Sensitivity of Long-Wavelength Dynamic Topography and Free-Air Gravity to Lateral Variations in Lower Mantle Viscosity

Abstract

Deflection of the Earth’s surface supported by mantle flow, known as dynamic topography, is associated with a free-air gravity anomaly because such topography is not isostatically compensated. Consequently, the ratio of the gravity anomaly to the dynamic topography, known as the admittance, has been used to estimate the amplitude of dynamic topography, which can be difficult to measure directly. However, at long wavelengths (e.g., spherical harmonic degrees 2 to 6) both dynamic topography and gravity anomalies, and thus the admittance, are sensitive to the mantle’s viscosity structure. Previous studies [e.g., Colli et al., 2016] demonstrate a reversal in sign of the free-air gravity anomaly resulting from lower mantle structures as the viscosity of the lower mantle is increased. This indicates potential complexity for inferring long-wavelength dynamic topography from observations of gravity anomalies, because the upper-lower mantle viscosity contrast is poorly constrained. We further investigated the relationship between dynamic topography and gravity anomalies by introducing lateral viscosity variations into a finite element model of global mantle flow. We find that the gravity anomaly above lower mantle density heterogeneity can change dramatically as we begin to introduce different models for lateral viscosity variations into the upper and lower mantle viscosity fields. In such models we find that the sign of the admittance varies laterally, with the horizontal gradients in mantle viscosity perturbing mantle flow patterns in ways that produce large changes gravity anomalies and smaller changes in dynamic topography. A spatially-varying admittance will greatly complicate estimation of dynamic topography from observed gravity, and may help to explain mismatches between observations of dynamic topography and predictions made using global mantle flow models. On the other hand, the reconciliation of such mismatches may help to constrain viscosity heterogeneity in the lower mantle. Colli, L., S. Ghelichkhan, and H. P. Bunge (2016), On the ratio of dynamic topography and gravity anomalies in a dynamic Earth, Geophysical Research Letters, 43(6), 2510-2516, doi:10.1002/2016GL067929.