Gravity Tides

Tides

Definition

Tidal Effect - Variations in gravity observations resulting from the attraction of the moon and sun and the distortion of the earth so produced*.

Superimposed on instrument drift is another temporally varying component of gravity. Unlike instrument drift, which results from the temporally varying characteristics of the gravimeter, this component represents real changes in the gravitational acceleration. Unfortunately, these are changes that do not relate to local geology and are hence a form of noise in our observations.

The sun and moon are massive bodies, and so contribute to the gravitational attraction at a point on the Earth's surface just as Earth materials do. The gravitational force is that which raises the ocean tides, so it is easy to see that it would vary with time, as the positions of the sun and moon vary with time as seen from a point on the Earth's surface. The magnitude of the solar or lunar contribution can be estimated using the simple formula to be discussed later. It is certainly comparable to the effect of crustal density variations. However, there is also a further effect included in tidal responses.

Just as the gravitational attraction of the sun and the moon distorts the shape of the ocean surface, it also distorts the shape of the earth. Because rocks yield to external forces much less readily than water, the amount the earth distorts under these external forces is far less than the amount the oceans distort. The size of the ocean tides, the name given to the distortion of the ocean caused by the sun and moon, is measured in terms of meters. The size of the solid earth tide, the name given to the distortion of the earth caused by the sun and moon, is measured in terms of centimeters.

This distortion of the solid earth produces measurable changes in the gravitational acceleration because as the shape of the earth changes, the distance of the gravimeter to the center of the earth changes (recall that gravitational acceleration is proportional to one over distance squared). The direct effect of the sun's and moon's gravity, and the distortion of the earth varies from location to location, but they can be large enough to produce variations in gravitational acceleration as large as 0.2 mGals. This effect would easily overwhelm the example gravity anomaly described previously.

An example of the variation in gravitational acceleration observed at one location (Tulsa, Oklahoma) is shown above**. These are raw observations that include both instrument drift (notice how there is a general trend in increasing gravitational acceleration with increasing time) and tides (the cyclic variation in gravity with a period of oscillation of about 12 hours). In this case the amplitude of the tidal variation is about 0.15 mGals, and the amplitude of the drift appears to be about 0.12 mGals over two days.

*Definition from the Encyclopedic Dictionary of Exploration Geophysics by R. E. Sheriff, published by the Society of Exploration Geophysics.

**Data are from: Wolf, A. Tidal Force Observations, Geophysics, V, 317-320, 1940.

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