Correcting for Latitude Dependent Changes

Correcting observations of the gravitational acceleration for latitude dependent variations arising from the earth's elliptical shape and rotation is relatively straight forward. By assuming the earth is elliptical with the appropriate demensions, is rotating at the appropriate rate, and contains no lateral variations in geologic structure (that is, contains no interesting geologic structure), we can derive a mathematical formulation for the earth's gravitational acceleration that depends only on the latitude of the observation. By subtracting the gravitational acceleration predicted by this mathematical formulation from the observed gravitational acceleration, we can effectively remove from the observed acceleration those portions related to the earth's shape and rotation.

The mathematical formula used to predict the components of the gravitational acceleration produced by the earth's shape and rotation is called the Geodetic Reference Formula of 1967. The predicted gravity is called the normal gravity.

How large is this correction to our observed gravitational acceleration? And, because we need to know the latitudes of our observation points to make this correction, how accurately do we need to know locations? At a latitude of 45 degrees, the gravitational acceleration varies approximately 0.81 mgals per kilometer. Thus, to achieve an accuracy of 0.01 mgals, we need to know the north-south location of our gravity stations to about 12 meters.

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