Ultra-highresolution topographic modelling of gravitational fields
Final Report Abstract
The short-wavelength constituents of the gravitational field are closely related to the topographic masses, so can be modelled from topographic data. Topographic gravity modelling techniques play a key role in geodesy and related disciplines, e.g., for the reduction, interpretation, densification and refinement of observed gravity information. In the context of ultra-high resolution gravity modelling, e.g., with km-resolution or better, a critical assessment of topographic modelling methods is required. This research programme has investigated topographic modelling techniques with ultra-high resolution. In the first part of the project, focus was placed on spectral domain techniques, whereby the topographic potential is computed via spherical harmonic series expansions. A number of experimental topographic potential models have been developed e.g., to degrees 2160, 5400, 10800 and higher for Earth and to degree 2160 for the Moon. The detail study of the models has demonstrated that the effect of series divergence is uncritical in Earth gravity field modelling to degree 2160, but comes into effect at higher resolution levels, e.g., over deep ocean trenches. In case of the Moon, series divergence is a limited factor when, e.g., models with a resolution of degree 720 or finer are used at low-lying surface points, e.g., inside deep craters. In the second part of the project, the widely used residual terrain modelling (RTM) technique has been investigated and improved. We have rectified the “RTM filter problem” (i.e., inconsistency between filtering in the topography and gravity domains) by developing filter corrections using spherical harmonic techniques. A testing environment was developed to investigate approximation errors in classical RTM techniques, and approximation errors associated with the so-called harmonic correction were characterized. A new RTM baseline technique – based on the combination of global numerical integration and spectral-domain forward modelling – was introduced that avoids the harmonic correction entirely. In the third part of the project, the improved spectral-domain techniques and RTM methods have been applied for the first-ever transformation of the Earth´s global topography at 90 m resolution to accurate topographic gravity effects. This computationally demanding task (about 1,000,000 CPU-hours) was solved through parallelization and advanced computational resources by the Leibniz Rechenzentrum (Munich). The result of this computational exercise is a novel data set (named SRTM2gravity) comprising full-scale and short-scale gravity effects at ~28 billion points covering Earth’s land topography The SRTM2gravity product is expected to be useful in geodetic applications (e.g., as input for future ultra-high resolution gravity fields or improved validation of future geopotential models such as EGM2020). In geophysics, SRTM2gravity can be used as modern gravimetric terrain correction around the globe, reducing the need for tedious computations of terrain effects. The SRTM2gravity data set has been released to the public for free use in science, teaching and by industry. In summary, this research programme has improved the theoretical and practical framework for topographic gravity modelling at ultra-high resolution, and delivered practically usable gravity products into the public domain for free use. The insights gained by this project are expected to be useful, e.g., for further study of topographic modelling techniques in Earth applications (e.g., forward modelling of ice and bathymetric signals) and in planetary sciences (e.g., high-resolution gravity modelling for Moon and Mars).
Publications
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(2019) A numerical study of residual terrain modelling (RTM) techniques and the harmonic correction using ultra-high-degree spectral gravity modelling. J Geod (Journal of Geodesy) 93 (9) 1469–1486
Hirt, Christian; Bucha, Blažej; Yang, Meng; Kuhn, Michael
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(2016) Topographic gravity modelling for global Bouguer maps to degree 2,160: Validation of spectral and spatial domain forward modelling techniques at the 10 microgal level, Journal of Geophysical Research – Solid Earth 121(9),6846–6862
Hirt, C., E. Reußner, M. Rexer und M. Kuhn
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(2016) Topographische Modellierung des Gravitationsfeldes. In: Handbuch der Geodäsie (Ed. W. Freeden und R. Rummel), Springer, Berlin, New York. ISBN 978-3-662-46900-2, doi: 10.1007/978-3-662-46900-2_9-1
Hirt, C.
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(2016), Topographic gravitational potential up to second-order derivatives: an examination of approximation errors caused by rock-equivalent topography (RET), Journal of Geodesy 90(9), 883-902
Kuhn, M. und C. Hirt
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(2017), Convergence and divergence in spherical harmonic series of the gravitational field generated by high-resolution planetary topography – a case study for the Moon, Journal of Geophysical Research – Planets, 122
Hirt, C. und M. Kuhn
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(2017), The relation between degree-2160 spectral models of Earth’s gravitational and topographic potential - a guide on global correlation measures and their dependency on approximation effects, Journal of Geodesy 91(10), 1179-1205
Hirt, C., M. Rexer, S. Claessens und R. Rummel
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(2018), Artefact detection in global digital elevation models (DEMs): The Maximum Slope Approach and its application for complete screening of the SRTM v4.1 and MERIT DEMs, Remote Sensing of Environment 207, 27-41
Hirt, C.
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(2018), Divergence-free spherical harmonic gravity field modelling based on the Runge–Krarup theorem: a case study for the Moon, Journal of Geodesy
Bucha, B., C. Hirt und M. Kuhn
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(2018), Solution to the spectral filter problem of residual terrain modelling (RTM), Journal of Geodesy 92(6), 675-690
Rexer, M., C. Hirt, B. Bucha und S. Holmes
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(2019), SRTM2gravity: an ultrahigh resolution global model of gravimetric terrain corrections, Geophysical Research Letters 46
Hirt, C., M. Yang, M. Kuhn, B. Bucha, A. Kurzmann and R. Pail
