac effect formula, and then he claimed that the Earth is rotating. Not by a long shot.
The RLGs are detecting the CORIOLIS EFFECT.

Let us imagine the Earth as a very large scale turntable. To detect the rotation of the turntable itself, you need the Sagnac effect. With the Coriolis effect, you have either of two possibilities: either the turntable is rotating or the ether drift is rotating above its surface.
What Michelson did is to substitute the Coriolis effect formula for the Sagnac effect formula, and then he claimed that the Earth is rotating. Not by a long shot.
The RLGs are detecting the CORIOLIS EFFECT.
A simple yes or no will suffice.
RLGs, as used in navigation systems, or scientific experiments, all use interferometers to measure the phase difference between the two light paths and calculate the rotation rate using the formula I showed above, which is the same formula Sagnac himself came up with.
It's a simple question  are these RLGs measuring rotation correctly or not? Forget about earth rate for a moment, just consider a RLG on a rotating platform turning at a given rate. Would you agree that commercial systems, such as the Honeywell GG1320, actually work correctly?

RLGs, as used in navigation systems, or scientific experiments, all use interferometers to measure the phase difference between the two light paths and calculate the rotation rate using the formula I showed above, which is the same formula Sagnac himself came up with.
No. Sagnac came up with the CORIOLIS EFFECT formula. Eight years later, Dr. L. Silberstein finally made the distinction, and proved that light interferometers were detecting the Coriolis effect indeed.
All interferometers are using the Coriolis effect formula, which features an area and the angular velocity.
It's a simple question  are these RLGs measuring rotation correctly or not? Forget about earth rate for a moment, just consider a RLG on a rotating platform turning at a given rate.
No.
If you have a geometrically symmetrical interferometer (square/circle) placed on a rotating platform, then the Coriolis effect formula will COINCIDE with the Sagnac effect formula. It is the only time they will do so.
However, if you now place that interferometer somewhere else, and it is stationary, trying to detect the supposed rotation of the Earth, it will only detect the Coriolis effect. Had the Earth been rotating, it would have registered the Sagnac effect as well.

If you have a geometrically symmetrical interferometer (square/circle) placed on a rotating platform, then the Coriolis effect formula will COINCIDE with the Sagnac effect formula. It is the only time they will do so.
Ok then. So go back to my previous question  help me understand your formula. You have a symmetrical (let's say square, to keep it simple) RLG on a rotating platform turning at a rate ω. The interferometer of the RLG detects a phase shift Δφ. You are now saying that both formulae would return the same result in this case, but you haven't actually explained how those terms fit into your formula, other than saying v=ωr.
Δt = (l1 + l2)/(c  v1  v2)  (l1 + l2)/(c + v1 + v2) = 2[(l1v1 + l2v2)]/c2
How would you get from a measured phase shift, Δφ, to a rotation rate, ω, using that formula and v=ωr?
You are also asserting that RLGs are in fact detecting the rotation of the ether. You posted a link in response to my point about latitude variation, but that link doesn't really explain the concept at all  it just says that variations in latitude were observed. Miller may have been an aether proponent, but he still very much subscribed to the round earth model, as the diagrams in that text show. You are proposing a flat earth, with aether / ether rotation that is both detectable by RLGs and also variable according to the sine of the latitude of the device. How do you explain the variation of the measurements with latitude? It makes no sense at all on a flat earth  what is so special about the equator, for example?

For an interferometer whose center of rotation coincides with its geometrical center, it's even simpler.
Circle
l = 2πr
v1 = v2
My formula: 2(2lv)/c^2 = 4lv/c^2 = 8πωr^{2}/c^2 = 8ωA/c^2
Square
dt = 8rv/c^2 (r = d/2, d = diagonal of the square) = 8ωA/c^2
Everything changes when the center of rotation no longer coincides with the geometrical center of the interferometer.
The ether drift field has a variable speed, latitude dependent. Remember, now I have the formula to PROVE that there is only one possibility for the registered Coriolis effect: it is the ether drift which is rotating above the surface of the Earth.

