Open AccessEffects of Isostasy On Large‐Scale Geoid Signal‐I. Geoid Anomaly Over an Earth‐Like Planet
Author(s) -
Hofstetter A.,
Lister C. R. B.
Publication year - 1989
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1989.tb00485.x
Subject(s) - geoid , geology , lithosphere , isostasy , equipotential surface , undulation of the geoid , geodesy , geophysics , asthenosphere , gravity anomaly , figure of the earth , free air gravity anomaly , planet , mantle (geology) , bouguer anomaly , seismology , geometry , tectonics , physics , paleontology , mathematics , oil field , astrophysics , measured depth
Summary The geoid anomaly due to lithospheric changes, such as cooling, is a second‐order quantity which is highly sensitive to the definition of isostasy. Many different terms must be summed over a range of depths, so a simplified test planet is required to make sure the algorithm is working correctly. Our model planet consists of an ocean underlain by lithosphere and asthenosphere; there are two ocean ridges along 0° and 180° longitudes, and two trenches along 90° and 270° longitudes. the oceanic plates are moving away from the ridge with a velocity of 5 cm yr ‐1 at the equator. Pressure is assumed constant at the compensation depth, which is itself an equipotential surface. We use the method of rings, in which a set of 18 rings about an arbitrary pole (observation point) cover the whole earth. This method allows the anomaly source depth to be taken into account. Changes in the equipotential surface height both above and below any ring induce mass changes due to infilling with sea‐water and mantle material, respectively. These mass changes cause further changes in the geoidal height over and below all the other rings, and the problem renders itself into a set of linear simultaneous equations. the final geoid is a product of seven second‐order effects. the direct dipole effect due to the density differences in the cooling lithosphere (Lister 1982) produces a geoidal elevation of ≤11 m and ≥−11 m over the ridge and the trench, respectively. the direct mass effect (Vening Meinesz 1946), due to the fact that a column on a sphere is pie‐shaped (and not straight sided as on a flat earth model), produces a geoidal elevation of ≤12 m and ≥−11 m over the ridge and the trench, respectively. the final geoidal elevation, due to the direct and indirect effects, is ≤26 m and ≥−26 m over the ridge and the trench, respectively.