Free Air Anomaly

Use the Gravity > Free Air, Bouguer Step by Step > Free Air Anomaly menu option (geogxnet.dll(Geosoft.GX.Gravity.FreeAirAnomaly;Run)*) to carry out the gravity free air correction.

Free Air Anomaly dialog options

Database	The name of the current database (displayed for information only).
Corrected gravity channel	Select the gravity channel (in milligals). In practice, this channel would already be corrected for Tide, Instrument Drift, and potentially height and base station. Script Parameter: GRAVRED.GRAVITY
Elevation channel	Select the elevation channel. This is the vertical elevation (positive up) of the instrument relative to the datum level. The datum level is generally the geoid (sea level); however, it could be set to a different height above see level (see Application Notes). By default, if there is a channel named "Elevation" in the database, it will be selected. Script Parameter: GRAVRED.ELEVATION
Output free air anomaly channel	Specify the name of the output free air anomaly channel. This channel will contain the data as if it was all collected on the same horizontal datum, generally the geoid surface, regardless of the topography. By default it is set to "FreeAir”. Script Parameter: GRAVRED.FREEAIR
Free air correction method	Select an elevation correction formula from the list: 0.308596 mGal/m 0.3086 mGal/m (Sheriff) Ellipsoid (Heiskanen & Moritz) - the full ellipsoid expression as a function of height and latitude from Heiskanen and Moritz ^[1]. Additional elevation correction formulas can be defined and stored in the file named "Gravity_Free_Air.lst" located in the folder %USERPROFILE%\Documents\Geosoft\Desktop Applications \etc. Script Parameter: GRAVRED.FREE_AIR
Latitude channel	This is a contextual parameter. If the Free air correction method selected is "Ellipsoid (Heiskanen & Moritz)", you will be prompted to provide the latitude channel required for the free air correction. By default, if thsere is a channel named "Latitude" in the database, it will be selected. Script Parameter: GRAVRED.LATITUDE

Application Notes

This GX assumes that:

A gravity database is currently loaded (see Import Gravity Survey).
Latitude, Longitude ground locations are defined.
Tide, drift, base station absolute gravity (see Gravity Corrections) have been applied.
The Latitude correction (the theoretical gravity at the station location) has been applied (see Latitude Correction).

Elevation Channel

For ground surveys this is the elevation of the sensor, which equates to the topography plus the instrument height. However, if you have already applied a height correction in Gravity Corrections, then the elevation should represent the height of the topography above the datum (generally the geoid or sea level).
For airborne surveys at a constant barometric height, a free air correction is not necessary because the gravity values are at the same height. Nonetheless, you may want to reduce the data to the geoid surface in which case you could apply the free air correction. For drape airborne surveys, provide the flight elevation above the datum (positive up) . For drape surveys, if you have already applied a height correction, the elevation should represent the height of the topography to which you height-corrected the data.
For shipborne surveys, normally the elevation is constant and a free air correction is not necessary.

Figure 1: Height (elevation) relative to datum level.

Free Air Anomaly

In order to calculate the free air correction at an accuracy of 0.01 milligals, the station height should be provided at an accuracy of 3cm [Dentith et al, 2014]

The free air correction is calculated and added to the gravity corrected up to this point. The expressions for the supported corrections are:

Where:

Hs: the station elevation (relative to the datum, positive up)in metres

L:  the latitude of the station

If you would like to provide alternate equation(s), define them in the file "Gravity_Free_Air.lst" located in the folder %USERPROFILE%\Documents\Geosoft\Desktop Applications \etc.

Each expression should be defined on one line and should consist of a unique name followed by the complete expression using the following syntax:

Where:

Input_Gravity: the variable containing the input gravity channel; designated by the variable $sGravity.

In the expression, you can also use the variables:

$rEm:        the conversion factor to convert the units of elevation to metres

$sElevation: the elevation channel

$sLatitude:  the latitude channel

For example, the syntax of the standard free air correction equation can be written as:

The last formula accounts for the non-line0.000000072124602\$rEm *\$sElevation) \$ rEm\$sElevation;{"}$arity of the free air anomaly as a function of both latitude and height above the geoid.

*The GX tool will search in the "...\Geosoft\Desktop Applications \gx" folder. The GX.Net tools, however, are embedded in the geogxnet.dll located in the "...\Geosoft\Desktop Applications \bin" folder. If running this GX interactively, bypassing the menu, first change the folder to point to the "bin" folder, then supply the GX.Net tool in the specified format.

References

[1] W. A. Heiskanen and H. Moritz, Physical Geodesy, (San Francisco: W. H. Freeman and Company, 1967).
[2] M. C. Dentith and S.T.Mudge, Geophysics for the Mineral Exploration Geoscientist, (Cambridge University Press, 2014), p. 103.
[3] R. J. Blakely, Potential Theory in Gravity and Magnetic Applications, (Cambridge: Cambridge University Press, 1995), p. 135.
[4] R. J. Blakely, Potential Theory in Gravity and Magnetic Applications, (Cambridge: Cambridge University Press, 1995), p. 136.
[5] R. E. Sheriff, Encyclopedic Dictionary of Exploration Geophysics, 2^nd ed., (Society of Exploration Geophysicists, 1984), p. 141.
[6] R. E. Sheriff, Encyclopedic Dictionary of Applied Geophysics, 4^thed., (Society of Exploration Geophysicists, 1991).