For an interferometer whose center of rotation coincides with its geometrical center, it's even simpler.
Circle
l = 2πr
v1 = v2
My formula: 2(2lv)/c^2 = 4lv/c^2 = 8πωr^{2}/c^2 = 8ωA/c^2
Square
dt = 8rv/c^2 (r = d/2, d = diagonal of the square) = 8ωA/c^2
Everything changes when the center of rotation no longer coincides with the geometrical center of the interferometer.
The ether drift field has a variable speed, latitude dependent. Remember, now I have the formula to PROVE that there is only one possibility for the registered Coriolis effect: it is the ether drift which is rotating above the surface of the Earth.
The formula I showed you was:
(https://wikimedia.org/api/rest_v1/media/math/render/svg/1fca22b83bfdd767eab6a619945053d2d289e800)
You've ended up with 8ωA/c^2
Where have Pi and λ gone?

Where have Pi and λ gone?
If you had actually read and understood the article you're plucking formulae out of, you would have noticed that (https://wikimedia.org/api/rest_v1/media/math/render/svg/18765e0151ef6616118b98412b0af8e53581b037). It really would be a good idea to understand what you're discussing before proudly taking a stance on it.
Now, it's still possible that sandy made a small (and largely insignificant for the purpose of this discussion) arithmetic error in his calculations. Can you find it?

Where have Pi and λ gone?
If you had actually read and understood the article you're plucking formulae out of, you would have noticed that (https://wikimedia.org/api/rest_v1/media/math/render/svg/18765e0151ef6616118b98412b0af8e53581b037). It really would be a good idea to understand what you're discussing before proudly taking a stance on it.
Now, it's still possible that sandy made a small (and largely insignificant for the purpose of this discussion) arithmetic error in his calculations. Can you find it?
I’m well aware of that equation, but I’m not really clear why you’ve brought it up. The reason I quoted the generalised sagnac formula is that it is the one used to get from the interferometer reading to a rotation rate  you can’t measure delta t directly, but you can measure the phase shift.
I’m just pointing out that the equation sandokhan has come up with is not actually the same as the one I showed  it is missing the Pi and λ terms. The latter is particularly important, as without it, the dimensions of the equation change.

Where have Pi and λ gone?
If you had actually read and understood the article you're plucking formulae out of, you would have noticed that (https://wikimedia.org/api/rest_v1/media/math/render/svg/18765e0151ef6616118b98412b0af8e53581b037). It really would be a good idea to understand what you're discussing before proudly taking a stance on it.
Now, it's still possible that sandy made a small (and largely insignificant for the purpose of this discussion) arithmetic error in his calculations. Can you find it?
I’m well aware of that equation, but I’m not really clear why you’ve brought it up. The reason I quoted the generalised sagnac formula is that it is the one used to get from the interferometer reading to a rotation rate  you can’t measure delta t directly, but you can measure the phase shift.
I’m just pointing out that the equation sandokhan has come up with is not actually the same as the one I showed  it is missing the Pi and λ terms. The latter is particularly important, as without it, the dimensions of the equation change.
Seems that SteelyBob can't even math or simply say no in response to a clear question.

I’m well aware of that equation, but I’m not really clear why you’ve brought it up.
Yes, that's rather apparent. Let's help you out.
 You provided a formula for Δϕ
 Sandokhan provided a proposed formula for Δt
 You were confused by this, so I showed you the relation between Δϕ and Δt  all that was required of you was simple algebra
 Since this still eludes you, we can conclude that even though "you are well aware of that equation", you do not understand it in the slightest.
it is missing the Pi and λ terms.
It's not missing anything at all. Once again, note that (https://wikimedia.org/api/rest_v1/media/math/render/svg/18765e0151ef6616118b98412b0af8e53581b037).
Are you with us yet? If we can make it past substitution, we might even be able to discuss physics at some point.

