Topographic gravity modeling for global Bouguer maps to degree 2160: Validation of spectral and spatial domain forward modeling techniques at the 10 microGal level

Abstract

Over the past years, spectral techniques have become a standard to model Earth's global gravity field to 10 km scales, with the EGM2008 geopotential model being a prominent example. For some geophysical applications of EGM2008, particularly Bouguer gravity computation with spectral techniques, a topographic potential model of adequate resolution is required. However, current topographic potential models have not yet been successfully validated to degree 2160, and notable discrepancies between spectral modeling and Newtonian (numerical) integration well beyond the 10 mGal level have been reported. Here we accurately compute and validate gravity implied by a degree 2160 model of Earth's topographic masses. Our experiments are based on two key strategies, both of which require advanced computational resources. First, we construct a spectrally complete model of the gravity field which is generated by the degree 2160 Earth topography model. This involves expansion of the topographic potential to the 15th integer power of the topography and modeling of short‐scale gravity signals to ultrahigh degree of 21,600, translating into unprecedented fine scales of 1 km. Second, we apply Newtonian integration in the space domain with high spatial resolution to reduce discretization errors. Our numerical study demonstrates excellent agreement (8 μGgal RMS) between gravity from both forward modeling techniques and provides insight into the convergence process associated with spectral modeling of gravity signals at very short scales (few km). As key conclusion, our work successfully validates the spectral domain forward modeling technique for degree 2160 topography and increases the confidence in new high‐resolution global Bouguer gravity maps.

Convergence and divergence in spherical harmonic series of the gravitational field generated by high‐resolution planetary topography—A case study for the Moon

“…Drawing an analogy between spectral gravity forward modeling for Earth and Moon using degree‐2160 topography models, the dependency of series divergence on the ruggedness of topography becomes clear. For Earth, spherical harmonic series were shown to sufficiently converge at the surface of the topography (heights above zero) for degree‐2160 topographic gravity models [ Hirt et al , ], while for the Moon, severe series divergence is evident for the gravity models of the same resolution class. This different behavior of the series for Earth and Moon needs further investigation in a follow‐up study.…”

“…A number of studies discuss or encounter the topic of series convergence versus divergence in the context of Earth's gravity field [e.g., Moritz, 1961Moritz, , 1978Moritz, , 1980Sjöberg, 1980;Jekeli, 1983;Wang, 1997;Shen, 2009;Hirt et al, 2016]. However, most of these focus on gravity modeling with lower resolution than considered here.…”

SRTM2gravity: An Ultrahigh Resolution Global Model of Gravimetric Terrain Corrections

“…The total gravitational effect of the 3″ MERIT topographic mass model is the sum of results from steps 2 and 3. To improve the spectral separation between both components, and to be able to reach sub‐mGal modeling accuracy, also very high‐frequency signals generated by the degree 2,160 topography at scales of ~10 km down to ~2 km were explicitly modeled and considered (Hirt et al, ; Rexer et al, ; also see ESM section S1.3).…”

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

“…Together with this paper, the TGF software will be released in the public domain for free use in geodetic and geophysical forward modelling computations. procedure [2,3], reduction of the gravity observations in boundary-value problem [4,5], for prediction of high-frequency gravity field constituents [6][7][8], and for the reduction of omission errors in height system definitions and unification [9].In the last few decades, considerable attention has been given to the forward modelling approaches, either in the spectral domain through spherical harmonic analysis (SHA) of height-density functions (globally, e.g., [10][11][12]; regionally, e.g., [13]) and spherical harmonic synthesis (SHS) for computation points, or in the spatial domain using analytical or numerical gravitational formulas of geometries. In the spectral domain, the evaluation of gravitational field relies on the spherical harmonic expansions of powers of the topography.…”

“…Together with this paper, the TGF software will be released in the public domain for free use in geodetic and geophysical forward modelling computations. procedure [2,3], reduction of the gravity observations in boundary-value problem [4,5], for prediction of high-frequency gravity field constituents [6][7][8], and for the reduction of omission errors in height system definitions and unification [9].…”