Physics
Scientific paper
Dec 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005agufmin23a1200w&link_type=abstract
American Geophysical Union, Fall Meeting 2005, abstract #IN23A-1200
Physics
1214 Geopotential Theory And Determination (0903), 1219 Gravity Anomalies And Earth Structure (0920, 7205, 7240), 1221 Lunar And Planetary Geodesy And Gravity (5417, 5450, 5714, 5744, 6019, 6250), 3255 Spectral Analysis (3205, 3280), 5417 Gravitational Fields (1221)
Scientific paper
The gravity and topography fields of the planets have long been used to infer properties of the crust and lithosphere. Because the relationship between the two is linear in the spectral domain, it is common to calculate their admittance and coherence spectra and to invert for parameters using a theoretical model. While the procedure for calculating observed admittance and coherence spectra is straightforward, a general descriptive model that employs as few assumptions as possible is currently lacking in both Cartesian and spherical coordinates. This paper addresses this deficiency. Two end member models currently exist, both of which assume that the lithosphere is deflected by loads applied to and below the surface. One model assumes that the applied surface and subsurface loads are perfectly in phase, whereas the model of Forsyth (1985) assumes that the two loads are uncorrelated. The two models have dramatically different predictions. As an example, the Bouguer coherence is exactly unity for the first model, but for the second, it declines from unity to zero with decreasing wavelength in a characteristic manner. If the assumed model is an accurate description of reality then both the theoretical admittance and coherence spectra should fit the observations. The shape of the coherence spectrum could help determine which of these two models is most appropriate for a given study region. I present a general lithospheric loading model in both spherical and Cartesian coordinates that contains the above two models as end members. The model assumes that loads applied to and beneath the surface are present and that the wavelength-dependent phase relationship between the two is arbitrary. In addition to the traditional parameters, the admittance and coherence spectra are found to depend upon a wavelength-dependent parameter, α_l or α(|k|), that is the average of the cosines of the phase differences of the applied loads. When α=±1, the loads are either perfectly in or out of phase, whereas when α=0, the loads are uncorrelated. If only the admittance were to be interpreted using a model such as Forsyth's, large errors in the inverted parameters could arise if the loads were in fact only partially correlated. Examples will be shown for the highlands of Mars, Venus, the Earth, and the Moon.
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