I’m well aware of that equation, but I’m not really clear why you’ve brought it up.
Yes, that's rather apparent. Let's help you out.
 You provided a formula for Δϕ
 Sandokhan provided a proposed formula for Δt
 You were confused by this, so I showed you the relation between Δϕ and Δt  all that was required of you was simple algebra
 Since this still eludes you, we can conclude that even though "you are well aware of that equation", you do not understand it in the slightest.
it is missing the Pi and λ terms.
It's not missing anything at all. Once again, note that (https://wikimedia.org/api/rest_v1/media/math/render/svg/18765e0151ef6616118b98412b0af8e53581b037).
Are you with us yet? If we can make it past substitution, we might even be able to discuss physics at some point.
Thank you, and my apologies  I hadn't spotted that he was still talking about 'dt'. Makes sense.
I'm curious as to how Sandokhan got to the formula  there's clearly some fairly significant errors along the way. I'm not talking about minor mistakes  I've no interest in derailing threads when somebody makes a minor mistake (witness this one from TB earlier here: https://forum.tfes.org/index.php?topic=18565.msg246662#msg246662 (https://forum.tfes.org/index.php?topic=18565.msg246662#msg246662)). But, for example, sandokhan says this:
Δt = (l1 + l2)/(c  v1  v2)  (l1 + l2)/(c + v1 + v2) = 2[(l1v1 + l2v2)]/c2
That looks fundamentally wrong to me  the simplification on the right isn't equal to the term on left. Thoughts?

He already showed you the assumptions and arithmetic required to arrive at Δt=8ωA/c^2. If you disagree with any of the steps, you'll have to pinpoint them

He already showed you the assumptions and arithmetic required to arrive at Δt=8ωA/c^2. If you disagree with any of the steps, you'll have to pinpoint them
Is my post not pinpoint enough? If the one term doesn't equal the other, then what follows or precedes it can't be right either, can it? Or am I missing something?

I'm curious as to how Sandokhan got to the formula
I have already the provided the link for the derivation of the formula.
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2117351#msg2117351
there's clearly some fairly significant errors along the way
You won't find any. It is a very straightforward derivation.
That looks fundamentally wrong to me  the simplification on the right isn't equal to the term on left. Thoughts?
Work out the term on the left, pretty tedious algebra, and you will arrive at the term on the right.
You also have the classic example from the very simple situation where the center of rotation coincides with the geometrical center:
(https://image.ibb.co/m909uq/fa2.jpg)
The formula is correct. What you have to deal with now, are the consequences.

For the case of v1=v2, the algebra isn't even particularly tedious.

My formula was also obtained by Professor P. Yeh in 1985, using phaseconjugate mirrors:
https://apps.dtic.mil/dtic/tr/fulltext/u2/a206219.pdf
Studies of phaseconjugate optical devices concepts
US OF NAVAL RESEARCH, Physics Division
Dr. P. Yeh
PhD, Caltech, Nonlinear Optics
Principal Scientist of the Optics Department at Rockwell International Science Center
Professor, UCSB
"Engineer of the Year," at Rockwell Science Center
Leonardo da Vinci Award in 1985
Fellow of the Optical Society of America, the Institute of Electrical and Electronics Engineers
(https://i.ibb.co/6Y9W45j/yeh5.jpg)
page 152 of the pdf document, section Recent Advances in Photorefractive Nonlinear Optics page 4
The MPPC acts like a normal mirror and Sagnac interferometry is obtained.
(https://i.ibb.co/MsS5Bb5/yeh4.jpg)
PhaseConjugate Multimode Fiber Gyro
Published in the Journal of Optics Letters, vol. 12, page 1023, 1987
page 69 of the pdf document, page 1 of the article
A second confirmation of the fact that my formula is correct.
Here is the first confirmation:
(https://image.ibb.co/mtGWny/mgrot6.jpg)
Selfpumped phaseconjugate fiberoptic gyro, I. McMichael, P. Yeh, Optics Letters 11(10):6868 · November 1986
http://www.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf (appendix 5.1)
Exactly the formula obtained by Professor Yeh:
φ = 2(φ_{2}  φ_{1}) = 4π(R_{1}L_{1} + R_{2}L_{2})Ω/λc = 4π(V_{1}L_{1} + V_{2}L_{2})/λc
Since Δφ = 2πc/λ x Δt, Δt = 2(R_{1}L_{1} + R_{2}L_{2})Ω/c^{2} = 2(V_{1}L_{1} + V_{2}L_{2})/c^{2}
CORRECT SAGNAC FORMULA:
2(V_{1}L_{1} + V_{2}L_{2})/c^{2}
The very same formula obtained for a Sagnac interferometer which features two different lengths and two different velocities.
What I did is to derive the formula in the context of the MichelsonGale experiment and also for ring laser gyroscopes. It is by far the biggest contribution to the field of light interferometry since 1913 when G. Sagnac conducted the first such experiment under strict conditions.

