Comparisons of Global Topographic/Isostatic Models To the Earth's Observed Gravity Field
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Date
1988-03
Authors
Rummel, R. (Reiner), 1945-
Rapp, Richard H.
Sünkel, Hans
Tscherning, Carl
Journal Title
Journal ISSN
Volume Title
Publisher
Ohio State University. Division of Geodetic Science
Abstract
The earth's gravitational potential, as described by a spherical harmonic expansion to degree 180, has been compared to the potential implied by the topography and its isostatic compensation using five different hypothesis. Initially, series expressions for the Airy/Heiskanen topographic/isostatic model were developed to the third order in terms of (h/R) where h is equivalent rock topography and R is a mean earth radius. Using actual topographic developments for the earth, we found the second and third terms of the expansion contributed (on average) 30% and 3%, respectively, of the first term, of the expansion. With these new equations it is possible to compute depths (D) of compensation, by degree, using three different criteria: I) the power in the actual field at a specified degree should be the same as implied by the Airy/Heiskanen model; II) the topographic isostatic reduced potential should show minimum correlation with the earth's topography; III) the norm of the residual potential should be a minimum. The results show that the average (over all degrees) depth implied by criterion I is 60 km while it is about 33 km for criteria II and III with smaller compensation depths at the higher degrees. Another model examined was related to the Vening-Meinesz regional hypothesis implemented in the spectral domain. The fifth model tested took D to be a constant of 30 km at all degrees. We have compared these model fields with the actual field in terms of anomaly, geoid undulation and percentage differences, as well as with correlation coefficients and anomaly maps in the Caribbean/South America region. The differences between all models is small with the exception of the model defined by criterion I is used where larger differences are seen. For example, the average percentage differences between the OSU81 potential model and the five models outlined above, from degrees 15 through 180 is 87.2(I), 80.5(II), 79.8(III), 80.l(VM), 80.5(D=30km). Finally oceanic and continental response functions are derived from the global data sets and comparisons made to locally determined values.