A Geodetic View on Isostatic Models

摘要

Before the background of more accurate and denser gravity data it is worthwhile to reassess geodetic isostasy. Currently, in geodesy isostatic models are primarily applied to gravity reduction as needed by geoid and gravity modeling. The selection of the isostatic model is based on four criteria: Isostatically reduced gravity anomalies should be (1) geophysically meaningful, (2) easy to compute, (3) small, smooth and therefore easy to interpolate and (4) the indirect effect, i.e. the change of potential and gravity due to isostatic mass replacement, should be small. In this study we analyze free air anomalies as well as isostatic anomalies based on the Airy-Heiskanen model and on the Pratt-Hayford model in regard to these criteria. Several facts suggest that free air anomalies are the most realistic type of isostatic anomalies. They reflect the actual isostatic compensation, are easy to compute and their indirect effect is negligibly small. However, they are not smooth due to the fact that local topographic loads are only partially compensated. Smoothness can be achieved by introducing either a mathematical low-pass filter or a hydrostatic isostatic model, such as the Airy-Heiskanen or the Pratt-Hayford model. In both cases the resulting isostatically reduced gravity anomalies fulfill all requirements. In order to improve the numerical efficiency, a new mathematical description of the Pratt-Hayford model is formulated. The level of smoothing with respect to free air anomalies is analyzed in global and regional contexts. It turns out that the mechanism of mass compensation in regions of large topographic loads is better described by the Airy-Heiskanen model, whereas the Pratt-Hayford model is more suitable for regions of deep ocean trenches.