Residual terrain modelling (RTM) in terms of the cap-modified spectral technique: RTM from a new perspective

We present two novel approaches to residual terrain modelling (RTM), one of which is practical and the other rather theoretical. The first provides a solution to the harmonic correction issue and the high-frequency error of the spectral filter problem. As its key feature, cap-modified spectral gravity forward modelling is applied to deliver near-zone gravity effects induced by the reference (smooth) topography. Thanks to its spectral nature, the sought gravity can be evaluated at the problematic points inside the smooth topography by regularized downward continuation (solution for the harmonic correction problem), and, at the same time, it is band-limited in spherical harmonics (solution for the high-frequency error). A validation over two mountainous areas, Switzerland and Slovakia, reveals that this technique is at least comparable with two other common RTM variants (RMS agreement up to 0.1 mGal). Finally, we formulate the theoretical RTM concept, showing that the harmonic correction issue and the spectral filter problem are caused by filtering of the mass model in the topography domain. When properly filtering gravity effects in the gravity domain, that is, avoiding the concept of the reference topography, both problems disappear. Limitations of both RTM approaches include the possible divergence effect of spherical harmonic series on the Earth’s surface and a conceptual inconsistency between two involved types of spherical harmonic coefficients. Applications of this study could be found in the development of combined gravity models (the fill-in procedure) or in the spectral enhancement of spherical harmonic gravity models.