Comment on Perturbations of the local gravity field due to mass distribution on precise measuring instruments: A numerical method applied to a cold atom gravimeter
This is a nice study of the gravitational acceleration due to masses near a cold atom gravimeter capable of nanometer per second squared resolution at 1 sample per second. The cold atom technique is capable of two powers of 1000 more sensitivity at higher frequencies. This is mainly concerned with things in the lab that will distort the readings, particularly for three axis operation.
My recommendation is the usual – use the sun-moon vector tidal signal – which is many times larger than these local perturbations as a reference signal. Get the instrument calibrated on all three axes, and then begin to image sources nearby. The sun moon tidal signal is the main component (about 95%) of the full variation over a month. Depending on latitude and longitude and absolute date and time, it varies roughly +/- 1000 nanometers/second^2 during a day. It is a full 3D vector. With a three axis instrument, it is usually only necessary to use a linear regression to fit the main signal. And offset and multiplier.
The residual after removing this simple calculated part of the signal is primarily atmospheric. Moisture and density and flows in the atmosphere. account for about 4.5% of the signal over long periods. During storms it varies.
The signal is so precise in timing and intensity that at any stable or mobile gravimeter it is possible to solve for the precise position and orientation of the instrument axes. This is necessary for mobile devices where it is expensive and tedious to locally find the orientation and absolute value of the field at the location. Using a readily available references signal that only requires the location of the sensor and the date and precise time, is what is needed to coordinate global imaging arrays.
For devices that wander – temperature, power supply, electric field, magnetic field, local atmospheric pressure – you can and should try to remove all those. But when you can, calibrate the sensor continuously. Even if there is ambiguity on any one axis, three orthogonal signals with a precise reference put strong constraints on the main level of the signal.
I have seen many accelerometer designs and attempts over the years. The noisy first attempts to measure the sun and moon signal (if I see someone say “earth tides”, I know they are getting closer). When the adapted accelerometer is actually calibrated to the sun moon signal, then it can truly be called a gravimeter.
Since this article talks about mass configurations, it missed on key point that Robert Forward and Joe Weber pointed out – if you move those masses in regular trajectories, the signal they produced can easily be picked up with dozens of different devices types now. MEMS, cold atom, electron gravimeters, Bose Einstein, electrochemical and others, These all gravimeters measure the gravitational potential gradient. The local atomic clocks and LIGO instruments and GPS networks are also going to be picking the changes due to solar, lunar and earthbased variations in the absolute potential. It is far easier to measure acceleration, which is why so many low cost devices are reaching “gravimeter” or “sun moon signal” stage.
I started out just after the year 2000 calibrating the global superconducting gravimeter array to measure the speed of gravity. My background it satellite orbit determination and using satellites to determine the structure and dynamics of the earths gravitational potential field. So I chose the Jet Propulsion Labs solar system ephemeris as a starting point. Simple Newtonian gravity is all that is needed.
The Suns acceleration at the station minus the suns acceleration on the center of the earth, plus the moon acceleration at the station minus the moons acceleration on the center of the earth. Add the centrifugal acceleration at the station from earth rotation. Take that vector and dot it into the station North, East and Vertical unit vectors. Use a linear regression to fit that to the signal.
The reference to a stable and easy-to-use modeling group is more important than local uses. https://ssd.jpl.nasa.gov/horizons.cgi
It took me almost a year to find the broadband seismometers in the IRIS.edu set of three axis seismometers that, when calibrated as accelerometers, showed enough of the tidal signal to match up. Since that depends on quiet times and instrument operation with someone else’s device for a completely different purpose, that is to be expected. But indeed all three axes will match with a linear regression. This paper’s authors can easily go beyond that. You understand instrument response (though you might want to use FFTs for impulse respond models, to match a larger community and many different kinds of devices, especially for MHz, GHz and higher frequencies).
It literally shocked me that Newtonian gravity works that well at one sample per second. I know that dynamic effects where time of flight matters require slightly different approaches. But for routine wearable navigation, and object detection, there are lots of people who can improve things. I wish I could attach images and spreadsheets here.
I did put a sample of thirty days of readings from Hsinchu China in a spreadsheet at https://gravitynotes.org/ at the top of the page “Sample Excel File of Regression” and I also put on for Mitsishiro Japan at https://hackaday.io/project/164550-low-cost-time-of-flight-gravimeter-arrays
The image is at https://hackaday.io/project/164550/gallery#21f5826751cf7b199a02263bd201e9bb and I can find the spreadsheet if you are interested. I recommend you just do it yourself, and ask me or someone for help if you get stuck. Having spent almost 20 years doing this, it seems easy and clear. But it was hard to believe that it is that simple. The reason it is that simple is because at frequencies faster than 1 Hz, the sun and moon do not move far. But one second is enough to show a clear change in the sum of squares of the regression. That is how you can search for the best position and orienation of the station.
