Eötvös Correction

Use the Moving Platform Gravity > Corrections by Steps > Eötvös Correction menu option (geogxnet.dll(Geosoft.GX.Gravity.EotvosCorrection;Run)*) to calculate the Eötvös correction.

Eötvös Correction dialog options

Eötvös equation	Select one of the three variations of the Eötvös correction. The difference between them is in the order of 0.2 milligals (mGal): Exact Glicken Harlan Correction equations are detailed in the Application Notes. Script Parameter: EOTVOS_CORRECTION.EQUATION [0 - Exact (default); 1 - Glicken; 2 - Harlan]
Time channel	Select the time channel from the drop-down list. If the current database includes a "Time" channel, it will be automatically selected. Script Parameter: EOTVOS_CORRECTION.TIME
Units	Specify whether the selected time channel is in hours or seconds. The Eötvös equation requires time in hours. If your time is in seconds, it will be converted automatically. Script Parameter: EOTVOS_CORRECTION.UNITS [0 - Hours; 1 - Seconds]
Latitude channel	Select the latitude channel from the drop-down list. If a channel named "Latitude" exists in the database, it will be selected by default. Script Parameter: EOTVOS_CORRECTION.LATITUDE
Heading channel	Provide the heading channel name. If it exists, it will be used; otherwise, it will be generated and saved to the database. Script Parameter: EOTVOS_CORRECTION.HEADING
Velocity channel	Provide the velocity channel name. If it exists, it will be used; otherwise, it will be generated and saved in units of knots. Script Parameter: EOTVOS_CORRECTION.VELOCITY
Altitude channel	For airborne surveys, select the channel containing altitude data. The Eötvös correction requires elevation relative to the ellipsoid. GPS elevations are typically referenced to the ellipsoid; however, if ellipsoidal elevation is not available, elevation relative to the geoid can be used as a fallback. The error introduced by substituting geoid-based elevation for ellipsoidal elevation is negligible. Script Parameter: EOTVOS_CORRECTION.ALTITUDE
Output Eötvös channel	Specify the name of the output channel for the Eötvös correction. Script Parameter: EOTVOS_CORRECTION.OUTPUT

Application Notes

Earth’s rotation produces an outward centrifugal acceleration. Objects moving across the rotating Earth experience an additional acceleration related to their east–west velocity. This effect is strongest at the equator and decreases with latitude.

• A body moving east (in the same direction as Earth’s rotation) experiences an increase in centrifugal acceleration.

• A body moving west experiences a decrease in centrifugal acceleration.

The vertical component of this acceleration, along with a small acceleration related to the motion of the curved Earth, is known as the Eötvös effect. This effect can reach up to 30 milligals (mGal) and must be accounted for in moving platform surveys.

Definition

The Eötvös effect is defined as:

The first term corresponds to the Eötvös effect, while the second term is a refinement with much smaller amplitude.

To account for Earth’s ellipsoidal shape, R can be expanded in terms of Earth’s major axis, flattening, latitude, and observation height, yielding the Exact equation below. Two other published variations of the Eötvös effect are also provided:

[Exact]:

[Harlan, 1968]¹:

[Glicken, 1962]²:

Where:

E	Eötvös correction (milligals)
R	Earth’s radius at latitude φ
V	Velocity (knots)
Ws	Angular velocity of Earth’s rotation = 7.2921158533 x 10-5 rad/s
a	Earth's equatorial radius (semi-major axis)
b	Earth's polar radius (semi-minor axis)
e	Earth’s eccentricity = 0.0818191908426
f	Earth's flattening = (a - b) / a
h	Observation height (above the geoid)
ra	Earth’s major axis = 6378137.0 m
rb	Earth’s minor axis = 6356752.3141 m
νe and νn	Velocities in the easting & northing directions, derived from heading and velocity channels
α	Heading (direction of movement of the vehicle, measured clockwise from true north)
ε	Earth's flattening correction toward the poles = (ra - rb) / ra
φ	Latitude of the vehicle

References