I'm curious as to how Sandokhan got to the formula
I have already the provided the link for the derivation of the formula.
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2117351#msg2117351
there's clearly some fairly significant errors along the way
You won't find any. It is a very straightforward derivation.
That looks fundamentally wrong to me  the simplification on the right isn't equal to the term on left. Thoughts?
Work out the term on the left, pretty tedious algebra, and you will arrive at the term on the right.
You also have the classic example from the very simple situation where the center of rotation coincides with the geometrical center:
(https://image.ibb.co/m909uq/fa2.jpg)
The formula is correct. What you have to deal with now, are the consequences.
From your link:
(https://image.ibb.co/dbZ7Kd/gsac2.jpg)
Keep it simple and just look at the first formula  it's just not correct. l/(cv)  l/(c+v) does not equal 2lv/c^{2}
It's easy to prove by plugging in some numbers  say l=1, c=3 and v=2.
The left hand side would give you 1/(32)  1/(3+2) = 1  1/5 = 4/5
The right hand side would give you 2 x 1 x 2 / 3^{2} = 4/9
Always happy to proven wrong, but that doesn't look right to me.

No.
c is a fixed constant, O(3x10^{5}km/hr).
v is either O(1) or O(30km/hr).
That is, c>>v.

No.
c is a fixed constant, O(3x10^{5}km/hr).
v is either O(1) or O(30km/hr).
That is, c>>v.
Ah, thank you  I see what you did now.

Recall that the device was described as an 'underground seismic observatory'.
The 'rotation of the earth' affects seismic waves:
https://gfzpublic.gfzpotsdam.de/rest/items/item_5005107_3/component/file_5005141/content
SUMMARY
Rotation of the Earth affects the propagation of seismic waves. The global coupling of spheroidal and toroidal modes by the Coriolis force over time is described by normalmode theory. The local action of the Coriolis force on the propagation of surface waves can be described by coefficients for the coupling between propagating Rayleigh and Love waves as derived by Snieder & SensSchonfelder.
....
The rotation of Earth as propagation medium exerts an additional force on moving matter—the Coriolis force. Depending on the angle of the polarization vectors of P and S waves with Earth’s rotation axis, the Coriolis force causes a small transverse component for P waves and a small longitudinal component for S waves. Moreover the Coriolis force causes a slow rotation of the shear wave polarization vector akin to the motion of a Foucault pendulum (Snieder et al. 2016b,a).
The Coriolis force 'causes a slow rotation' and the effect is compared to watching a rotating Foucault Pendulum. In the Foucault Pendulum we allegedly (https://wiki.tfes.org/Foucault_Pendulum) watch the pendulum rotate, not the earth. So the device is observing rotating seismic waves and we are assuming that it is the earth rotating and that the movement isn't coming from the seismic waves rotating, like many other things rotate above us diurnally.

