A framework for layer-based spectral forward-modelling of Earth’s gravitational field with respect to a reference sphere or a reference ellipsoid
20/09/2016 | 09:15 | Session 2: Model Development
Author(s): Moritz Rexer, Christian Hirt and Sten Claessens
Moritz Rexer, Christian Hirt and Sten Claessens
Spectral forward modelling of Earth’s gravitational potential is a classical problem in geophysics and physical geodesy. Conventionally it is done in spherical approximation along with rock-equivalent (single-density) mass models, changing the geometry of the masses. In the last decade layer-based (multi-density) forward modelling has been proposed for the spherical approximation with layers referenced to a sphere. This concept can likewise be applied to a recently developed forward modelling approach that uses an oblate ellipsoid as reference body for the layers, instead. With the ellipsoid as a reference spectral forward modelling becomes compatible with various global geopotential models (GGMs) available via IAG’s ICGEM.
We present the theoretical framework for and solutions to spherical-harmonic forward modelling of volumetric layers of constant density. We recapitulate the spherical case and provide new expressions for the ellipsoidal case. The methods yield solutions to what we refer to as Spherical Topographic Potential (STP) and Ellipsoidal Topographic Potential (ETP). Both – STP and ETP – can be computed efficiently using binominal series expansions whose convergence characteristics are studied. ETP and STP show characteristic differences in the spectral domain and agree quite well in the space domain when evaluated w.r.t. the correct reference body.
For a proof of concept we use layer-boundaries from the Earth2014 topography data set to explicitly model the potential of layers for solid Earth, oceans, ice-sheets and lakes at 10km-resolution. We validate the combined potential of all layers against satellite observations and ground-truth data over Antarctica. This allows us to quantify the benefit of layer-based modelling as opposed to single-density modelling. In the same way we can show the improvements of introducing the ellipsoidal reference in forward modelling. While the ETP is preferable for applications that require consistency with GGMs or highest accuracy, the somewhat simpler STP is deemed to be sufficient for most geophysical applications where the spherical level of approximation appears to be the norm.