Band - limited topographic mass distribution generates full - spectrum 4 gravity field – gravity forward modelling in the spectral and spatial

24 Most studies on gravity forward modelling in the spectral domain truncate the gravitational 25 potential spectra at a resolution commensurate with the input topographic mass model. This 26 implicitly assumes spectral consistency between topography and implied topographic potential. 27 Here we demonstrate that a band-limited topographic mass distribution generates gravity signals 28 with spectral energy at spatial scales far beyond the input topography’s resolution. The spectral 29 energy at scales shorter than the resolution of the input topography is associated with the 30 contributions made by higher-order integer powers of the topography to the topographic 31 potential. The p-th integer power of a topography expanded to spherical harmonic degree n is 32 found to make contributions to the topographic potential up to harmonic degree p times n. New 33 numerical comparisons between Newton’s integral evaluated in the spatial and spectral domain 34 show that this previously little addressed truncation effect reaches amplitudes of several mGal 35 for topography-implied gravity signals. Modelling the short-scale gravity signal in the spectral 36 domain improves the agreement between spatial and spectral domain techniques to the microGal37 level, or below 10-5 in terms of relative errors. Our findings have important implications for the 38 use of gravity forward modelling in geophysics and geodesy: The topographic potential in 39 spherical harmonics must be calculated to a much higher harmonic degree than resolved by the 40 input topography if consistency between topography and implied potential is sought. With the 41 improved understanding of the spectral modelling technique in this paper, theories and computer 42 implementations for both techniques can now be significantly better mutually validated. 43 44