Recall that the device was described as an 'underground seismic observatory'.
The 'rotation of the earth' affects seismic waves:
https://gfzpublic.gfzpotsdam.de/rest/items/item_5005107_3/component/file_5005141/content
SUMMARY
Rotation of the Earth affects the propagation of seismic waves. The global coupling of spheroidal and toroidal modes by the Coriolis force over time is described by normalmode theory. The local action of the Coriolis force on the propagation of surface waves can be described by coefficients for the coupling between propagating Rayleigh and Love waves as derived by Snieder & SensSchonfelder.
....
The rotation of Earth as propagation medium exerts an additional force on moving matter—the Coriolis force. Depending on the angle of the polarization vectors of P and S waves with Earth’s rotation axis, the Coriolis force causes a small transverse component for P waves and a small longitudinal component for S waves. Moreover the Coriolis force causes a slow rotation of the shear wave polarization vector akin to the motion of a Foucault pendulum (Snieder et al. 2016b,a).
The Coriolis force 'causes a slow rotation' and the effect is compared to watching a rotating Foucault Pendulum. In the Foucault Pendulum we allegedly (https://wiki.tfes.org/Foucault_Pendulum) watch the pendulum rotate, not the earth. So the device is observing rotating seismic waves and we are assuming that it is the earth rotating and that the movement isn't coming from the seismic waves rotating, like many other things rotate above us diurnally.
I'm not really clear what you're suggesting  are you saying that Coriolis is, or isn't a real effect?
It's not really clear what your point is  seismic observations are a major reason why people keep building ever more precise RLGs. They are also interested in slight variations in the earth's rotational axis, amongst other things. But seismic activity manifests as oscillatory motion, whereas as constant rotation is just that  constant rotation. See that graph again:
(https://i.imgur.com/DZuMslA.png)
The earth rate is the constant line, whereas the seismic activity is the oscillatory signal superimposed on it. If not was just seismic activity, the oscillation would be around zero.

It says that the seismic waves are rotating, like a Foucault Pendulum:
https://inside.mines.edu/~rsnieder/Snieder16Fouc.pdf
Earth’s rotation leads to a slow rotation of the transverse polarization of S waves; during the propagation of S waves the particle motion behaves just like a Foucault pendulum.
The device is watching something rotate, and it is assumed to be caused by the rotation of the earth.

It says that the seismic waves are rotating, like a Foucault Pendulum:
https://inside.mines.edu/~rsnieder/Snieder16Fouc.pdf
Earth’s rotation leads to a slow rotation of the transverse polarization of S waves; during the propagation of S waves the particle motion behaves just like a Foucault pendulum.
The device is watching something rotate, and it is assumed to be caused by the rotation of the earth.
The paper referenced says, "But we know that Earth’s rotation affects Earth’s normal modes [Backus and Gilbert, 1961] and surface waves [Tromp, 1994]. This raises the question: what is the exact imprint of Earth’s rotation on seismic body wave propagation?"
So yes, they are studying Earth’s rotation impact on these waves. What of it?

The problem is that this is an indirect conclusion, rather than a direct one. If you are floating in a featureless environment in outer space and see an object travel past you at a set speed, you generally could not know whether it is you who was moving or whether it was the object that was moving.

The problem is that this is an indirect conclusion, rather than a direct one. If you are floating in a featureless environment in outer space and see an object travel past you at a set speed, you generally could not know whether it is you who was moving or whether it was the object that was moving.
What indirect conclusion?
And who or what is floating in a featureless environment in outer space? We’re talking about earths rotation impacting seismic waves and such, here on earth, not in space. And rlg’s & pendulums and stuff here on or just above earth. What does featureless space have to do with this?

It has everything to do with it. Look into relative motion. If you are watching something move, you can't tell whether it is you and perhaps your environment that is moving or whether it is the body is moving. This is extremely basic and and I am surprised that you are having trouble understanding this.

Your referenced article debunks your 'relative motion' statement right from the start. Scientists that study any seismic activity know that this is a very intermittent phenomenon. The very steady baseline rotation rate on the graph isn’t related to seismic activity at all, it’s the measured rotation of the earth. You can see that there’s a deviation of the rate both above and below the steady baseline. The sheer mass of the earth would preclude any sudden changes of the rotation rate like that. You can take a gyroscope and put it on an airplane, and it will still be influenced by the earth’s rotation but couldn’t be influenced by any seismic activity.

