11 The Marine Geoid and Satellite Altimetry
187
large n, then the RMS amplitude of gravity anomalies can be used to infer the RMS
amplitude of geoid slopes.
In the absence of isostatic compensation (Watts, 2001) and upward continuation,
gravity is proportional to the product of topography and density contrast, to first
order (Parker, 1973). By “density contrast” is meant the change in density across
the topography, that is, from air to rock or sediment on land, and from water to rock
or sediment on the sea floor.
Because the density contrasts across land and seafloor topography are very different, one should not expect a clear relationship in the spherical harmonic spectra
of topography and gravity, as the spherical harmonic coefficients combine data on
land and at sea. Even so, I have plotted these in Fig. 11.2, using spherical harmonic
coefficients supplied in the EGM2008 model (Pavlis et al., 2008).
Fig. 11.2 Degree variance spectra of Earth topography (top), gravity anomaly (middle), and crossspectral coherency between these (bottom), derived from the EGM2008 gravity field model
187
large n, then the RMS amplitude of gravity anomalies can be used to infer the RMS
amplitude of geoid slopes.
In the absence of isostatic compensation (Watts, 2001) and upward continuation,
gravity is proportional to the product of topography and density contrast, to first
order (Parker, 1973). By “density contrast” is meant the change in density across
the topography, that is, from air to rock or sediment on land, and from water to rock
or sediment on the sea floor.
Because the density contrasts across land and seafloor topography are very different, one should not expect a clear relationship in the spherical harmonic spectra
of topography and gravity, as the spherical harmonic coefficients combine data on
land and at sea. Even so, I have plotted these in Fig. 11.2, using spherical harmonic
coefficients supplied in the EGM2008 model (Pavlis et al., 2008).
Fig. 11.2 Degree variance spectra of Earth topography (top), gravity anomaly (middle), and crossspectral coherency between these (bottom), derived from the EGM2008 gravity field model