Other
Scientific paper
Dec 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006agufm.t51f..01t&link_type=abstract
American Geophysical Union, Fall Meeting 2006, abstract #T51F-01
Other
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, 1240 Satellite Geodesy: Results (6929, 7215, 7230, 7240)
Scientific paper
Bill Haxby made many significant contributions during his career. But I believe his discovery as a graduate student of a simple relation between geoid anomalies and depth of compensation was the most significant (W.F. Haxby and D.L. Turcotte, On isostatic geoid anomalies, J. Geophys. Res. 83, 5473-5478, 1978). The Bougher gravity formula relates the local gravity anomaly Δ g to the height h of the local uncompensated topography: Δ g=2π Gρ_c h, where ρc is the crustal density and G is the universal gravitational constant. Bill discovered a similar relationship between the local geoid anomaly Δ N and the height h of the local compensated topography: Δ N=-2π Gρ_c h w_c /g, where wc is the depth of compensation and g is the local surface gravity. At the time Bill made this discovery SEASAT altimetry data had just become available. This data of sea surface elevation provided a direct measurement of the geoid anomalies over the oceans. Bill utilized this data and his formula to constrain lithospheric structures over ocean ridges, continental margins, and lithospheric swells (i.e. the Hawaiian swell). Subsequently the constraint has been applied to other structures such as transform faults and large planetary impact structures. It would appear highly appropriate to refer to Bill's formula as the Haxby geoid formula, also to refer to correlations between geoid and topography as Haxby diagrams. The Bougher gravity formula shows that the gravity anomaly is proportional to excess mass in an uncompensated lithosphere. For compensated topography this mass excess is zero. The Haxby geoid formula shows that the geoid anomaly is proportional to the dipole distribution of mass in the lithosphere. Subsequently it was shown that the force required to maintain isostatic topography is also proportional to this dipole distribution of mass and therefore to the geoid anomaly.
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