Gravity/Topography Transfer Function and Isostatic Geoid Anomalies

This lecture combines thin-elastic plate flexure theory with the solution to Poisson's equation to develop a linear relationship between gravity and topography. This relationship can be used in a variety of ways. (1) If both the topography and gravity are measured over an area that is several times greater then the flexural wavelength, then the gravity/topography relationship (in the wavenumber domain) can be used to estimate the elastic thickness of the lithosphere and/or the crustal thickness. There are many good references on this topic including Dorman and Lewis [1972], McKenzie and Bowin, [1976]; Banks et al., [1977]; Watts, [1978]; McNutt, [1979]. (2) At wavelengths greater than the flexural wavelength where features are isostaticallycompensated, the geoid/topography ratio can be used to estimate the depth of compensation of crustal plateaus and the depth of compensation of hot-spot swells [Haxby and Turcotte, 1978]. (3) If the gravity field is known over a large area but there is rather sparse ship-track coverage, the topography/gravity transfer function can be used to interpolate the seafloor depth among the sparse ship soundings [Smith and Sandwell, 1994].