The Wiki covers that. See the section Corrections for Latitude.
The wiki covers this? Covers it in muddled thinking and errors, and anyone wanting to learn something about gravimetry and gravimeters should look elsewhere – even Wikipedia is a better choice.
Where to start? From the wiki, as quoted above:–
If the objective of gravity surveys is merely to look for deviations from a round earth reference model with the vibrating gravity theory, then the final computed number in meters per second squared would becomes meaningless for the purpose of discussion. Any modifications to the reference values are constructed on an entirely theoretical basis.
The above page tells us that there is a theoretical model and that the goal of gravity surveys is to modify that model.
Frankly, the wiki gets this bass ackwards. It also mentions a fictitious "vibrating gravity theory" – where did that derp come from?
First, the theoretical model, which has an equation (cited above) giving the theoretical value of gravitational acceleration at the geoid level for anywhere on Earth, accurate to one tenth of a mgal (
milligal) – that's 0.00001 m/s². There is also a more elaborate equation which gives results accurate to a ten-thousandth of a mgal (0.0000001 m/s² – a thousand times more accurate) if needed. Pick your location, plug the latitude into the equation and you get a theoretical value for acceleration at geoid level (generally, but not always, equal to sea level).
Next, the gravity survey. Surveyors measure the acceleration directly with an absolute gravimeter, or the difference from a known, accurate measurement of gravitational acceleration with a relative gravimeter. Then there are corrections applied to the
measured value,
not the theoretical value. The theoretical value is for geoid level, but an absolute gravimeter measurement at Emigrant Gap, CA on Interstate 80, is at 1582m or 5190ft above sea level. Gravity does reduce with height, so a correction to give the expected value at geoid level is applied to the measurement – this is the Free Air correction. There is also a great deal of rock in those 1582m above the geoid and this is also corrected for – this is the Bouguer correction.
Let's say the surveyors are instead using a relative gravimeter and the known accurate measurement they are comparing with is at Sacramento, CA. A Latitude correction is applied to the Sacramento figure to account for the 42 minutes and 55 seconds difference in latitude between Sacramento and Emigrant Gap, because gravity does vary with latitude.
Note well –
no corrections are applied to the theoretical value – all corrections are applied to the
measured data. All these corrections are to give a measurement for gravitational acceleration corrected to geoid level, as if the surveyors were actually measuring at the theoretical geoid level, so comparisons can be made from other places, also corrected to the geoid level, making sure surveyors are comparing apples with apples, not coconuts with bananas.
The corrected, measured values are then compared with the theoretical values and the difference, if any, noted – this difference is the gravitational anomaly. Maps of the gravitational anomaly over a given area are used for many purposes, including oil and mineral prospecting, and are a valuable tool. The Nash dome in Texas was the first oil discovery made using an early type of gravimeter (in the 1920s) and many have followed since.
What's missing from the wiki, or any of the examples you've mentioned, are numbers: actual data and actual calculations. Do your vaguely expressed doubts stand up to examination? It's time to do some more calculations using a more reliable introductory guide.
https://gpg.geosci.xyz/content/gravity/gravity_introduction.htmlThe data reduction formulas are given on
https://gpg.geosci.xyz/content/gravity/gravity_data.htmlLet's use the Emigrant Gap site to start with. I'll assume the geoid coincides with sea level for these calculations and I'll use the suggested "crustal" density figure for Bouguer calculations. The Free Air correction is 0.3086 x 1582 = 488.2mgal, which is added to the measured figure. The Bouguer correction is 0.04191 x 1582 x 2.67 = 177.0mgal which is subtracted from the measured figure. The net adjustment is therefore 488.2 - 177.0 = +311.2mgal and would be applied to a measurement made by an absolute gravimeter.
If the surveyor was instead using a relative gravimeter, the latitude correction would also be made for the difference in latitude between Sacramento and Emigrant Gap, which is 42.9 nautical miles or 79.5km. Latitude of Sacramento is 38° 34' 54"N and Emigrant Gap is 39° 17' 49"N, so I'll use 39° as an average. Latitude correction is therefore 0.811 x sin(2x39) x 79.5 = 63.1mgal and this is subtracted from the measurement to directly compare with the Sacramento figure. The net adjustment for a relative gravimeter is therefore +311.2 - 63.1 = +248.1mgal.
The acceleration figure I found for Sacramento was 9.80033m/s², which is 980.033 Gal, or 980,033mgal, but an adjustment of 311.2 mgal (or 248.1mgal) is hardly significant compared to the headline figure, or the figures cited from around the world, but we'll have a look at the extremes of that range (9.772 to 9.829m/s²) to make sure. These were all made with absolute gravimeters, so we can ignore latitude corrections.
Quito in Ecuador is at 2850m above sea level. Free air correction is 0.3086 x 2850 = 879.5mgal. Bouguer correction is 0.04191 x 2850 x 2.67 = 318.9mgal. The net adjustment is +879.5 - 318.9 = +560.5mgal. The cited acceleration figure is 9.772 m/s², which is 977,200 mgal. 560.5mgal are pretty small beer next to the headline figure.
Thule Air Base in Greenland, now known as Pituffik Space Base, is at 76.5m above sea level. Free air correction is 0.3086 x 76.5 = 23.6mgal. Bouguer correction is 0.04191 x 76.5 x 2.67 = 8.56. Net correction is +23.6 - 8.56 = +15.04mgal. This is tiny in comparison to the cited 9.829 m/s² or 982,900mgal.
The cited gravitational acceleration figures are so many orders of magnitude larger than the corrections applied to their direct measurement that there is no justifiable hope the corrections might account for the differences across the world. An upwardly accelerating flat earth would still self-destruct in less than half a day.
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