It says that the seismic waves are rotating, like a Foucault Pendulum:
https://inside.mines.edu/~rsnieder/Snieder16Fouc.pdf
Earth’s rotation leads to a slow rotation of the transverse polarization of S waves; during the propagation of S waves the particle motion behaves just like a Foucault pendulum.
The device is watching something rotate, and it is assumed to be caused by the rotation of the earth.
You've completely changed your position from the start of our discussion here. I'm curious as to whether you've changed your mind  in which case will you change the wiki to reflect this?  or whether you are just adapting your default 'disagree' position to suit what's in front of you. At the start, your argument was all about the noise levels in the rotation graphs. Then, as you realised that, in fact, a lot of the sources you yourself presented did in fact have very accurate, low noise graphs in them, you've pivoted to an argument based on the fact that the gyros are in fact measuring something other than rotation, even though that is precisely what there are designed to do.
Could you very carefully and precisely explain what exactly you think is going on in this graph please?
(https://i.imgur.com/DZuMslA.png)
We have some very obvious seismic activity  clearly oscillatory in nature, superimposed on a flat line that is bang on the generally agreed earth rotation rate. Are you arguing that the flat line is also some kind of seismic activity? And that this activity is somehow a constant, steady state rotation, whose magnitude varies with the sine of the latitude? So it is magically zero on a circle around the monopole North Pole that we call the equator but whose significance is what, precisely, on a flat earth?

Actually, the Wiki page accurately says that those types of devices are looking at rotational seismic phenomena right here  https://wiki.tfes.org/Ring_Laser_Gyroscope__Seismology
Not sure why you keep reposting that graph. It's not raw data. As you pointed out earlier, the angular rate on that one is faster other graphs we saw which are uncorrected for latitude and this data is reprocessed and visualized. Other visualizations we saw in this thread have radically different views.
GINGERino is not a regular seismograph, it is a special tool which studies "rotational seismology" 
https://physicsworld.com/a/ringlaserrevealssubtleseismicmotion/
Seismic shift: GINGERino is deep below these mountains
A laser gyroscope located deep beneath the Gran Sasso mountain in central Italy has made the first deepunderground measurements of the rotational motion that passing seismic waves generate in the Earth’s crust. The ability to make such measurements could boost our understanding of the strain that rocks undergo before an earthquake takes place, say the scientists who carried out the research.
Earthquakes release large amounts of pentup energy in the form of seismic waves, which propagate in all directions from the quake’s epicentre. When those waves reach the Earth’s surface they can cause the ground to move along one or more orthogonal axes – up and down, back and forth, and side to side. But seismic waves can also generate much smaller rotational motions, in which the ground rotates around one or more of the three axes.
According to Gilberto Saccorotti of Italy’s National Institute for Geophysics and Volcanology (INGV), rotational motion is important to measure for a number of reasons. For one thing, seismologists can determine the speed of a seismic wave – and so better understand the kind of rock it propagates through – by comparing the magnitudes of the rotational and translational motions that it generates. In addition, better measurements of ground rotation during strong earthquakes would allow for more robust building regulations. “Circular motion, like horizontal motion, can be very dangerous,” he says. “Structures haven’t been designed with that in mind but are instead meant to resist vertical forces, i.e. their own weight.”
Frequency shift
Ringlaser gyroscopes, on the other hand, are designed specifically to measure rotational motion. These devices record the very tiny differences in frequency between two laser beams sent in opposites directions around an optical circuit that is fixed rigidly to the ground. The frequency offset reflects the rate at which the ground rotates. Ring lasers in Germany, New Zealand and the US have been detecting earthquakes’ rotational ground movements for about the last two decades, but the fact that these instruments are located at or just below ground level exposes them to disturbances – be they of natural or human origin – that originate close to the Earth’s surface.
In the latest work, Saccorotti and colleagues at the INGV and Italy’s National Institute for Nuclear Physics (INFN) used a ring laser called GINGERino, consisting of four 3.6 mlong sides mounted on a block of granite. Housed 1400 m underground at the Gran Sasso National Laboratory, the device is largely shielded from the tiny variations in air pressure that can trouble ring lasers at shallower depths. It is the forerunner of an experiment called Gyroscopes in General Relativity (GINGER), which will use at least three large ring lasers arranged at right angles to one another to try and measure the very subtle “framedragging” effect predicted by Einstein’s general theory of relativity.
Using GINGERino, the INFNINGV group was able to record a magnitudeseven earthquake that occurred under the Atlantic Ocean during a week of datataking in June 2015. The researchers say that although their data exhibit a poor signaltonoiseratio, they were still able to detect rotational motion generated by the earthquake’s seismic waves in the rock surrounding the lab.
Potential earthquake precursors
According to Saccorotti, the result shows the feasibility of installing a longterm experiment in the Gran Sasso lab – be it GINGER or a single, larger ring laser. Such a device would systematically record rotational ground motions over a two to fouryear period. This would allow the detailed study of the elastic deformation of rock caused by the gradual buildup of energy across a geological fault ahead of an earthquake. “That deformation can include rotational motion, so having a very sensitive device in a lownoise environment opens up interesting possibilities for studying a potential earthquake precursor”, he says, pointing out that Gran Sasso is in one of the most seismically active regions of Italy.
Ulrich Schreiber of the Technical University of Munich, who collaborates with the Italian group, points out that the field of “rotational seismology” is now quite well established, thanks to the availability of improved ringlaser gyroscopes. But he nevertheless praises the latest work. “GINGERino is a prototype instrument that has still to mature a fair bit before reaching its full potential,” he says. “But being able to observe rotational motion from remote earthquakes in a deepunderground laboratory is an important step forward.”
It's a new field of "rotational seismology" which is "able to observe rotational motion from remote earthquakes".

