Preprints
https://doi.org/10.5194/se-2021-145
https://doi.org/10.5194/se-2021-145

  09 Dec 2021

09 Dec 2021

Review status: this preprint is currently under review for the journal SE.

Benchmark forward gravity schemes: the gravity field of a realistic lithosphere model WINTERC-G

Bart Root1,5, Josef Sebera2,3, Wolfgang Szwillus3, Cedric Thieulot4, Zdenek Martinec5, and Javier Fullea6,5 Bart Root et al.
  • 1Delft University of Technology, Department of Space Engineering, Delft, the Netherlands
  • 2Astronomical Institute of the Czech Academy of Sciences, Prague, Czech Republic
  • 3Christian Albrechts University, Department of Geosciences, Kiel, Germany
  • 4Utrecht University, , Utrecht, the Netherlands
  • 5Dublin Insitute for Advanced Studies, School of Cosmic Physics, Dublin, Ireland
  • 6Universidad Complutense de Madrid (UCM), Physics of the Earth and Astrophysics department, Madrid, Spain

Abstract. Several alternative gravity forward modelling methodologies and associated numerical codes with their own advantages and limitations are available for the Solid Earth community. With the upcoming state-of-the-art lithosphere density models and accurate global gravity field data sets it is vital to understand the opportunities and limitations of the various approaches. In this paper, we discuss the four widely used techniques: global spherical harmonics (GSH), tesseroid integration (TESS), triangle integration (TRI), and hexahedral integration (HEX). A constant density shell benchmark shows that all four codes can produce similar precise gravitational potential fields. Two additional shell tests were conducted with more complicated density structures: lateral varying density structures and a Moho density interface between crust and mantle. The differences between the four codes were all below 1.5 percent of the modeled gravity signal suitable for reproducing satellite-acquired gravity data. TESS and GSH produced the most similar potential fields (< 0.3 percent).

To examine the usability of the forward modelling codes for realistic geological structures, we use the global lithosphere model WINTERC-G, that was constrained, among other data, by satellite gravity field data computed using a spectral forward modeling approach. This spectral code was benchmarked against the GSH and it was confirmed that both approaches produce similar gravity solution with negligible differences between them. In the comparison of the different WINTERC-G-based gravity solutions, again GSH and TESS performed best. Only short-wavelength noise is present between the spectral and tesseroid forward modelling approaches, likely related to the different way in which the spherical harmonic analysis of the varying boundaries of the mass layer is performed. The Spherical harmonic basis functions produces small differences compared to the tesseroid elements especially at sharp interfaces, which introduces mostly short-wavelength differences. Nevertheless, both approaches (GSH and TESS) result in accurate solutions of the potential field with reasonable computational resources. Differences below 0.5 percent are obtained, resulting in residuals of 0.076 mGal standard deviation at 250 km height.

The biggest issue for TRI is the characteristic pattern in the residuals that is related to the grid layout. Increasing the resolution and filtering allows for the removal of most of this erroneous pattern, but at the expense of higher computational loads with respect to the other codes. The other spatial forward modelling scheme HEX has more difficulty in reproducing similar gravity field solutions compared to GSH and TESS. These particular approaches need to go to higher resolutions, resulting in enormous computation efforts. The hexahedron-based code performs less than optimal in the forward modelling of the gravity signature, especially of a lateral varying density interface. Care must be taken with any forward modelling software as the approximation of the geometry of the WINTERC-G model may deteriorate the gravity field solution.

Bart Root et al.

Status: open (until 25 Jan 2022)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse

Bart Root et al.

Data sets

WINTERC-G: a global upper mantle thermochemical model from coupled geophysical–petrological inversion of seismic waveforms, heat flow, surface elevation and gravity satellite data Fullea, Javier; Lebedev, Sergei; Martinec, Zdenek; Celli, Nicolas; https://zenodo.org/record/5730195

Model code and software

Global Spherical Harmonic package (GSH) Bart Root https://github.com/bartroot/GSH

Tesseroids Leonardo Uieda https://github.com/leouieda/tesseroids/

Bart Root et al.

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Short summary
Several alternative gravity modelling techniques and associated numerical codes with their own advantages and limitations are available for the Solid Earth community. With the upcoming state-of-the-art lithosphere density models and accurate global gravity field data sets it is vital to understand the differences of the various approaches. In this paper, we discuss the four widely used techniques: spherical harmonics, tesseroid integration, triangle integration, and hexahedral integration.