On the pitfalls of Airy isostasy and the isostatic gravity anomaly in general

Abstract

Isostatic gravity anomalies provide a measure of the Earth's gravity field free from the gravitational attractions of the topography and its isostatic compensation, most commonly represented by a variation in the depth of a compensating density contrast, for example the Moho. They are used by both geodesists and geophysicists alike, though often for different purposes. Unfortunately though, the effect of subsurface loading on the lithosphere renders transfer function (admittance) methods unusable when surface and subsurface loads coexist. Where they exist, subsurface loads are often expressed in the Bouguer anomaly but not in the topography, and it is shown here that this phase disconnect cannot be faithfully represented by either realor complex-valued analytic admittance functions. Additionally, many studies that employ the isostatic anomaly ignore the effects of the flexural rigidity of the lithosphere, most often represented as an effective elastic thickness (Te), and assume only Airy isostasy, i.e. surface loading of a plate with zero elastic thickness. The consequences of such an omission are studied here, finding that failure to account for flexural rigidity and subsurface loading can result in (1) over- or underestimates of both inverted Moho depths and dynamic topography amplitude, and (2) underestimates of the size of topographic load that can be supported by the plate without flexure. An example of the latter is shown over Europe. Finally, it is demonstrated how low values of the isostatic anomaly variance can actually be biased by these anomalies having low power at the long wavelengths while still possessing high power at middle to short wavelengths, compared to the corresponding Bouguer anomaly power spectrum. This will influence the choice of best-fitting isostatic model if the model is chosen by minimization of the isostatic anomaly standard deviation.