An analysis of local changes in gravity due to deformation

Summary

Deformation causes changes in gravity even though the measuring station is fixed relative to the center of the earth and the total mass in the vicinity of the station does not change. Deformation has two effects: the density at a point changes in response to changes in local stresses and the point itself moves relative to the station. The general expression derived here shows that the gravity change depends on the uplift immediately beneath the station and the deformation of cavities at depth — cracks, pores, magma reservoirs, etc. The approximation is made that density is uniform except for cavities, but no assumptions about the constitutive behavior of the medium are necessary.

The gravity change studied here shows interesting analogies with the gravity effect due to buried bodies with anomalous density. For example, I find that the net volume change due to deformation can be found by integrating the gravity anomaly over the earth's surface, in analogy with the calculations for excess mass.

The theory is especially useful when both deformation and net fluid flow into or out of the system occurs. The results are applied to uplift and gravity changes observed during the great Alaskan earthquake, the Matsushiro earthquake swarm, and a draw-down operation at the Wairakei geothermal field. The data at Wairakei are used to estimate the net amount of water taken from the aquifer. The data at Matsushiro is not sufficiently precise to discriminate between the various mechanisms that have been proposed, but the Alaskan earthquake data suggest that no dilatancy or fluid flow occurred between the survey in 1962 and the resurvey in 1964 just after the event.