Static deformations and gravity changes at the Earth's surface due to atmospheric loading

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W. Rabbel
J. Zschau


Deformations and gravity changes at the Earth's surface due to regional and global air pressure variations are estimated for a radially stratified Earth. The results are as follows:
- Vertical displacements of seasonal character have maximum amplitudes of ±0.5 cm. (Anti-)Cyclones can cause vertical displacements of up to ±2.5 cm.
- Horizontal displacements have amplitudes less than ±2.5 mm.
- Horizontal principal strains may have amplitudes up to 10-8. They reduce to about ±1.5✻10-9 for seasonal changes in the air pressure distribution.
- The total gravity perturbation consisting of the Newtonian attraction of air masses and of self-gravitation due to the elastic deformation may go up to ±20 μgal in the case of (anti-)cyclones, and ±3 μgal in the case of seasonal air pressure changes.
- The total tilt due to seasonal air pressure variations can be as high as ±1.5 mseca. For passing (anti-)cyclones this value may go up to ±10 mseca.

All the above values have to be modified in the direct vicinity of coastlines. The modification is only slight for the displacements and the secondary gravity effect, but it is important for the other components. There, the necessary modification may amount to several hundred percent depending on the type of deformation component and on the distance to the coastline. Precise air pressure corrections of radial displacements and gravity changes cannot be achieved by using a single regression coefficient. Either the characteristic wavelengths of the pressure distribution have to be taken into account or the following two-coefficient correction equations have to be used:

  Radial displacement:      = -0.90 - 0.35 (p - )
  Primary gravity:               gp =  0.36 + 0.41 (p - )
  Secondary gravity:          gs = -0,17 - 0.08 (p - )
  Total gravity:                    gp + gs
with u = radial displacement in mm, gp, gs, g = primary, secondary and total gravity, respectively, in μgal, p = local pressure variation in mbar, = average of the pressure variation in a surrounding area of 2,000 km (in mbar) and   the same average, except for setting the pressure values equal to zero over ocean areas. These corrections have been tested for seasonal air pressure variations and they have proved to be highly precise. The average errors are less than 0.5 mm, 0.1 μgal, 0.1 μgal and 0.2 μgal for the radial displacements, the primary, secondary and total gravity changes, respectively. The maximum errors are less than 1 mm in the case of the radial displacements, 0.3 μgal and 0.2 μgal for the primary and secondary gravity changes, respectively, and 0.4 μgal for the total gravity changes. Due to a small, spatially constant error term these values apply strictly only to spatial differences of the above deformation components. The differences, however, can be taken between any two points on the Earth's surface.

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Rabbel, W., & Zschau, J. (1984). Static deformations and gravity changes at the Earth’s surface due to atmospheric loading. Journal of Geophysics, 56(1), 81-99. Retrieved from
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