Solution to the spectral filter problem of residual terrain modelling (RTM)

In physical geodesy, the residual terrain modelling (RTM) technique is frequently used for highfrequency gravity forward modelling. In the RTM technique, a detailed elevation model is high-pass filtered in the topography domain, which is not equivalent to filtering in the gravity domain. This in-equivalence, denoted as spectral filter problem of the RTM technique, gives rise to two imperfections (errors). The first imperfection are unwanted low-frequency (LF) gravity signals, and the second imperfection are missing high-frequency (HF) signals in the forward-modelled RTM gravity signal. This paper presents new solutions to the RTM spectral filter problem. Our solu1 Institute for Astronomical and Physical Geodesy · Institute for Advanced Study, Technische Universität München Arcisstrasse 21, D-80333 München Tel.: +49-(0)89-289-23190 Fax: +49-(0)89-289-23178 E-mail: [email protected],[email protected] 2 Department of Theoretical Geodesy, Slovak University of Technology in Bratislava Radlinského 11, 81005 Bratislava, Slovakia E-mail: [email protected] 3 SGT Inc. Greenbelt, USA tions are based on explicit modelling of the two imperfections via corrections. The HF correction is computed using spectral-domain gravity forward modelling that delivers the HF gravity signal generated by the long-wavelength RTM reference topography. The LF correction is obtained from pre-computed global RTM gravity grids that are low-pass filtered using surface or solid spherical harmonics. A numerical case study reveals maximum absolute signal strengths of ∼ 44 mGal (0.5 mGal RMS) for the HF correction and ∼ 33 mGal (0.6 mGal RMS) for the LF correction w.r.t. a degree-2160 reference topography within the data coverage of the SRTM topography model (56◦S ≤ φ ≤ 60◦N). Application of the LF and HF corrections to precomputed global gravity models (here the GGMplus gravity maps) demonstrates the efficiency of the new corrections over topographically rugged terrain. Over Switzerland, consideration of the HF and LF corrections reduced the RMS of the residuals between GGMplus and groundtruth gravity from 4.41 to 3.27 mGal, which translates into ∼ 26 % improvement. Over a second test area (Canada), our corrections reduced the RMS of the residuals between GGMplus and ground-truth gravity 2 Moritz Rexer1 et al. from 5.65 to 5.30 mGal (∼ 6 % improvement). Particularly over Switzerland, geophysical signals (associated,e.g., with valley fillings) were found to stand out more clearly in the RTM-reduced gravity measurements when the HF and LF correction are taken into account. In summary, the new RTM filter corrections can be easily computed and applied to improve the spectral filter characteristics of the popular RTM approach. Benefits are expected, e.g., in the context of the development of future ultra-high resolution global gravity models, smoothing of observed gravity data in mountainous terrain and geophysical interpretations of RTM-reduced gravity measurements.