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.
Highlights
Dedicated gravimetric satellite missions such as NASA’s GRACE and ESA’s GOCE missions have generated unprecedented views of the Earth’s gravity field (Pail et al, 2015)
We present a benchmark study comparing three space-domain and one spectral-domain approach applied to the layered WINTERC-G 3-D density model, in order to assess the usability of the model including the uncertainty resulting from different forward modelling approaches
To assess the applicability of this choice we select 85 four different forward modelling codes to understand the differences in forward modelled gravitational potential, resulting from WINTERC-G: the Global Spherical Harmonics spectral code based on Root et al (2016), a tesseroid forward modelling code based on Uieda et al (2016), a triangle-element forward modelling code by Sebera et al (2018), and a hexahedron-element code incorporated in geodynamical ASPECT modelling software (Kronbichler et al, 2012; Heister et al, 2017)
Summary
Dedicated gravimetric satellite missions such as NASA’s GRACE and ESA’s GOCE missions have generated unprecedented views of the Earth’s gravity field (Pail et al, 2015). One of the latest global gravity field model, XGM2016 (Pail et al , 30 2018), depicts a detailed map of the gravity anomalies caused by density variations in the Earth’s interior Such variations provide information on the density distribution within the Earth with homogeneous (global) quality that can be used in joint inversion studies of the subsurface combining gravity data with petrological and seismological constraints (Kaban et al , 2014), such like the latest global lithosphere and upper mantle model WINTERC-G (Fullea et al, 2020). The model is represented as independent 40 lithospheric/upper mantle columns that are laterally distributed on a spherical triangular grid (Wang and Dahlen, 1995). 50 we are driven by the need to quantify the effect of different discretizations and numerical approaches used to represent the real distribution of the Earth’s 3-D density distribution and its associated gravity field
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