Characterisation of the gravity field generated by a degree-2160 topography model
20/09/2016 | 09:30 | Session 2: Model Development
Author(s): Elisabeth Reußner, Christian Hirt, Moritz Rexer and Michael Kuhn
Elisabeth Reußner, Christian Hirt, Moritz Rexer and Michael Kuhn
Spectral models of Earth’s topography, such as the Earth2012 and Earth2014 models, can be used to compute the topographic gravitational potential via binomial series, e.g., for the construction of Bouguer gravity maps in the spectral domain. They also can provide the long-wavelength reference surface for residual terrain modelling (RTM), e.g., for short-scale augmentation of global gravity field models (GGM). Recent research has highlighted that a spectral topography model, truncated to harmonic degree n, generates a gravity field with spectral energy at ultra-short scales, far beyond the band-limitation of the input model.
In this contribution a complete model of the topographic potential, which is generated by a degree-2160 topography model, is developed and characterized. The topographic potential model, computed as binomial series expansion of the first 25 integer powers of the degree-2160 topography (spectral gravity forward modelling), is complete to degree and order 21,600. The modelling thus takes into account the first 10 multiples of the input-bandwidth of degrees 0 to 2,160. Global 3D-synthesis of gravity values from the topography model reveals maximum signal strengths of 40 mGal (RMS about 0.7 mGal) associated with spectral window of degrees [2,161 to 4320], and maximum signals of 9 mGal (0.07 mGal RMS) with spectral window [4321 to 6480]. Even at ultra-high degrees, e.g., beyond 12,960, signal contributions locally exceed the 1 mGal-level and so may be significant for rigorous gravity forward modelling.
A complete topographic potential model, as presented here, is crucially important for any comparison of spectral gravity forward modelling with numerical integration (Newton’s integral) in the space domain. Such comparisons are capable of validating the topographic component of modern Bouguer gravity maps constructed in spherical harmonics. Also, this degree-21,600 topographic potential model can be useful in the context of RTM-forward modelling, where the short-scale signals (in band [2,161- 21,600]) from this model correct the spectral inconsistency between high-pass filtered gravity and topography.