Geoid height versus topography for a plume model of the Hawaiian swell

Abstract

We use a three-dimensional variable-viscosity convection model of a stationary plume beneath a drifting lithosphere to study the factors that control the geoid-to-topography ratio (GTR) of the Hawaiian swell. The rate of melting in the plume is predicted using a batch melting parameterization, and the melt is assumed to migrate to the surface where it builds a volcanic edifice, equivalent to the Hawaiian island chain. Viscous stresses, elastic deformation of the lithosphere and (optionally) the volcanic material deposited on the ocean floor are included in the calculation of surface topography and the corresponding geoid. The derivation of the GTR from the model imitates methods that have previously been used to estimate the ‘observed’ GTR for the Hawaiian swell. The first method we use here is that of Marks and Sandwell [J. Geophys. Res. 96 (1991) 8045–8055], which applies bandpass filters to retain only wavelengths from 400 to 4000 km as most characteristic of the swell topography and geoid, and the GTR is estimated from the slope of the regression line of geoid versus topography. Another group of methods analyzes the data along profiles drawn across the hotspot swell and eliminates the unwanted signals, e.g. the volcanic islands and the flexural moat around them, by cutting out parts of the sections. The GTR is then calculated from curves which best fit the topography and geoid profiles on the swell flanks only. In our plume model, when the effects of the volcanic surface loading are included, Marks and Sandwell’s method yields 4.4 m/km for the GTR, while profile-fitting on the swell flanks gives 7–8.5 m/km. Ignoring the volcanic load leads to 7–8 m/km in all processing methods. The observed GTR for the Hawaiian swell has been reported to lie between 4 and 5 m/km. Analysis of the data processing methods shows that the applied bandpass filters cannot completely remove the signal due to the volcanic edifice and lithospheric flexure and this causes apparent GTRs around 4 m/km. The ‘pure’ swell model containing no volcanic load on the surface demonstrates that the Hawaiian swell may have a proper GTR near 7 m/km.