Wait, this whole time the vague mentions of rotational seismic phenomena/rotating seismic waves were just describing Rayleigh surface waves?
Is your argument now that RLGs cant measure long period rotation of the earth because they're also measuring very small rotational movements associated with shortlived elliptical oscillations during seismic wave propagation?

The ring laser gyros in question must be firmly attached to the ground as per the attached article. They do, indeed, measure rotation from some source. It has been implied that the source of the rotation is seismic waves. Most gyroscopes in operation are NOT attached to the ground in any way and still measure a steady 15 degrees per hour rotation. What are they measuring? I submit that they are measuring the steady rotation of the earth. The gyroscopes I had access to also measured a change in the z axis while moving from location to location that wouldn’t be seen on a flat earth. The ring laser gyro argument that it’s just measuring some constant, steady, rotating seismic phenomenon is thus debunked.

Actually, the Wiki page accurately says that those types of devices are looking at rotational seismic phenomena right here  https://wiki.tfes.org/Ring_Laser_Gyroscope__Seismology
Nobody is saying the devices aren't used for seismology. They absolutely are. They are extremely sensitive, and can measure tiny rotations, several orders of magnitude less than the earth's rotation. They are also using them for studying variations in the earth's axis of rotation, amongst other things.
Not sure why you keep reposting that graph. It's not raw data.
I keep posting it for several reasons. Firstly, it's from a site that you linked to. Moreover, it clearly shows earth rate, with far less noise than the apparently unacceptable amount in the examples you have cherry picked for use in the wiki. You kept saying that the amount of noise rendered the various other examples meaningless, but now here we have one with fa less noise, and you've pivoted to some nebulous claim about it measuring seismic activity. You aren't clear though on what, precisely, it is measuring. Seismic activity is, by it's nature, oscillatory. The graph in the example clearly shows a steady state rotation. If it's a steady state rotation, then it must be rotating.
Your request for 'raw data' is also curious, as when you had raw data, such as from the Canadian Honeywell test, you didn't understand what it was, despite it actually demonstrating earth rate, if you knew what to do with the data.
As you pointed out earlier, the angular rate on that one is faster other graphs we saw which are uncorrected for latitude and this data is reprocessed and visualized. Other visualizations we saw in this thread have radically different views.
GINGERino is not a regular seismograph, it is a special tool which studies "rotational seismology" 
...
It's a new field of "rotational seismology" which is "able to observe rotational motion from remote earthquakes".
Yes, it absolutely is. Rotational motion...because it's a highly sensitive rotation detector. Which is why the graph I've shown you, from the site that you linked to, clearly shows oscillatory seismic activity superimposed on the steady state earth rotation.
I suppose the ultimate question really is: 'what RLG data would convince you that the earth was actually rotating?'
You seem to be rejecting every piece of data for a variety of reasons...eg too much noise in a simple device, but then an ultra sensitive device with much less noise must be detecting something else other than earth rate, despite it clearly measuring earth rate.