I am telling you this because it works, any groups with basic math and physics skills can learn it. It is not just locking the instrument to the sun and moon that is important, but locking into NASA, JPL and global groups.
NOW. My recommendation. PLEASE use what you have here and weigh the sun and moon against your instrument where you know the shapes and signals from known masses of different compositions. The instrument calibration to the much larger sun moon signal – albeit slowly varying give one set of constraints. If you cannot “see” that signal and fit it precisely, you are doing something wrong or we all need to look deeper. But that simple linear regression (three sets of multiplier and offset) is only six numbers and you have lots of data to use to determine them
So you have everything you need to precisely calibrate your instrument globally, and you can test the signal shapes for controlled “orbits” and arbitrary controlled rotations of signal masses. I think your atom interferometer is capable of much higher frequencies at high gain. Having a base you can know that you are locked in and removing the biggest sources of noise.
If anyone is out there, PLEASE, try this at MHz frequencies in a cave or tunnel. That should be easy for many of the existing instruments or designs. The tunnel because gravity should go through the earth and materials with no attenuation. The high sampling rates for massive oversampling on the sun moon signal (you can measure the speed of gravity for me on all three axes and look for polarization). The short and precisely timed samples for global correlation networks with earthquake seismic waves as reference. You are NOT trying to pick up the earthquake itself, we are not there yet. Just the spreading surface and body waves. The surface waves are more obvious. I consider the worlds expert at LIGO on “Newtonian noise” to be Jan Harms. He worked out many examples. I think his poor job was “get rid of all that annoying earth noise, we “astronomers” must only look at distant things, not anything on the mundane earth”. Yeah, I think like that because I don’t know them. But it is the way they are behaving.
I found some surf groups who love the big ocean waves. You might not know they use models and datastream to precisely predict exactly how large the waves will be. I think the are able to get it to a foot on average.
Anyway, there are also drones that can map the wave surface from different angles and stitch into a fairly precise 3D model of the waves over time. Then a simple 3D calculation from every element of water Newtonian acceleration at detector locations, and you have a nice complex, NOT GAMEABLE, signal that you can use for testing and to improve designs.
Robert Forward wrote about lab sources in the 1970s and maybe before. Joe Weber stressed to me how important his work was. I am going through those old models now, because even me with no resources or lab skills can make a sun moon gravimeter that can track moving masses. But I wish that Liang Cheng Tu and that group at Glascow would quit trying to commercialize a trivial MEMS gravimeter application, and go after the main goal – global, every day use of gravity signals for imaging, detection and characterization, communication.
Yes, I have also tracked field generation as well. But the gravitational field is so much more energy dense than electricity and magnetism. The gravitational acceleration field at the earth’s surface is equivalent to static or dynamic magnetic fields on the order of 380 Tesla. So you need lasers and pulse generators, massive amounts of real time data – to move everyday object and vehicles with fields. But I just want to get the earthquake early warning, gravitational tomography for the interior of the earths core and the suns interior and the moons interior – first. Communication is possible at low power levels. But that is a hard one and I am getting old and tired.
I apologize for this being so long. If you have any questions you can reach me here. I am also going to clean up my notes at GravityNotes.Org and post the software I used. You are sitting there trying to get nm/s2 and you have these huge sun moon variations to use. And now we can finally start tracking people, packages, cars, trucks, planes, ocean waves and currents, atmospheric waves and currents. I want to set up a regular array just for the planets. Any high school group can buy (if some people I won’t mention would get off their and sell some working gravimeters so people can get going) a small array of gravimeter, go through the sun moon calibration, argue endlessly about earth tides and atmospheric effects, join global networks and begin to understand gravitational engineering 101.
Some of my current questions and goals:
Ground truth the GRACE data – particularly ocean currents and wave heights. Ground truth ocean wave height from other sensors — LOTS of them.Ground truth the local climate and meteological models and sensors. Correlate with the regional weather radar and with GPS signal and lidar profiles of the atmosphere used for meteorology. Check for overlaps with global magnetometer arrays. Check for overlaps for global seismometer arrays. Upgrade seismometers as gravimeters for early warning. Check for solar mass ejections, model the granule mass and project their signal. Look inside the sun. Look inside “black holes”. The gravitational potential is NOT a singularity. See if the signal goes directly through the whole earth or it it is attenuated or refracted. Give DARPA a cave imaging tool. Give World Magnetic Model local orientation signals that are not sensitive to magnetic variations or where that can be calibrated and treated as a separate data stream. Combine the earth geopotential and earth magnetic potential models and look for overlaps and false classification of phenomena. Exactly how are the gravitational potential and the magnetic field related at picometer level? ( I think they are just different size fluctuations of the same stuff) Push into the THz (Tera samples per second and higher) region. Do full quantum modelling of objects of different compositions (molecular) and see if it is really necessary to keep gravity and electromagnetism separate.
Richard Collins, Director, The Internet Foundation