Topographic/isostatic evaluation of new‐generation GOCE gravity field models

Hirt, Christian; Kühn, Michael; Featherstone, Will; Göttl, Franziska

doi:10.1029/2011jb008878

Cited by 51 publications

(59 citation statements)

References 46 publications

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“…We constructed spherical harmonic models of topography for Titan from RADAR-based topography (21,31,35) referenced to the geoid (36); for Earth from the Earth2012 topography/bathymetry model (referenced to sea level) (22); and for Mars from the Mars Orbiter Laser Altimeter (MOLA)-derived, aeroid-referenced topography model (37,38). A robust spherical harmonic expansion for Titan's topography is available only up to degree (ℓ) 6 (ref.…”

Section: Spherical Harmonic Topographymentioning

confidence: 99%

Global drainage patterns and the origins of topographic relief on Earth, Mars, and Titan

Black

Perron

Hemingway

et al. 2017

Science

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River systems reveal planetary tectonics Earth, Mars, and Titan have all hosted rivers at some point in their histories. Rivers erode the landscape, leaving behind signatures that depend on whether the surface topography was in place before, during, or after the period of liquid flow. Black et al. developed two metrics to measure how well river channels align with the surrounding large-scale topography (see the Perspective by Burr). Earth's plate tectonics introduce features such as mountain ranges that cause rivers to divert, processes that clearly differ from those found on Mars and Titan. Science , this issue p. 727 ; see also p. 708

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Section: Spherical Harmonic Topographymentioning

confidence: 99%

Global drainage patterns and the origins of topographic relief on Earth, Mars, and Titan

Black

Perron

Hemingway

et al. 2017

Science

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“…The height of this layer, the rock-equivalent height, can be computed in planar approximation [e.g., Balmino et al, 1973;Rummel et al, 1988;Hirt et al, 2012b] or in spherical approximation [e.g., Claessens, 2003;Mladek, 2006]. It is customary to replace ocean water, fresh lake water, and ice by equivalent rock layers, resulting in negative RET heights over all of Earth's oceans [e.g., Hirt et al, 2012b].…”

Section: Topographic Potentialmentioning

confidence: 99%

“…[18] Where information about radial variations in density within the topography is available, the topography can be replaced by a layer of constant density and the same mass as the original layer: the equivalent rock topography/rockequivalent topography (ERT/RET) [e.g., Balmino et al, 1973;Tsoulis, 1999;Hirt et al, 2012b]. The height of this layer, the rock-equivalent height, can be computed in planar approximation [e.g., Balmino et al, 1973;Rummel et al, 1988;Hirt et al, 2012b] or in spherical approximation [e.g., Claessens, 2003;Mladek, 2006].…”

Section: Topographic Potentialmentioning

confidence: 99%

“…It describes the masses of (i) Earth's visible topography, (ii) ocean water, (iii) major ice sheets of Greenland and Antarctica, and (iv) major inland lakes (of North America and Asia) using a single constant mass density of 2670 kg m À3 . The compression of water and ice masses was accomplished as described in Hirt et al [2012b, 24 kg. For all spherical approximations tested in this study, we use the GRS80 semimajor axis a as the reference sphere radius R.…”

Section: General Remarksmentioning

confidence: 99%

“…Topography can be either uncompensated [e.g., Hirt et al, 2012b], or an isostatic compensation can be assumed [e.g., Rummel et al, 1988;Grafarend and Engels, 1993]. See Tsoulis [2001] and Göttl and Rummel [2009] for a further discussion on isostatic compensation mechanisms and the topographic-isostatic potential.…”

Section: Introductionmentioning

confidence: 99%

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Ellipsoidal topographic potential: New solutions for spectral forward gravity modeling of topography with respect to a reference ellipsoid

Claessens

Hirt

2013

JGR Solid Earth

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[1] Forward gravity modeling in the spectral domain traditionally relies on spherical approximation. However, this level of approximation is insufficient for some present day high-accuracy applications. Here we present two solutions that avoid the traditional spherical approximation in spectral forward gravity modeling. The first solution (the extended integration method) applies integration over masses from a reference sphere to the topography and applies a correction for the masses between ellipsoid and sphere. The second solution (the harmonic combination method) computes topographic potential coefficients from a combination of surface spherical harmonic coefficients of topographic heights above the ellipsoid, based on a relation among spherical harmonic functions introduced by Claessens (2005). Using a degree 2160 spherical harmonic model of the topographic masses, both methods are applied to derive the Earth's ellipsoidal topographic potential in spherical harmonics. The harmonic combination method converges fastest and-akin to the EGM2008 geopotential model-generates additional spherical harmonic coefficients in spectral band 2161 to 2190 which are found crucial for accurate evaluation of the ellipsoidal topographic potential at high degrees. Therefore, we recommend use of the harmonic combination method to model ellipticity in spectral-domain forward modeling. The method yields ellipsoidal topographic potential coefficients which are "compatible" with global Earth geopotential models constructed in ellipsoidal approximation, such as EGM2008. It shows that the spherical approximation significantly underestimates degree correlation coefficients among geopotential and topographic potential. The topographic potential model is, for example, of immediate value for the calculation of Bouguer gravity anomalies in fully ellipsoidal approximation.Citation: Claessens, S. J., and C. Hirt (2013), Ellipsoidal topographic potential: New solutions for spectral forward gravity modeling of topography with respect to a reference ellipsoid,

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Band‐limited topographic mass distribution generates full‐spectrum gravity field: Gravity forward modeling in the spectral and spatial domains revisited

Hirt

Kühn

2014

JGR Solid Earth

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Most studies on gravity forward modeling in the spectral domain truncate the gravitational potential spectra at a resolution commensurate with the input topographic mass model. This implicitly assumes spectral consistency between topography and implied topographic potential. Here we demonstrate that a band-limited topographic mass distribution generates gravity signals with spectral energy at spatial scales far beyond the input topography's resolution. The spectral energy at scales shorter than the resolution of the input topography is associated with the contributions made by higher-order integer powers of the topography to the topographic potential. The pth integer power of a topography expanded to spherical harmonic degree n is found to make contributions to the topographic potential up to harmonic degree p times n. New numerical comparisons between Newton's integral evaluated in the spatial and spectral domain show that this previously little addressed truncation effect reaches amplitudes of several mGal for topography-implied gravity signals. Modeling the short-scale gravity signal in the spectral domain improves the agreement between spatial and spectral domain techniques to the μGal level, or below 10 À5 in terms of relative errors. Our findings have important implications for the use of gravity forward modeling in geophysics and geodesy: The topographic potential in spherical harmonics must be calculated to a much higher harmonic degree than resolved by the input topography if consistency between topography and implied potential is sought. With the improved understanding of the spectral modeling technique in this paper, theories, and computer implementations for both techniques can now be significantly better mutually validated.

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Topographic/isostatic evaluation of new‐generation GOCE gravity field models

Cited by 51 publications

References 46 publications

Global drainage patterns and the origins of topographic relief on Earth, Mars, and Titan

Global drainage patterns and the origins of topographic relief on Earth, Mars, and Titan

Ellipsoidal topographic potential: New solutions for spectral forward gravity modeling of topography with respect to a reference ellipsoid

Band‐limited topographic mass distribution generates full‐spectrum gravity field: Gravity forward modeling in the spectral and spatial domains revisited

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