Your referenced article debunks your 'relative motion' statement right from the start. Scientists that study any seismic activity know that this is a very intermittent phenomenon. The very steady baseline rotation rate on the graph isn’t related to seismic activity at all, it’s the measured rotation of the earth. You can see that there’s a deviation of the rate both above and below the steady baseline. The sheer mass of the earth would preclude any sudden changes of the rotation rate like that. You can take a gyroscope and put it on an airplane, and it will still be influenced by the earth’s rotation but couldn’t be influenced by any seismic activity.
RET claims the earth's rotation is affected by seismic activity so your statement makes zero sense.

My statement makes sense 100% because I just showed that a gyro will measure the earth's rotation minus any seismic activity. You did state that the earth's rotation is affected by seismic activity, did you not? I never disputed that fact. Any affect is very intermittant and localized. The earth's rotation always returns to the expected base rate very quickly. If I was in China looking at a gyro on a ship I would never even observe any seismic activity on it if there was a huge earthquake in California, but we might get an alert to be on the lookout for a tsunami.

I think the important point here is that earth is, at a local level, essentially a rigid body, but in the global scale, it’s far from rigid. You have a series of tectonic plates, floating around on viscous material, with the whole thing rotating away. So if you measure the rate of rotation at a particular spot, you’ll get the aggregate rate of rotation, with any local seismic activity, or oscillatory motion, superimposed on top. Moreover, the entire system is changing slowly  the axis of rotation changes over time, and the whole thing wobbles slightly as well. It’s fascinating stuff, and amazing that we now have devices of such sensitivity.
What we see in all of the graphs, in all of the papers and websites that we’ve discussed so far, is absolutely aligned with that  it all points to the same thing.

The earth is like a large bell, held together with lots of rubber bands, that’s slowly rotating. Occasionally one of the rubber bands slips and the pieces slap together and there’s a slight ringing sound heard. The main points of this analogy are that the rotation is a separate phenomenon from the ringing. The ringing could be compared to seismic activity. This seismic activity could very intermittently have a small localized effect on the rotation rate, but that effect would quickly subside and be negligible after a short period of time. The other interesting thing about this phenomenon is that scientists have been studying this for quite a while and have verified that the vibrations propagated out and the resonant frequency observed after an earthquake match that of a large spherical body. If you want to get heavily into math you can confirm this for yourself in the zetetic way.
Another thought: Think of yourself on a merrygoround. You have a gyroscope in your lap. It will measure a steady rate of rotation. Now if you suddenly move yourself backwards and forwards your gyroscope will measure a quick deviation in the rotation rate both positive and negative but the overall base rate will stay steady. The deviations in the ring laser gyroscope would be simular to measuring your sudden movements in your seat that only adds or subtracts from the underlying rotation rate of the merrygoround. This is another illustration of the difference between the rotation of the earth and it's seismic activity. These are two separate and distinct characteristics.

Nicely put, thank you.