Density interface topography recovered by inversion of satellite gravity gradiometry observations

Abstract

A radial integration of spherical mass elements (i.e. tesseroids) is presented for evaluating the six components of the second-order gravity gradient (i.e. second derivatives of the Newtonian mass integral for the gravitational potential) created by an uneven spherical topography consisting of juxtaposed vertical prisms. The method uses Legendre polynomial series and takes elastic compensation of the topography by the Earth’s surface into account. The speed of computation of the polynomial series increases logically with the observing altitude from the source of anomaly. Such a forward modelling can be easily applied for reduction of observed gravity gradient anomalies by the effects of any spherical interface of density. An iterative least-squares inversion of measured gravity gradient coefficients is also proposed to estimate a regional set of juxtaposed topographic heights. Several tests of recovery have been made by considering simulated gradients created by idealistic conical and irregular Great Meteor seamount topographies, and for varying satellite altitudes and testing different levels of uncertainty. In the case of gravity gradients measured at a GOCE-type altitude of \(\sim \)300 km, the search converges down to a stable but smooth topography after 10–15 iterations, while the final root-mean-square error is \(\sim \)100 m that represents only 2 % of the seamount amplitude. This recovery error decreases with the altitude of the gravity gradient observations by revealing more topographic details in the region of survey.