Cap integration in spectral gravity forward modelling: near- and far-zone gravity effects via Molodensky’s truncation coefficients

SUMMARY High resolution and accurate digital terrain models (DTMs) are frequently used as input data sets to define the topographic masses in gravity forward modelling, for example, for terrain corrections in the context of regional gravity modelling. However, over vegetated areas such as forests and scrublands, the radar- and image-based digital elevation models (DEMs) may contain a tree bias, and therefore do not represent the bare-ground surface. The presence of vegetation-induced signals in DEMs, denoted here the tree-canopy effect, will introduce errors in the gravity forward modelling. In this study, the role of the tree-canopy effect in gravity forward modelling calculations is numerically investigated. First, spectral forward modelling techniques were applied to analyse a global tree-canopy bias model with a horizontal resolution of 1 km x 1 km and to quantify its effect on global gravity forward modelling results. We demonstrate that tree-canopy signals in the DEM produce a positive bias in the topographic gravitational field over vegetated areas, with values ranging from 0 to ∼2.7 mGal for gravity disturbances. Second, the role of the tree-canopy effect in high-frequency gravity forward modelling is studied using well-known residual terrain modelling (RTM) techniques. As DEM data sets, we used the 3″ SRTM (Shuttle Radar Topography Mission Digital 9 m Elevation Database) V4.1 (containing vegetation biases) and the 3″ MERIT-DEM (Multi-Error-Removed Improved-Terrain Digital elevation model) as a representation of the bare-ground elevations. Using Tasmania and the Amazon rainforest regions as test areas with significant tree-canopy signals we show that the tree-height effect on RTM calculations is of high-frequency nature, with rather small signals which reach in extreme cases amplitudes of ∼1–2 mGal occurring at forest boundaries. Third, using ground gravity observations, validation experiments were performed over the Australian Alps, Tasmania and the Canadian Rocky Mountains. All validation experiments show that the bare-ground elevation model MERIT-DEM performs better than SRTM V4.1 in terms of reduction of the discrepancies between modelled and observed gravity values. As a general conclusion, bare-ground DEM models should be preferred in any gravity forward modelling application to avoid or reduce the tree-canopy effect.

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Cap integration in spectral gravity forward modelling up to the full gravity tensor

Journal of Geodesy ◽

10.1007/s00190-019-01277-3 ◽

2019 ◽

Vol 93 (9) ◽

pp. 1707-1737 ◽

Cited By ~ 2

Author(s):

Blažej Bucha ◽

Christian Hirt ◽

Michael Kuhn

Keyword(s):

Forward Modelling ◽

Gravity Forward Modelling

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TGF: A New MATLAB-based Software for Terrain-related Gravity Field Calculations

Remote Sensing ◽

10.3390/rs12071063 ◽

2020 ◽

Vol 12 (7) ◽

pp. 1063

Author(s):

Meng Yang ◽

Christian Hirt ◽

Roland Pail

Keyword(s):

Density Distribution ◽

Gravity Field ◽

Mass Density ◽

Computation Time ◽

Spherical Approximation ◽

Constant Density ◽

Forward Modelling ◽

Gravity Effects ◽

Residual Terrain Modelling ◽

Elevation Model

With knowledge of geometry and density-distribution of topography, the residual terrain modelling (RTM) technique has been broadly applied in geodesy and geophysics for the determination of the high-frequency gravity field signals. Depending on the size of investigation areas, challenges in computational efficiency are encountered when using an ultra-high-resolution digital elevation model (DEM) in the Newtonian integration. For efficient and accurate gravity forward modelling in the spatial domain, we developed a new MATLAB-based program called, terrain gravity field (TGF). Our new software is capable of calculating the gravity field generated by an arbitrary topographic mass-density distribution. Depending on the attenuation character of gravity field with distance, the adaptive algorithm divides the integration masses into four zones, and adaptively combines four types of geometries (i.e., polyhedron, prism, tesseroid and point-mass) and DEMs with different spatial resolutions. Compared to some publicly available algorithms depending on one type of geometric approximation, this enables accurate modelling of gravity field and greatly reduces the computation time. Besides, the TGF software allows to calculate ten independent gravity field functionals, supports two types of density inputs (constant density value and digital density map), and considers the curvature of the Earth by involving spherical approximation and ellipsoidal approximation. Further to this, the TGF software is also capable of delivering the gravity field of full-scale topographic gravity field implied by masses between the Earth’s surface and mean sea level. In this contribution, the TGF software is introduced to the geoscience community and its capabilities are explained. Results from internal and external numerical validation experiments of TGF confirmed its accuracy at the sub-mGal level. Based on TGF, the trade-off between accuracy and efficiency, values for the spatial resolution and extension of topography models are recommended. The TGF software has been extensively tested and recently been applied in the SRTM2gravity project to convert the global 3” SRTM topography to implied gravity effects at 28 billion computation points. This confirms the capability of TGF for dealing with large datasets. Together with this paper, the TGF software will be released in the public domain for free use in geodetic and geophysical forward modelling computations.

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